Solve math problems with calculators built for geometry, algebra, trigonometry, logarithms, and matrix operations. Clear formulas and worked results make them useful for students, teachers, and engineers.
Triangle, circle, polygon, 3D shape, area, perimeter, and volume calculators.
Rotate a 2D point by any angle about any center. See the rotation matrix, new coordinates, displacement, and a table of common rotations (90°, 180°, 270°). Presets and rotation rules included.
Calculate all sides, area, perimeter, altitudes, and radii of a 30-60-90 special right triangle. Enter any one side and get every property from the same ratio setup.
Calculate all sides, area, perimeter, altitudes, and radii of a 45-45-90 isosceles right triangle. Enter any one side and get every property from the same triangle definition.
Analyze a triangle from three angles (AAA). Classify triangle type, compute side ratios, and fully solve when a side length is provided.
Solve an AAS triangle given two angles and a non-included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius.
Verify and solve acute triangles from 3 sides. Check that all angles are under 90°, compute all properties including circumcenter inside the triangle, and compare with right and obtuse triangles.
Calculate the angle between two 2D or 3D vectors using the dot product formula. Includes magnitudes, dot product, cross product, projection, parallel/perpendicular detection, and visual gauge.
Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds. See trigonometric values, DMS notation, quadrant, and a full common-angles reference table.
Calculate the area, width, inner/outer circumference, and average radius of an annulus (ring shape) from outer and inner radii. Includes presets for washers, rings, and pipes.
Calculate area, circumference, radius, and diameter of a circle. Supports solving from radius, diameter, circumference, or area with unit selection, presets for common objects, sector/arc calculati...
Calculate area, perimeter, diagonals, and angles for any quadrilateral type — rectangle, square, parallelogram, rhombus, kite, or general. Includes type selector, presets, comparison visualization,...
Calculate area, perimeter, diagonals, angles, and median of a trapezoid. Supports general, isosceles, and right trapezoid types with unit selection, presets, side proportion visualization, and a re...
Solve an ASA triangle given two angles and the included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius.
Calculate the base of a triangle using multiple methods: area and height, three sides with Heron's formula, perimeter minus known sides, or SAS with the law of cosines.
Find the center of an ellipse from the general equation Ax²+Bxy+Cy²+Dx+Ey+F=0 or standard form parameters. Computes center, semi-axes, eccentricity, foci, area, and circumference.
Find the centroid, incenter, circumcenter, and orthocenter of a triangle from three vertex coordinates. Computes area, perimeter, side lengths, and angles.
Enter the sides of two right triangles to check if they are similar. Compare side ratios, scale factor, angle measurements, area ratio, and perimeter ratio.
Find the center and radius of a circle from three points, a general equation, or two endpoints of a diameter. Shows area, circumference, and both equation forms.
Calculate the diameter of a circle from its radius, circumference, or area. Also computes radius, circumference, area, arc length, sector area, and chord length.
Convert between standard form (x−h)²+(y−k)²=r² and general form x²+y²+Dx+Ey+F=0. Find center, radius, area, and circumference from either equation form.
Comprehensive circle calculator: enter any one property (radius, diameter, circumference, or area) and compute all others plus sector area, arc length, segment area, and chord length.
Calculate arc length, chord length, and circumference of a circle. Supports degrees and radians, with sagitta, sector area, and arc-to-chord ratio.
Enter radius, diameter, circumference, or area and get every circle measurement: inscribed square, hexagon, triangle sides, circumscribed square, area ratios, and more.
Calculate the perimeter (circumference) of a circle from radius, diameter, or area. Also find arc length, sector perimeter, chord length, and area with unit conversions.
Explore and compute results for major circle theorems: inscribed angle, central angle, tangent-chord, secant-secant, tangent-tangent, power of a point, and Thales' theorem.
Calculate the area of a circular segment from radius and central angle. Includes chord length, arc length, sagitta, sector area, and minor/major segment toggle.
Find the circumcenter, circumradius, centroid, incenter, orthocenter, perpendicular bisector equations, area, and perimeter of a triangle from 3 vertex coordinates.
Bidirectional calculator: enter circumference to find area, area to find circumference, or enter radius/diameter to get both. Unit conversions, real-world presets, and formula reference.
Calculate the circumference of a circle from radius or diameter. Also computes area, arc length for a given angle, and sector area. Includes unit selector, common-circle presets, and reference table.
Convert circumference to diameter and vice versa. Also shows radius, area, C/d ratio (π), π approximation comparisons, real-world object table, and history of π.
Calculate the circumscribed circle of a triangle from its sides. Find the circumradius, circumcenter coordinates, circumcircle area, Euler line distance, and area ratios. Includes presets and...
Calculate the circumscribed circle (circumcircle) of a triangle or regular polygon. Find the circumradius, circle area, area ratios, and perimeter comparisons in one view.
Classify any triangle by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Enter 3 sides or 3 angles to see full properties and classification.
Complete the square for any quadratic ax²+bx+c. Get vertex form, vertex coordinates, axis of symmetry, discriminant, roots, and step-by-step solution.
Solve quadratic equations by completing the square. Enter coefficients a, b, c and see the step-by-step solution, vertex form, discriminant, roots, and graph properties.
Practice completing the square with generated problems. Enter your answer for h and k, check if correct, and get step-by-step solutions with multiple difficulty levels.
Calculate the total and lateral surface area of a cone, with breakdown ratios, unrolled sector angle, and real-world presets for common conical objects.
Calculate the lateral, base, and total surface area of a cone from radius and height or slant height. Includes apex angle, unrolled sector angle, presets, and reference table.
Calculate the volume, surface area, lateral area, and slant height of a cone. Supports multiple solve modes, unit conversion, and real-world presets.
Enter the sides and angles of two triangles to check congruence. Tests SSS, SAS, ASA, AAS, and HL criteria, identifies which criterion matched, solves missing values, and compares areas.
Calculate the area of a crescent or lune formed by two overlapping circles. Enter radii and distance between centers to find crescent area, overlap area, and union area.
Calculate the cross-sectional area, shape, and perimeter when slicing 3D solids (sphere, cylinder, cone, cube, rectangular prism, ellipsoid) at any height or angle.
Calculate cross-sectional area, perimeter, moment of inertia, and section modulus for circles, rectangles, triangles, pipes, ellipses, and I-beams.
Calculate all properties of a cube: surface area, volume, face diagonal, space diagonal, inscribed and circumscribed sphere radii from side length, diagonal, surface area, or volume.
Calculate all properties of a cube from its edge length: volume, surface area, face diagonal, space diagonal, circumscribed and inscribed sphere radii. Reverse-solve from volume, surface area, or d...
Calculate total and lateral surface area of a cube from side length, volume, face diagonal, or space diagonal. Includes formula reference and comparison table.
Calculate the surface area, volume, face area, edge length, and diagonals of a cube from side, diagonal, volume, or surface area. Includes cost estimator and reference table.
Calculate cube volume, surface area, face diagonal, space diagonal, inscribed and circumscribed sphere properties from side length. Includes scaling table and dimension comparison.
Calculate the volume of a cylinder in cubic feet. Enter radius or diameter and height in inches, feet, cm, or meters. See volume in ft³, gallons, and liters plus the surface-area breakdown.
Calculate the volume of a cylinder in cubic inches. Enter radius or diameter and height in inches, feet, cm, or meters. See in³, ft³, gallons, liters, and surface area.
Calculate cylinder volume in cubic yards. Enter radius or diameter and height in inches, feet, yards, cm, or meters. See yd³, ft³, gallons, and material weight estimates for concrete and gravel.
Calculate the volume, surface area, face diagonals, space diagonal, and all face areas of a cuboid (rectangular prism). Cube detection, unit selector, and real-world presets.
Calculate the surface area of a cuboid (rectangular box) from length, width, and height. See total area, each face pair, lateral area, volume, and all diagonals with visual breakdowns.
Calculate the volume of a cuboid (rectangular box) from length, width, and height. Convert to cm³, m³, in³, ft³, liters, and gallons. See surface area, diagonals, and face breakdowns.
Calculate the circumference of a cylinder from its radius or diameter. Also find volume, surface area, lateral area, and base area with unit conversions.
Find the diameter of a cylinder from its circumference, radius, volume + height, or surface area + height. Displays all cylinder properties with unit conversions.
Calculate the total, lateral, and base surface area of a cylinder from radius and height. Supports open-top cylinders, diameter input, presets for cans and tanks.
Calculate the volume, surface area, and capacity of a cylinder. Includes fill level, liter/gallon conversion, diameter mode, and presets for common cylinders.
Calculate the volume of a cylinder in US gallons, imperial gallons, liters, and cubic feet. Enter radius or diameter and height in any unit with adjustable fill level.
Calculate the volume of a cylinder in liters, milliliters, gallons, and cubic units. Enter radius or diameter with height in any measurement unit.
Calculate the area, perimeter, apothem, circumradius, inradius, angles, and diagonals of a regular decagon from side length, circumradius, or apothem.
Calculate the diagonal of a rectangle, square, cube, cuboid, or regular polygon. Find face diagonals, space diagonals, angles, and the number of diagonals.
Calculate the diagonal of a rectangle from its length and width using the Pythagorean theorem. Also find area, perimeter, diagonal angle, and aspect ratio.
Diagonalize a 2×2 or 3×3 matrix online. Find eigenvalues, eigenvectors, matrices P and D where A = PDP⁻¹, determinant, trace, and characteristic polynomial with step-by-step results.
Calculate the diameter of a cone from radius, slant height and height, volume and height, or lateral area and slant height. Also shows volume, lateral area, total surface area, and slant height.
Find rectangle dimensions from area and perimeter, area and one side, perimeter and one side, or diagonal and one side. Shows length, width, area, perimeter, diagonal, and aspect ratio.
Calculate the distance between two points in 2D or 3D using Euclidean, Manhattan, Chebyshev, and Minkowski metrics. Bearing, direction angle, component breakdown, and distance metrics reference.
Calculate ellipse area from semi-major and semi-minor axes. Also shows circumference (Ramanujan approximation), eccentricity, foci distance, linear eccentricity, directrix, and flattening.
Calculate all properties of an ellipse from semi-major and semi-minor axes. Includes area, circumference (Ramanujan), eccentricity, foci distance, directrix, latus rectum, and flattening.
Calculate ellipse circumference using Ramanujan I, Ramanujan II, infinite series, and RMS approximations. Compare accuracy of each method. Also shows area, eccentricity, and h parameter.
Calculate the perimeter (circumference) of an ellipse using Ramanujan, series expansion, Padé, and naive approximations. Compare methods side-by-side with area, eccentricity, and foci.
Convert an ellipse between standard form and general form. Find center, semi-axes, eccentricity, foci, vertices, co-vertices, area, and circumference from either equation form.
Calculate the volume, approximate surface area (Knud Thomsen), and cross-sectional areas of an ellipsoid from three semi-axes. Sphere detection, presets for egg, Earth, and rugby ball.
Find the equation of a circle from two endpoints of a diameter. Computes center (midpoint), radius, standard form, general form, area, and circumference.
Convert between standard and general forms of a sphere equation. Enter center and radius or general-form coefficients to get both equations, center, radius, volume, and surface area.
Calculate all properties of an equilateral triangle from side length, area, perimeter, or height. Includes area, height, perimeter, circumradius, inradius, and angles (always 60°).
Calculate exterior angles for triangles and regular polygons. Uses the exterior angle theorem for triangles and the 360°/n formula for polygons. Shows angle sums, interior-exterior pairs, and visua...
Calculate exterior angles of a triangle from interior angles or side lengths. Verify the exterior angle theorem, see remote interior angle pairs, and compare all angles visually.
Find the foci of an ellipse from semi-axes or the general equation. Computes foci coordinates, distance between foci, eccentricity, linear eccentricity, vertices, center, and key ellipse properties.
Calculate the volume, lateral surface area, total surface area, and slant height of a truncated cone (frustum). Two radii + height or slant height, with real-world presets.
Convert a circle equation from general form (x²+y²+Dx+Ey+F=0) to standard form ((x−h)²+(y−k)²=r²). Find center, radius, area, circumference, and diameter with step-by-step solutions.
Convert a circle equation from general form to standard form step by step. Shows completing the square process, center, radius, area, circumference, and detailed algebraic walkthrough.
Solve rectangle problems algebraically. Find missing dimensions from area, perimeter, or diagonal. Computes length, width, area, perimeter, diagonal, and aspect ratio with multiple solve modes.
Calculate the dimensions, area, perimeter, diagonal, and golden spiral decomposition of a golden rectangle. Explore the Fibonacci connection, art & architecture examples, and successive square...
Calculate cone height from slant height, volume, lateral area, total surface area, or diameter. Shows all cone properties including volume, surface area, and half-angle with visual breakdowns.
Calculate the height of a cylinder from volume and radius, surface area and radius, lateral area and radius, or volume and diameter. Includes step-by-step formulas, reference tables, and visual bre...
Calculate the height of a square pyramid from slant height, volume, lateral area, total surface area, or lateral edge. Shows all pyramid properties including volume, surface area, and edges.
Calculate total surface area, curved surface area, base area, and volume of a hemisphere. Includes full sphere comparison bars, unit selection, presets for bowls and domes, and a reference table.
Calculate the area, perimeter, apothem, circumradius, inradius, diagonals, and angles of a regular heptagon (7-sided polygon) from side length, area, perimeter, apothem, or circumradius.
Calculate area, perimeter, apothem, diagonals, circumscribed and inscribed circles for a regular heptagon. Enter any one measurement to find all properties.
Calculate triangle area from three side lengths using Heron's formula. See semi-perimeter, inradius, circumradius, altitudes, medians, angles, and a visual sketch.
Calculate volume, slant height, lateral area, total surface area, base area, perimeter, and apothem of a regular hexagonal pyramid. Includes visual breakdowns, presets, and reference data.
Calculate the total surface area, lateral surface area, and base area of a regular hexagonal pyramid from base side and slant height or base side and height. Includes SA breakdown, presets, and ref...
Calculate volume, lateral surface area, and total surface area of a regular or irregular hexagonal pyramid. Enter base side length, height, and apothem.
Calculate wall volume, inner volume, total surface area, wall thickness, and estimated weight of a hollow cylinder (pipe, tube, annular ring) from outer/inner radii and height.
Calculate inscribed angles, central angles, arc length, chord length, sagitta, sector area, and segment area for a circle. Includes Thales' theorem detection and a reference table.
Solve integrals of the form ∫ dx/(ax² + bx + c) by completing the square. Shows the completed square form, integral type (arctan or partial fractions), step-by-step solution, and formula references.
Calculate all interior and exterior angles of a triangle from 3 sides (SSS) or 2 known angles. Verifies angle sum = 180° and exterior sum = 360°. Includes remote interior angle theorem, presets, an...
Calculate interior angles, angle sums, and exterior angles of regular and custom polygons. Uses the (n−2)×180° formula. Supports polygons from 3 to 100 sides with visual breakdowns.
Calculate the area, perimeter, centroid, and bounding box of any irregular polygon using the shoelace formula. Enter up to 10 vertex coordinates and see step-by-step cross products.
Calculate the area, perimeter, diagonals, and angles of an irregular trapezoid from two parallel sides and two legs or height. Includes visual comparison bars, presets, and a reference table.
Enter three side lengths to check whether they form a right triangle using the Pythagorean theorem. See all angles, deviation from 90°, area, perimeter, and a table of Pythagorean triples.
Calculate all properties of a 45-45-90 isosceles right triangle from a leg or hypotenuse. Find area, perimeter, inradius, circumradius, and height to hypotenuse with presets and reference table.
Find the hypotenuse of an isosceles right triangle from its leg, or find the leg from the hypotenuse. Includes step-by-step solution, all triangle properties, visual bars, and a reference table.
Calculate the area, perimeter, diagonals, height, median, and angles of an isosceles trapezoid from its parallel sides and leg or height.
Calculate the area, perimeter, diagonals, angles, height, and median of an isosceles trapezoid from two parallel sides and a leg or height. Includes visual bars, presets, and a formula reference ta...
Calculate the apex angle and base angles of an isosceles triangle from the equal sides and base. Verifies the angle sum equals 180° and shows area, perimeter, height.
Complete isosceles triangle solver. Enter base + leg, base + height, or leg + apex angle to compute all sides, angles, area, perimeter, altitudes, circumradius, and inradius.
Find the equal side of an isosceles triangle from the base plus height, area, perimeter, apex angle, or base angle. Computes all triangle properties.
Calculate the height of an isosceles triangle from the equal sides and base, or from the equal side and apex angle. Shows area, perimeter, angles, inradius, and circumradius.
Find the equal side (a) of an isosceles triangle given the base with height, area, perimeter, or apex angle. Shows all triangle properties.
Calculate the area, perimeter, angles, inradius, and diagonals of a kite from diagonals or from sides and angle. Includes presets, visual breakdown, and reference table.
Calculate the lateral (curved) surface area of a cone from its radius and height or slant height. Includes total surface area, volume, half-angle, SA breakdown, and reference table.
Calculate the lateral surface area of a trapezoidal prism from the four sides of the trapezoid base and prism length. Includes total surface area, volume, individual face areas, breakdown bars, and...
Calculate the lateral (side) surface area of cylinders, cones, prisms, pyramids, and frustums. Compare lateral vs base area with visual breakdown bars and a formula reference table.
Calculate the lateral (curved) surface area of a cylinder from radius and height. Also shows total surface area, volume, diameter, circumference, space diagonal, SA breakdown, and reference table.
Calculate the latus rectum of a parabola, ellipse, or hyperbola. Find focus, directrix, eccentricity, and key relationships between conic section parameters.
Solve any triangle using the Law of Cosines. Enter two sides and the included angle (SAS) or three sides (SSS) to find all angles, area, perimeter, and more.
Solve any triangle using the Law of Sines. Enter two angles and one side or two sides and one angle to find all missing values, with ambiguous-case detection.
Compute the best-fit line using least squares regression. Enter up to 10 data points to get slope, intercept, R², correlation coefficient, standard error, residuals table, and predictions.
Find the length and width of a rectangle when you know the perimeter and one additional property: area, diagonal, or length-to-width ratio. Shows all rectangle properties, dimension bars, and a ref...
Find the distance between two points in 2D or 3D space using the distance formula. Shows step-by-step calculation, midpoint, direction vector, and slope.
Calculate the length of a rectangle from area and width, perimeter and width, or diagonal and width. Get the full rectangle properties from the same input set.
Generate magic squares of order 3, 4, or 5. View the magic constant, sum verification, color-coded grid, and mathematical properties.
Find the midpoint of a line segment in 2D or 3D. Also calculates distance, slope, line equation, direction angle, and section formula for any ratio. Presets and reference table included.
Calculate all three midsegments of a triangle from vertex coordinates or side lengths. Compare the medial triangle to the original with areas, perimeters, and visual bars.
Find the missing side of a right triangle using the Pythagorean theorem. Enter any two sides, get the third plus area, angles, perimeter, inradius, and more.
Calculate Möbius strip properties: surface area, edge length, number of sides, Euler characteristic. Explore topology concepts with different half-twist counts.
Calculate the area, perimeter, apothem, circumradius, inradius, diagonals, and angles of a regular nonagon (9-sided polygon) from side length, area, perimeter, apothem, or circumradius.
Solve any oblique (non-right) triangle. Input any 3 known values — sides or angles — and compute all 6 elements, area, perimeter, altitudes, medians, and angle bisectors.
Solve obtuse triangles from 3 sides or 2 sides + angle. Detect the obtuse angle, classify, find all properties including altitude through the obtuse vertex, and compare with a right triangle.
Find the orthocenter of a triangle from three vertex coordinates. Compare orthocenter, centroid, circumcenter, and incenter positions with area and Euler line analysis.
Calculate the volume of a parallelepiped using the scalar triple product of 3 edge vectors. Also find surface area, space diagonal, face diagonals, and edge angles.
Calculate the area, perimeter, diagonals, and angles of a parallelogram from base + height or two sides + included angle. Detects rectangles, rhombuses, and squares.
Calculate the perimeter of a parallelogram from side lengths, diagonals and angle, or area and height. Find area, diagonals, heights, and angles with visual comparison.
Generate Pascal's triangle up to 15 rows. View binomial coefficients, row sums, highlight patterns, search for values, and explore mathematical properties.
Check if a number is a perfect cube. Find cube roots, nearest perfect cubes, prime factorization, and explore cubes in any range with a reference table of cubes 1–20.
Check if a number is a perfect square, find square roots, nearest perfect squares, prime factorization, and sum-of-squares decomposition. Reference table of squares 1–25.
Check if a quadratic expression ax² + bx + c is a perfect square trinomial. Get factored form, discriminant, vertex, roots, and step-by-step verification.
Calculate the perimeter (circumference) and area of any common shape: circle, rectangle, triangle, square, regular polygon, or ellipse. Includes shape comparison and isoperimetric ratio.
Calculate the perimeter of any quadrilateral from four side lengths or vertex coordinates. Detect shape type, compute diagonals and area, and compare side lengths visually.
Calculate the perimeter of a rectangle when you know the area and one dimension or aspect ratio. Find length, width, diagonal, and compare to the minimum perimeter (square).
Calculate the perimeter of a right triangle from any two sides. Find all three sides, area, angles, inradius, circumradius, and altitude. Includes Pythagorean triples table.
Calculate the perimeter of a circular sector from the radius and central angle. Find arc length, sector area, chord length, and segment area with visual breakdowns.
Calculate the perimeter of a triangle when side lengths are fractions. Get the result as a simplified fraction and decimal, plus LCD computation, area, and angles.
Calculate the perimeter of a triangle from three vertex coordinates. Find side lengths, area, centroid, angles, and triangle classification using the distance and Shoelace formulas.
Calculate the perimeter of a rectangle from length and width, from area and one side, or from diagonal and one side. Also find area, diagonal, and aspect ratio.
Find the perpendicular line through a point given a line equation. Calculate point-to-line distance, intersection point, and perpendicular slope with step-by-step solutions.
Calculate interior, exterior, and central angles of any regular polygon. Also find the sum of interior angles, number of diagonals, area, apothem, and circumradius.
Calculate the number of diagonals in any polygon using n(n−3)/2. Also computes interior angle, exterior angle, and area of regular polygons. Includes a comparison table for 3–20 sides.
Calculate volume, base area, lateral surface area, and total surface area of prisms with triangular, rectangular, pentagonal, hexagonal, or trapezoidal bases.
Calculate face angle, dihedral angle, lateral edge angle, and apex angle of a regular pyramid. Supports square, triangular, pentagonal, and hexagonal bases. Also find volume and surface area.
Calculate the volume, lateral area, total surface area, and slant height of square, rectangular, and triangular pyramids. Includes famous pyramid presets and a reference table.
Calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²). Find hypotenuse, legs, area, perimeter, angles, inradius, and circumradius.
Calculate the area, perimeter, angles, and diagonal of any quadrilateral. Enter four sides and one diagonal to compute properties and classify the shape.
Calculate the area of a quarter circle from its radius, diameter, full circle area, or arc length. Compare quarter, half, and full circle areas side by side.
Calculate the area, perimeter, arc length, centroid, and moment of inertia of a quarter circle (quadrant). Enter radius or diameter to compute the full quadrant geometry.
Calculate the perimeter of a quarter circle from its radius, diameter, arc length, or area. See the breakdown of curved arc vs straight edges with visual bars.
Calculate the radius of a circle from the diameter, circumference, area, arc length, or sector area. Instant results with all circle properties, visual bars, and a reference table.
Calculate the radius of a cone from volume & height, surface area & slant height, lateral area, base area, or circumference. Shows all cone properties with visual breakdowns.
Calculate the radius of a cylinder from volume & height, surface area & height, lateral area & height, circumference, or base area. All cylinder properties shown with visual breakdowns.
Calculate the radius of a sphere from diameter, circumference, surface area, volume, or spherical cap area. Shows all sphere properties with visual comparisons and a reference table.
Calculate all rectangle properties from length and width: area, perimeter, diagonal, aspect ratio, circumradius, and golden rectangle check. Presets for screens, paper sizes, sports fields.
Calculate the angle a rectangle's diagonal makes with its sides. Enter length and width to get diagonal angles, diagonal length, area, perimeter, and aspect ratio with visual bars.
Comprehensive rectangle solver — enter any two of length, width, area, perimeter, or diagonal and calculate all remaining properties from the same setup.
Find the scale factor between two rectangles. Calculate area ratio (k²), perimeter ratio, similarity check, and dimensional comparisons with visual bars and reference data.
Calculate volume, surface area (total and lateral), face diagonals, and space diagonal of a rectangular prism (cuboid). Includes presets for common boxes, rooms, and shipping containers.
Calculate the volume, surface area, face areas, face diagonals, space diagonal, and lateral area of a rectangular prism (box). Includes unit selector, presets, and reference table.
Calculate the volume, surface area, slant heights, lateral edge, and face areas of a rectangular pyramid. Includes unit selector, presets, and famous pyramids reference.
Calculate the area, perimeter, apothem, circumradius, interior/exterior angles, and number of diagonals of a regular 12-sided polygon (dodecagon) from side length, circumradius, or apothem.
Calculate all properties of a regular hexagon from side length, area, perimeter, apothem, or circumradius. Includes area, perimeter, apothem, diagonals, circumradius, inradius, and angles.
Calculate all properties of a regular octagon from side length, area, perimeter, apothem, or circumradius. Includes area, perimeter, apothem, three types of diagonals, circumradius, and angles.
Calculate all properties of a regular pentagon from side length, area, perimeter, apothem, or circumradius. Includes area, perimeter, apothem, diagonals, circumradius, and golden ratio connections.
Calculate the area of any regular polygon from the number of sides and side length, apothem, or circumradius. Also shows perimeter, interior angle, diagonal count, and comparison table.
Calculate area, perimeter, apothem, circumradius, inradius, interior angle, exterior angle, and diagonals for any regular polygon from 3 to 20 sides. Comparison table of all shapes included.
Calculate the perimeter of any regular polygon from side length, area, apothem, or circumradius. Also computes area, interior angle, diagonals, and more with visual comparisons.
Calculate all properties of a rhombus from side and angle, or from diagonals. Includes area, perimeter, diagonals, incircle radius, height, and angles.
Calculate volume, slant height, lateral surface area, total surface area, base area, half-angle, and base circumference of a right circular cone.
Calculate volume, lateral surface area, total surface area, base area, diameter, and base circumference of a right circular cylinder.
Calculate volume, two slant heights, lateral surface area, total surface area, base area, and lateral edge length of a right rectangular pyramid.
Calculate volume, slant height, lateral surface area, total surface area, base area, lateral edge, and dihedral angle of a right square pyramid.
Calculate the area, perimeter, slant side, diagonals, all four angles, and midsegment of a right trapezoid from two parallel sides and the height. Includes presets, visual bars, and a reference table.
Calculate area, perimeter, diagonals, angles, and oblique leg length of a right trapezoid with one pair of right angles.
Find the angles of a right triangle given any two sides. Compute both acute angles, all sides, area, perimeter, inradius, and trigonometric ratios.
Solve any right triangle from two known values — legs, hypotenuse, or angles. Computes all sides, angles, area, perimeter, inradius, circumradius, and altitude. Includes Pythagorean triple presets.
Solve any right triangle from 2 known values. Enter two sides or one side + one acute angle to compute all sides, both angles, area, perimeter, altitude to hypotenuse, inradius, circumradius, and P...
Find any missing side or angle of a right triangle. Enter two sides or one side and one acute angle. Shows all trig ratios for both acute angles, area, perimeter, inradius, and circumradius.
Comprehensive right triangle trig calculator. Enter any 2 known values (sides or angles) and get all 6 trig functions, cofunction identities, complementary angles, area, perimeter, inradius, and ci...
Solve any triangle from two sides and the included angle (SAS). Computes the third side via Law of Cosines, remaining angles, area, perimeter, altitudes, medians, inradius, and circumradius.
Calculate scale factor from original and scaled dimensions, or apply a scale factor to find new dimensions. Area (k²) and volume (k³) scaling, map and model presets, 2D scaling, and common scales r...
Solve any triangle using 3 sides or 2 sides + included angle. Computes all angles, area, perimeter, altitudes, medians, circumradius, inradius, and classifies by angles and sides.
Calculate sector area, arc length, chord length, and segment area from radius and central angle. Supports degrees and radians with presets for pizza slices, clocks, and pie charts.
Verify or solve for missing segment lengths using the segment addition postulate AB + BC = AC. Supports multiple collinear points with distance tables and visual number lines.
Calculate the area, perimeter, arc length, radius, diameter, and centroid of a semicircle. Solve from radius, diameter, area, or perimeter with unit conversion and presets.
Enter the legs of two right triangles to check similarity. Shows scale factor, angle comparison, area ratio (k²), perimeter ratio (k), and side-by-side analysis with visual bars and reference table.
Enter the three sides of triangle A and one side of triangle B to find all missing sides, the scale factor, area ratio, and perimeter ratio between similar triangles.
Solve similar triangles by entering known sides to find missing lengths, scale factor, area ratio, perimeter ratio, and all triangle properties.
Calculate the slant height, lateral surface area, total surface area, and volume of cones, pyramids (square, triangular, hexagonal), and frustums from base dimensions and vertical height.
Calculate the slant height of a cone from radius and height, lateral surface area, or total surface area. View all cone properties including volume, surface areas, and apex angle.
Calculate volume, surface area, and diagonal of 8 common 3D shapes: sphere, cube, cylinder, cone, rectangular prism, triangular prism, pyramid, and torus. Compare shapes side by side.
Calculate all sides, area, perimeter, and heights of 30-60-90 and 45-45-90 special right triangles. Enter any one side to find the rest.
Calculate all properties of a sphere: radius, diameter, volume, surface area, great circle area, and great circle circumference from any single known value.
Calculate surface area, volume, circumference, and great circle area of a sphere. Solve from radius, diameter, surface area, or volume with unit selection, presets for common balls, hemisphere brea...
Calculate the surface area of a sphere from radius, diameter, volume, or circumference. Also get hemisphere SA, spherical cap area, and volume with reference tables.
Calculate the volume and surface area of a sphere. Solve from radius, diameter, circumference, surface area, or volume. Includes presets for common spheres like basketballs and Earth.
Calculate the surface area, volume, base radius, solid angle, and sphere fraction of a spherical cap from sphere radius + cap height or base radius + cap height.
Calculate the arc length of Archimedean, logarithmic, and Fermat spirals. Set parameters, number of turns, and view radius growth, pitch angle, and turn data.
Calculate the area, perimeter, diagonal, circumradius, and inradius of a square from side length, diagonal, perimeter, or area. Compare with rectangles.
Calculate all properties of a square: side, diagonal, perimeter, area, inradius, and circumradius from any single known value.
Calculate the diagonal of a square from side length, area, perimeter, or circumradius. Also shows side, area, perimeter, and the diagonal-to-side ratio.
Calculate the area of a rectangle in square feet from length and width in inches, feet, yards, centimeters, or meters. Also converts to sq in, sq yd, sq m, and acres.
Calculate the area of a triangle in square feet. Enter base and height, three sides (Heron's formula), or two sides with an included angle. Converts between sq ft, sq in, sq yd, sq m, and acres.
Calculate square footage from length and width in any unit. Convert between sq ft, sq m, sq yd, and acres. Includes cost estimator, room presets, and a common sizes reference table.
Calculate the square footage of a circle from radius, diameter, or circumference. Converts area to sq ft, sq in, sq yd, sq m, and acres.
Calculate properties of a square inscribed in a circle. Find diagonal, side length, areas of both shapes, area ratio (2/π), and wasted space from radius, side, or diagonal.
Calculate the area of a circle in square inches from radius, diameter, or circumference. Convert to sq ft, sq cm, and sq mm.
Expand and evaluate (a + b)² and (a − b)² step by step. See each term, verification, term-proportion bars, algebraic identity reference, and common examples.
Calculate the perimeter of a square from its side length, area, or diagonal. Includes reference tables, visual comparisons, and multiple solving modes.
Calculate volume, surface area, slant height, lateral area, dihedral angle, and lateral edge of a square pyramid from base side and height.
Calculate the volume of a square pyramid from base side and height, or find a missing dimension from volume. Multiple solving modes with reference table and visual comparison.
Solve the ambiguous SSA triangle case — enter two sides and a non-included angle to find 0, 1, or 2 possible triangles. Shows all angles, sides, area, and perimeter for each solution.
Solve any triangle from three sides using the Law of Cosines and Heron's formula. Computes all angles, area, perimeter, heights, medians, inradius, and circumradius.
Solve a triangle from three sides (SSS). Compute all angles, area, perimeter, heights, medians, inradius, and circumradius using Heron's formula and the Law of Cosines.
Find the standard and general form equations of a circle from center coordinates (h, k) and radius r. Calculate area, circumference, diameter, and visualize the equation components.
Convert the standard form equation of a circle (x−h)²+(y−k)²=r² to general form x²+y²+Dx+Ey+F=0. View step-by-step expansion, coefficients, and circle properties.
Calculate properties of regular star polygons: area, perimeter, inner/outer radii, point angles, edge lengths. Supports 5 to 12-pointed stars with presets.
Explore the string girdling the Earth problem. Add extra string length to a rope around a sphere and see how high it rises — the answer is independent of sphere size!
Calculate the total and lateral surface area of a cylinder from its radius and height. Includes volume, base area, circumference, SA breakdown bars, wall-thickness mode, and a reference table of co...
Calculate the total surface area, lateral surface area, slant height, volume, and face breakdown of square, rectangular, and triangular pyramids. Includes presets for real-world pyramids.
Calculate the total and lateral surface area of a rectangular prism (cuboid) from length, width, and height. View face-pair breakdown, volume, space diagonal, and visual comparison bars.
Calculate the total and individual face surface areas, volume, space diagonal, and edge length of a rectangular prism (box). Supports open-top boxes with presets for common objects.
Calculate the total and lateral surface area of a rectangular pyramid from base length, width, and pyramid height. View slant heights, base area, each triangular face area, and visual breakdown.
Calculate the total and lateral surface area of a square pyramid from its base side length and slant height or pyramid height. Includes volume, lateral edge, SA breakdown bars, and a reference tabl...
Calculate the total and lateral surface area of a triangular prism from triangle side lengths and prism height. View each face area, volume, and visual breakdown bars.
Calculate the total and lateral surface area, volume, and face-by-face breakdown of a triangular prism. Supports isosceles, equilateral, and scalene triangle cross-sections.
Calculate the surface-area-to-volume ratio for spheres, cubes, cylinders, and rectangular prisms. Compare shapes at equal volume to find the most efficient geometry. Includes sphericity index, comp...
Calculate the tangent line from an external point to a circle. Find tangent length, tangent points, slopes, angles between tangent lines, and the power of a point.
Calculate tangent line properties from an external point to a circle. Find tangent length, tangent points, angles, and power of a point. Includes ratio bars, 8 presets, and a reference table.
Calculate the volume, surface area, height, circumradius, inradius, and midsphere radius of regular and irregular tetrahedra from edge lengths.
Calculate the volume, surface area, cross-section area, tube circumference, and outer/inner diameter of a torus from its major and minor radii. Includes presets for donuts, tires, and rings.
Calculate the surface area and volume of a torus (donut shape) from its major radius R and minor radius r. Includes outer/inner diameters, circumferences, cross-section area, SA/V ratio, proportion...
Calculate all four angles of a trapezoid from sides and height or from two known angles. Shows angle bars, area, perimeter, diagonals, and midsegment with reference tables.
Complete trapezoid calculator. Enter parallel sides, height, and optional legs for area, perimeter, midsegment, diagonals, and angles. Supports right, isosceles, and general trapezoids.
Calculate the height of a trapezoid from area and parallel sides, from all four sides using the Pythagorean theorem, from a leg and base angle, or from a diagonal. Multiple input modes with visual...
Calculate the midsegment (median) of a trapezoid from two parallel sides, or from area and height. Shows midsegment visualization, area, perimeter, height, and reference table.
Calculate the perimeter of a trapezoid from four sides, from bases and height (isosceles), from bases with angles, or from partial measurements. Visual bars, reference table, and full property brea...
Find any missing side of a trapezoid — a base or a leg — from known sides, area, height, angles, or perimeter. Multiple modes, visual bars, angle display, and reference table.
Calculate the volume, surface area, base area, and lateral faces of a trapezoidal prism. Enter the parallel sides, trapezoid height, and prism length to get full geometric results with visual break...
Calculate all three altitudes of a triangle from its side lengths. Find the orthocenter coordinates, classify the triangle (acute/obtuse/right), and compare altitude lengths. Includes presets and r...
Calculate all three angle bisector lengths of a triangle from its sides. Find the incircle radius, incenter coordinates, and segment ratios using the angle bisector theorem. Includes presets and re...
Find missing angles of a triangle. Enter one or two known angles to find the rest, or enter three side lengths to compute all angles using the Law of Cosines. Includes preset triangles, category ta...
Calculate all three angles of a triangle from three side lengths using the law of cosines. Shows angle classification, radian conversion, sum verification, area, and full triangle properties.
Calculate triangle area, perimeter, angles, altitudes, circumradius, inradius, and classification. Supports base-height, Heron's formula, and SAS methods with unit selection and a complete 15-prop..
Calculate the area of any triangle using 4 methods: base × height, Heron's formula (3 sides), SAS (2 sides + included angle), or coordinate geometry (3 vertices). Includes classification, inradius..
Calculate triangle area from three sides using Heron's formula. Also computes perimeter, all angles, altitudes, medians, circumradius, inradius, and classifies by angle and side type.
Calculate the area, perimeter, all angles, altitudes, circumradius, and inradius of a triangle from two sides and the included angle (SAS method). Includes triangle classification, presets, and ref...
Solve triangles from two sides and a non-included angle (SSA). Detects 0, 1, or 2 solutions. Computes area, perimeter, all angles/sides, circumradius, inradius, and altitudes for each valid triangle.
Check if two triangles are congruent by entering their sides and angles. Determines which congruence criterion applies — SSS, SAS, ASA, AAS, or HL — with detailed explanations, preset pairs, and a...
Convert triangle angles between degrees, radians, and gradians. Enter any combination of angle units, verify the angle sum equals 180°, and see all three angles in every unit system with visual pro...
Find the height of a triangle using multiple methods: area + base, three sides (Heron), or vertex coordinates. Computes all three altitudes, area, and angles.
Check if three side lengths form a valid triangle. See all three inequality checks, surplus/deficit, triangle classification (acute/right/obtuse, scalene/isosceles/equilateral), area, and angles.
Calculate the inscribed circle (incircle) of a triangle from three sides. Find inradius, incenter coordinates, incircle area, contact triangle, and circle-to-triangle area ratio.
Calculate all three medians of a triangle from its side lengths. Find the centroid coordinates, area, median lengths, and reverse-solve sides from medians. Includes presets and reference table.
Calculate the perimeter of a triangle from three sides with automatic triangle inequality validation. Also computes area, angles, semi-perimeter, classification, radii, and altitudes.
Demonstrate the triangle proportionality theorem — a line parallel to one side of a triangle divides the other two sides proportionally. Enter triangle sides and a dividing line position to verify...
Calculate side ratios, area ratios, and perimeter ratios between two similar triangles. Enter corresponding sides to find all proportional relationships from the same pair of figures.
Find the scale factor between two similar triangles. Enter corresponding sides to compute the linear scale factor k, area ratio k², volume ratio k³, perimeter ratio, and verify similarity.
Find a missing side of a triangle using the Law of Cosines, Law of Sines, Pythagorean Theorem, or subtract known sides from the perimeter. Select a method, enter known values, and get the unknown s...
Find the missing side length of a triangle using the Law of Cosines, Law of Sines, or perimeter subtraction. Multiple solving modes, preset triangles, reference table, and side proportion bars.
General-purpose triangle solver. Enter any valid combination of sides and angles (SSS, SAS, ASA, AAS, SSA) and compute all remaining sides, angles, area, perimeter, and more.
Calculate all three sides of a triangle given three angles and one known side using the law of sines. Supports AAS, ASA, and area-based modes. Shows triangle type, perimeter, area, and altitude.
Test if two triangles are similar using AA, SAS, or SSS similarity criteria. Verify corresponding side ratios, find scale factors, and identify matching angles and sides.
Calculate the slopes of all three sides of a triangle from vertex coordinates. Determine perpendicularity, parallelism, and classify the triangle by its slope properties.
Demonstrate that the interior angles of a triangle sum to 180°. Find the missing third angle, compute exterior angles, and explore the Exterior Angle Theorem with visual bars and reference tables.
Compute comprehensive triangle properties from three vertex coordinates including sides, angles, area (shoelace formula), perimeter, centroid, incenter, circumcenter, and orthocenter.
Calculate volume, surface area (total and lateral), base area, perimeter, and edge lengths of a triangular prism. Supports any triangle base with unit conversion and presets.
Calculate the volume and surface area of a triangular pyramid (tetrahedron). Supports regular and irregular modes with base triangle dimensions or full vertex coordinates.
Find an unknown position using triangulation (angles) or trilateration (distances) from 2-3 known reference points. Applications in GPS, surveying, and navigation.
Solve any triangle using trigonometric functions. Enter sides and angles to find all missing measurements using Law of Sines, Law of Cosines, and standard trig identities.
Calculate volume, lateral surface area, and total surface area of a truncated cone (frustum). Enter top radius, bottom radius, and height or slant height.
Calculate the volume of a truncated cone (frustum) with multiple input methods. Convert between cubic inches, cubic feet, liters, and gallons.
Enter any angle in degrees or radians to find sin, cos, tan, csc, sec, cot, (x, y) coordinates, quadrant, and reference angle on the unit circle. Common angles table included.
Explore the vertical angles theorem. Enter one angle to find its vertical angle (equal) and both adjacent supplementary angles. Supports multi-line intersection mode, angle relationship tables, and...
Calculate the volume and surface area of a hemisphere. Enter radius or diameter, get volume in multiple units (liters, gallons, cubic feet), curved surface area, base area, total surface area, and...
Calculate volume and surface area of a triangular prism. Supports equilateral, right, and scalene base triangles with prism length input.
Calculate the volume of a solid of revolution using the disk or washer method with Simpson's rule numerical integration. Supports linear, quadratic, square root, sine, and custom polynomial functions.
Convert volume to weight using material density. Supports 30+ materials (water, steel, concrete, gold, wood, and more), multiple volume and weight units, and custom densities.
Understand WHY completing the square works through geometric area interpretation. See algebraic steps alongside visual area models, comparison bars, and step breakdowns.
Find the width of a rectangle from area & length, perimeter & length, diagonal & length, or area & perimeter. Shows all rectangle properties including area, perimeter, diagonal, and aspect ratio wi...
Sine, cosine, tangent, distance, angle, and vector calculators.
Calculate the distance between two points in 2D space using Euclidean, Manhattan, or Chebyshev metrics. Also computes midpoint, slope, and component breakdown.
Calculate the Euclidean distance between two points in 3D space, plus midpoint, direction cosines, direction angles, and 2D projection comparisons.
Calculate the inverse cosine (arccos) of any value from −1 to 1. Returns the angle in degrees and radians, plus related trig values, quadrant, and unit circle position.
Calculate the inverse sine (arcsin) of any value from −1 to 1. Returns the angle in degrees and radians, plus cosine, tangent, quadrant, reference angle, and unit circle position.
Calculate the inverse tangent (arctan) of any value. Supports both atan(x) and atan2(y,x) modes for full 360° angle resolution. Returns degrees, radians, quadrant, and related trig values.
Detailed inverse tangent calculator with Taylor series approximation, convergence analysis, step-by-step computation, and relationship to other inverse trig functions.
Calculate atan2(y, x) with full quadrant awareness. Enter y and x coordinates to find the angle in degrees and radians, quadrant, reference angle, magnitude, and normalized direction vector.
Find the complement (90° − θ) and supplement (180° − θ) of any angle. See cofunction identities, trig values of both angles, and the explement. Includes angle pair tables and visual bars.
Convert a complex number from polar/trigonometric form r(cos θ + i sin θ) to rectangular form a + bi. Shows real part, imaginary part, Euler form, conjugate, and quadrant.
Convert a complex number from rectangular form a + bi to trigonometric (polar) form r(cos θ + i sin θ). Shows modulus, argument, exponential form, quadrant, reciprocal, and De Moivre powers.
Identify and analyze conic sections from the general equation Ax² + Bxy + Cy² + Dx + Ey + F = 0. Find the type, center, foci, vertices, eccentricity, and standard form for circles, ellipses, parabo...
Find consecutive integers that sum to a target value, generate integer sequences, and explore even and odd consecutive integers with formulas and visualizations.
Calculate the distance between two points in a coordinate plane using Euclidean, Manhattan, Chebyshev, and Minkowski metrics with midpoint, slope, and angle analysis.
Calculate the inverse cosine (cos⁻¹) of any value from −1 to 1. Returns the angle in degrees, radians, and gradians with unit circle visual.
Calculate cos(2θ) using all three double-angle formulas: 1−2sin²θ, 2cos²θ−1, and cos²θ−sin²θ. Verify equality, explore special angles, and visualize form comparisons.
Calculate the cosecant of any angle in degrees, radians, or gradians. Shows all 6 trig functions, quadrant sign chart, common values table, and reference identities.
Calculate the hyperbolic cosine cosh(x) and all six hyperbolic functions. Includes identity verification, comparison table, and custom range generator.
Calculate the cosine of any angle in degrees or radians. View all six trig functions, quadrant, reference angle, and a complete common cosine values table.
Calculate cosine similarity between two vectors in 2D–5D. Shows dot product, magnitudes, angle, similarity gauge, and component breakdown table.
Calculate the cotangent of any angle in degrees or radians. Shows all 6 trig functions, quadrant visual, common values table, and identity reference.
Find coterminal angles by adding or subtracting 360° (2π). Shows reference angle, quadrant, trig values, and generates a table of N coterminal angles.
Calculate the distance between two points in 2D or 3D space. Shows midpoint, slope, line equation, displacement vector, and step-by-step solution with coordinate visualization.
Calculate distances between two points using Euclidean, Manhattan, Chebyshev, and Minkowski metrics in 2D or 3D with step-by-step breakdown and visual comparison.
Calculate the perpendicular distance from a point to a plane in 3D space. Shows signed distance, normal vector, foot of perpendicular, formula breakdown, and verification.
Calculate double angle formulas for sin(2θ), cos(2θ), and tan(2θ). Shows all three cos(2θ) forms, verification table, original vs double angle comparison, and identity reference.
Explore sin(2θ), cos(2θ) in three forms, and tan(2θ) with step-by-step proofs, power-reducing derivations, and a comparison table.
Verify all double-angle identities for any angle. Compare LHS vs RHS, check error margins, and explore power-reducing and half-angle connections.
Calculate Euclidean distance in 2D to 10D with step-by-step breakdown, component analysis, and comparison with Manhattan and Chebyshev distances.
Calculate sin(θ/2), cos(θ/2), and tan(θ/2) with automatic sign by quadrant, three tan forms, and double-angle back-verification.
Calculate sinh(x) and all 6 hyperbolic functions. Shows identity verification, comparison with regular trig, common values table, and inverse hyperbolic results.
Calculate the hypotenuse or missing leg of a right triangle, plus area, angles, altitude, inradius, and special triangle detection.
Find the intersection point of two lines in slope-intercept, point-slope, or general form. Shows angle between lines, parallel/perpendicular detection, and coordinate visualization.
Calculate the inverse cosine (arccos) of any value from −1 to 1. Get the principal value in degrees and radians, general solutions, related trig values, and a reference table.
Calculate the inverse cosine (arccos) of any value. Get results in degrees, radians, gradians, and turns with domain checking, related trig values, and a common values reference table.
Calculate the inverse sine (arcsin) of any value. Get results in degrees, radians, gradians, and turns with domain checking, unit circle visualization, and all 6 inverse trig comparisons.
Calculate arcsin (sin⁻¹) of any value from −1 to 1. Shows result in degrees, radians, gradians, general solution, domain check, and common values reference.
Calculate arctan(x) or atan2(y,x) with full quadrant support. Get results in degrees, radians, gradians, and turns with quadrant identification, common values table, and atan-vs-atan2 comparison.
Calculate arctan (tan⁻¹) of any value. Get results in degrees, radians, gradians, and turns. Includes atan2 mode, common values table, and visual range indicator.
Calculate all six inverse trig functions simultaneously: arcsin, arccos, arctan, arccsc, arcsec, arccot. Enter a value and see every result with domain checking, identities, and visual comparison.
Solve any triangle using the law of cosines. Find unknown sides or angles, compute area, perimeter, circumradius, inradius, and classify the triangle type.
Solve triangles using the law of sines. Handles AAS, ASA, and SSA configurations including the ambiguous case with 0, 1, or 2 solutions.
Find the line where two planes intersect in 3D space. Computes direction vector, parametric equations, a point on the line, and the angle between the planes.
Calculate Manhattan (taxicab/L1) distance in 2D, 3D, or N dimensions. Compare with Euclidean and Chebyshev distances with component breakdown and grid visualization.
Calculate phase shift, amplitude, period, and vertical shift for y = A·sin(Bx + C) + D. Visualize the function with an interactive SVG graph and key-point tables.
Convert between polar (r, θ) and rectangular (x, y) coordinates. Bidirectional conversion with quadrant visualization, unit circle reference, and batch table.
Solve right triangles with the Pythagorean theorem. Find any side, angles, area, perimeter, altitude, inradius, circumradius, and detect special triples.
Generate Pythagorean triples up to any limit, find triples containing a given number, and check whether three numbers form a valid Pythagorean triple.
Convert rectangular (x, y) to polar (r, θ) coordinates in degrees, radians, or gradians. Quadrant detection, batch mode, visual plot, and reference table.
Find the reference angle for any angle in degrees or radians. Shows coterminal angle, quadrant, trig values, ASTC sign chart, and unit circle visualization.
Calculate sec(θ) = 1/cos(θ) in degrees, radians, or gradians. All 6 trig functions, identity verification, asymptote warnings, sign chart, and common values.
Calculate sin, cos, tan, csc, sec, and cot of any angle. Shows quadrant analysis, ASTC rule, Pythagorean identity check, full 0°–360° reference table, and exact values.
Calculate the sine of any angle in degrees. Shows radians equivalent, all 6 trig functions, sine curve visual, common values table, and custom range generator.
Calculate sin(θ) for any angle with exact values, Taylor series approximation, all 6 trig functions, quadrant visual, and standard angle reference table.
Calculate sin(2θ) using the double-angle formula 2·sin(θ)·cos(θ). Step-by-step solution, identity verification, projectile range, and triangle area applications.
Calculate the sine of any angle in degrees, radians, or gradians. Shows all 6 trig functions, quadrant analysis, exact values, sine wave visual, and reference table.
Compute singular values of 2×2 and 3×3 matrices. Shows σ₁, σ₂, σ₃, condition number, rank, Frobenius norm, and step-by-step eigenvalue decomposition.
Convert numbers to and from standard form (scientific notation). Shows mantissa, exponent, engineering notation, SI prefix, expanded form, and arithmetic operations.
Convert between standard notation, scientific, engineering, hexadecimal, and word forms. Shows place value breakdown, SI prefix reference, and magnitude comparison.
Compute exact and decimal values for all six sum and difference trig identities. Step-by-step derivation, intermediate values, and exact forms for special angles.
Calculate supplementary angles (180° − θ), complementary angles (90° − θ), and explement (360° − θ). Visual angle bars, trig identities, and common angle pair tables.
Calculate the tangent of any angle in degrees, radians, or gradians. See all 6 trig functions, asymptote warnings, quadrant identification, and a common values table.
Calculate the tangent of the angle between two lines using slopes or equations. Detect parallel and perpendicular lines, find acute and obtuse angles, with visual intersection diagram.
Calculate tanh(x) and all six hyperbolic functions. Compare tanh vs sigmoid, verify identities, explore common values with visual saturation curves.
Multi-purpose theta calculator: convert between degrees, radians, gradians, and turns. Find all 6 trig values, reference angle, quadrant, coterminal angles, and unit circle visualization.
Verify 24+ trig identities for any angle. Pythagorean, reciprocal, double angle, half angle, sum/product formulas with pass/fail status and error analysis.
Solve right and oblique triangles. Enter sides and angles to find all unknowns, area, circumradius, and inradius. SSS, SAS, ASA, AAS, SSA modes included.
Calculate all 6 trig functions, reciprocals, and inverses for any angle. Quadrant analysis, unit circle visual, and special angles reference table.
Calculate trig functions for degree inputs. Convert between DMS and decimal degrees, generate range tables, and reference common angle values.
Calculate union, intersection, difference, and symmetric difference of two sets. Venn diagram, Jaccard similarity, power set size, and complement analysis.
Addition, multiplication, rounding, base conversion, and number operation calculators.
Calculate the absolute change, relative change, and percentage change between two values. Compare increase vs decrease with visual change bars and a multi-scenario comparison table.
Compute absolute values, distances between numbers, solve absolute value equations and inequalities, explore properties with a number line visual, batch mode, and comprehensive reference table.
Add or subtract two fractions with different denominators. See the LCD, step-by-step simplification, mixed number form, and decimal equivalent with a common-denominators reference table.
Add 2 to 5 fractions with any denominators. See the common denominator, step-by-step simplification, result as fraction, mixed number, and decimal. Visual fraction bars show each fraction and the sum.
Add multiple numbers with a step-by-step carry method, running total, digit-by-digit breakdown, place value table, and a number line visualization. Includes a practice mode with random problems.
Calculate the arithmetic mean, median, mode, range, geometric mean, harmonic mean, RMS, standard deviation, and more from any list of numbers. Supports weighted averages, distribution visualization...
Calculate the simple and weighted average of multiple percentages. See why simple vs weighted averages differ, with a weight contribution table and visual weight bars.
Add two binary numbers with step-by-step carry method. View results in binary, decimal, hexadecimal, and octal. Includes bit-by-bit breakdown table, overflow detection, and visual carry chain.
Divide binary numbers with long division steps. View quotient and remainder in binary, decimal, hex, and octal. Includes step-by-step division table and precision control for fractional results.
Convert fractions to binary representation and vice versa. Analyze repeating patterns, precision loss, and IEEE 754 floating-point representation. Includes conversion steps table and visual bit pat...
Multiply binary numbers using the partial products method with step-by-step visualization. View results in binary, decimal, hex, and octal. Includes partial products table and Booth's algorithm co..
Perform bitwise AND, OR, XOR, NOT, and shift operations on integers. View step-by-step bit-by-bit computation, truth tables, binary/hex/octal representations, presets, and a bit visualization.
Subtract binary numbers using the borrow method and two's complement. Compare both methods side-by-side with results in binary, decimal, hex, and octal. Includes borrow chain visualization and..
Compute ⌈x⌉ (ceiling), ⌊x⌋ (floor), round, and trunc for any number. Compare all rounding modes, see fractional part, step function visualization, ceiling division, and a full comparison table.
Analyze a decimal or perform decimal arithmetic. Convert decimals to fractions, percents, and scientific notation, inspect place value, and review rounding targets in one tool.
Convert decimal integers to binary, octal, and hexadecimal. Includes binary-to-decimal reverse conversion, step-by-step division method, bit visualization, two's complement, batch mode, and a powe..
Convert any decimal to a simplified fraction or mixed number. Supports repeating decimals, batch mode, Egyptian fractions, visual fraction bars, and a reference table of common conversions.
Convert decimal degrees to degrees and decimal minutes with latitude, longitude, and bearing support, DMS preview, range checks, presets, and reference tables.
Convert decimals to percentages and vice versa. Includes basis points, per mille, batch mode, fraction display, visual percentage bar, and a reference table of common conversions.
Divide fractions step-by-step using the keep-change-flip method. Supports mixed numbers, whole number divisors, reciprocal display, visual fraction bars, presets, and a detailed steps table.
Check if a number is divisible by 2–12 and any custom divisor. See divisibility rules, digit sums, prime factorization, all divisors, visual grid, and a range checker with color-coded results.
Divide numbers with long-division steps, quotient and remainder, simplified fraction, decimal precision control, inverse verification, divisibility rules table, and visual progress bars.
Find every factor (divisor) of a number, view factor pairs, check prime or composite status, sum of divisors, perfect number test, divisibility rules, and factor magnitude visualization.
Compute n! with step-by-step multiplication, permutations, combinations, double factorial, Stirling approximation, trailing zeros, digit count, growth visualization, and a reference table up to 25!.
Compute floor division, compare it with truncation, inspect Euclidean remainders, and test batch or growth scenarios for integer grouping.
Compute the floor ⌊x⌋ of any real number. Compare floor, ceiling, round, and truncate side-by-side, explore the fractional part, visualize the step function, and browse a comparison table for a ran...
Convert any fraction or mixed number to a decimal. Detects repeating decimals, shows long division steps, supports batch mode, and includes a reference table of 20 common fractions.
Convert any fraction to a percentage and vice versa. Includes letter grade mapping, visual pie representation, basis points, batch mode, and a reference table of 20 common fractions.
Calculate the Greatest Common Divisor (GCD) of two or more numbers using the Euclidean algorithm or prime factorization method. View step-by-step solutions, Bézout coefficients, LCM, and coprimalit...
Find the greatest common factor and least common multiple of 2 to 4 numbers with factor tables, fold steps, divisor lists, and common-multiple outputs.
Find the Greatest Common Factor (GCF) of two numbers using factor listing or a Venn diagram. Simplify fractions, see common factors, and explore the GCF-LCM relationship.
Compare two or more numbers with number-line visualization, digit-by-digit comparison, distance, midpoint, ratio, relative difference, sorted ordering, and properties table.
Convert between improper fractions and mixed numbers. Features visual representation, batch mode, number line position, preset examples, and a conversion reference table.
Perform addition, subtraction, multiplication, and division on integers. Shows sign rules, number properties (even/odd, prime, factors), absolute values, presets, a sign rules reference table, and...
Analyze any integer: even/odd, prime check, full prime factorization, all divisors, digit sum, digital root, binary/hex/octal representation, nearest primes, and number classification.
Find the modular multiplicative inverse a⁻¹ mod m using the Extended Euclidean Algorithm with step-by-step EEA table, Euler method, verification, and invertible-elements reference.
Test whether modulo is associative by comparing (a mod m) mod n vs a mod (m mod n). Side-by-side steps, visual bars, counter-example scanner, and coincidence detector.
Multiply numbers using the lattice (grid/Napier) method step-by-step. Visualize the lattice grid, diagonal sums, carries, and compare with the standard algorithm. Supports presets and a detailed st...
Calculate the Least Common Multiple (LCM) of two or more numbers using prime factorization or listing multiples. Step-by-step solutions, GCD relationship, multiplier bars, and common multiples.
Calculate LCM for 2–5 numbers using prime factorization. Step-by-step pairing, prime factor comparison table, power-contribution bars, and highlighted multiples grid.
Add aligned whole numbers or decimals with a long-addition layout, carry table, running-total visual, estimate check, and target comparison.
Perform long division step-by-step with bring-down and subtract stages. Detect repeating decimals, display quotient as fraction and decimal, explore presets, and view a detailed steps table.
Multiply numbers step-by-step showing partial products, place value shifts, carries, and the final sum. Includes presets, a partial products table, carry visualization, and grid-method comparison.
Subtract aligned whole numbers or decimals with a vertical layout, regrouping table, running remainder visual, target check, and answer verification.
Convert degrees and decimal minutes to decimal degrees with sign control, minute carry handling, range checks, radian output, presets, and reference tables.
Perform all four operations on mixed numbers — add, subtract, multiply, divide. Converts to improper fractions, shows step-by-step solution, visual parts, and simplification.
Calculate modular arithmetic with clock visualization, congruence checker, modular inverse, equivalence class display, multiple mod conventions, and a properties reference table.
Handle negative modulo correctly across truncated, floored, and Euclidean conventions. Language comparison table, number-line visual, and range-scan highlighting where results differ.
Multiply numbers with a partial-products breakdown, multi-factor chain, sign rule analysis, times table reference, progress bars, and a properties reference table.
Find the multiplicative inverse (reciprocal) for integers, fractions, decimals, and mixed numbers. Verify that a × a⁻¹ = 1 and explore inverse properties in batch mode.
Find x such that ax ≡ 1 (mod m) with full Extended Euclidean Algorithm steps, Euler theorem method, brute-force verification, Bézout identity, and all inverse pairs table.
Multiply fractions and mixed numbers step-by-step. Features cross-cancellation, area model visual, presets, GCD simplification, and a detailed steps table.
Educational tool to identify operands, operators, and structure in arithmetic expressions. Parses expressions, counts operands, shows operator precedence, expression breakdown table, and a visual e...
Evaluate mathematical expressions with step-by-step PEMDAS/BODMAS breakdown. Shows each operation in order, highlights parentheses and exponents, provides rules reference table and common mistakes.
Multiply numbers using the partial products method. Visual area model, step-by-step breakdown of each digit pair, comparison with the standard algorithm, and contribution analysis.
Convert between ppm, ppb, ppt, percent, mg/L, and µg/L. Includes a dilution calculator, magnitude scale visualization, conversion table, and reference limits for water quality and air quality.
Calculate the percentage increase or decrease between two values. Find percent change, new value from a percent, or the original value. Includes multiplier, reverse change, compound growth table, a...
Calculate the symmetric percent difference between two values. Choose from five reference bases, view absolute and relative differences, ratio, log ratio, sensitivity analysis, and visual compariso...
Calculate percent error between experimental and theoretical values. Includes absolute, relative, and signed error, tolerance checking, multiple-measurement statistics, and visual error bars.
Calculate X% of Y%, apply it to a value, chain three percentages, or reverse-find the missing percent. Step-by-step breakdown, comparison table, visual bar, and presets included.
Calculate the sale price after a percentage discount, see the exact dollar savings, apply a second coupon, add sales tax, and compare savings across discount levels. Discount comparison table, coup...
Calculate percentages of time, elapsed-time percentages, remaining durations, reverse total timelines, and scaled durations with hh:mm:ss outputs and checkpoint tables.
Convert percent to decimal and decimal to percent, with batch conversion, optional scientific notation, fraction output, and a visual bar. Includes a common conversions reference table.
Convert any percentage to a simplified fraction, mixed number, and decimal. Supports fraction-to-percent conversion, batch mode, visual part-of-whole display, and a 22-row common conversions refere...
Measure progress toward a goal from a starting point, see remaining percentage and amount, track stretch-goal progress, and estimate the pace needed per period.
Calculate percentages with four modes: find X% of Y, what percent X is of Y, find the base, and percentage change. Includes visual bars, comparison table, and mental math shortcuts.
Calculate the new value after a percentage decrease, find the percent decrease between two values, reverse-calculate the original value, or model compound decay. Decay table, half-life indicator, v...
Calculate the new value after a percentage increase, find the percent increase between two values, reverse-calculate the original, or project compound increases. Growth table, visual bars, and quic...
Work out one percentage of another percentage, apply the result to a base value, compare two percentage rates, chain three percentages, or solve for a missing factor.
Measure percentage-point and basis-point changes between two rates, convert them to dollar impact on a base amount, and compare moves across scenarios.
Break down any number by place value. Shows expanded form, word form, standard form, scientific notation, digit visualization, base conversions, and contribution percentages.
Decompose any number into its prime factors with an interactive factor tree, exponent notation, divisor count, sum of divisors, Euler's totient, composition bar, and full divisor table.
Calculate the integer quotient, remainder, decimal quotient, and fraction form of any division. Verify with the Euclidean division theorem, explore a division table, and see visual grouping of the...
Find the reciprocal (multiplicative inverse) of integers, fractions, decimals, and mixed numbers. Verify the product identity, compute power reciprocals, and explore reciprocal properties with visu...
Calculate relative change, absolute change, percentage change, relative difference, and symmetric relative change between two values. Includes visual comparison bars, presets, and a reference table.
Calculate the remainder from division, verify the division algorithm, compare truncated/floored/Euclidean conventions, check modular congruence, and explore remainders over a range with visual bars.
Round numbers to the nearest 5, 10, 25, 50, 100, 1000, or any custom interval. Compare rounding intervals, process batches of numbers, and visualize where values fall between multiples.
Round invoice totals, line items, and tax-inclusive amounts to the nearest cent with discount, shipping, payment, and method comparisons.
Round order totals, monthly spending plans, and budget estimates to the nearest dollar with tax, tip, fee, and frequency analysis.
Round counts, totals, and projections to the nearest hundred, compare group totals, and see how estimate bands change under different rounding methods.
Round values to two decimal places with hundredths and thousandths guidance, method comparison, repeated-value drift, batch rounding, and interval visualization.
Round decimals to the nearest integer with method comparison, repeated-value drift analysis, batch rounding, and a number-line visual between whole numbers.
Round interest, fees, and payoff balances to the nearest penny while tracking exact interest, daily accrual, repeated drift, and payment scenarios.
Round values to the nearest ten, compare rounding methods, test grouped totals, and see cutoff bands for reports, estimates, and planning.
Round values to one decimal place with digit-by-digit guidance, method comparison, repeated rounding drift, batch analysis, and a tenth-interval visual.
Round populations, sales, budgets, and inventory totals to the nearest thousand with method comparisons, group scenarios, and batch analysis.
Round decimals to the nearest thousandth, inspect deciding digits, compare rounding methods, and measure repeated rounding drift.
Round numbers to any decimal place using six different methods -- half up, half down, banker's rounding (half even), ceiling, floor, and truncation. Compare all methods side-by-side with a..
Convert numbers to and from scientific notation, perform arithmetic operations (add, subtract, multiply, divide) on scientific numbers, view engineering notation with SI prefixes, and explore magni...
Compute sgn(x) for any number or expression, see absolute value connection, product-of-signs rule, power rule, number line visualization, sign table for a range, and properties reference.
Count significant figures in any number, round to N sig figs, view digit-by-digit significance breakdown, convert to scientific notation, and compare rounding levels with a visual precision bar.
Subtract fractions with unlike denominators using the LCD method. Supports mixed numbers, borrowing, step-by-step solution table, visual fraction bars, and presets.
Subtract multiple numbers with step-by-step borrowing visualization, running totals, base conversion, cumulative progress bars, and a comprehensive properties reference table.
Calculate sum, product, arithmetic/geometric/harmonic means, sum of squares, power sums, and cumulative totals for any set of numbers.
Check whether a fraction produces a terminating decimal, factor the denominator, preview repeating digits, and compare nearby denominators.
Calculate unit rates for prices, speed, pay, productivity, or fuel efficiency with comparison tables, benchmark scaling, and better-value checks.
Interactive explorer of 12 real-world modulo applications: clock arithmetic, even/odd, cyclic indexing, day of week, hashing, digit extraction, color cycling, leap year, and more.
Calculate weighted averages with dynamic value–weight pairs, GPA letter-grade mode, weight normalization, contribution breakdown table, and visual weight-distribution bars.
Equation solving, polynomial, matrix, and linear system calculators.
Add or subtract two polynomials with up to 4 terms each. See the combined result, degree, leading coefficient, step-by-step like-term combination, and a polynomial operations reference table.
Calculate the antilogarithm (inverse logarithm) for base 10, base e (natural), or any custom base. See the result, scientific notation, verification, and a reference table of common antilog values.
Calculate Bessel functions of the first kind J_n(x) and second kind Y_n(x). View values, derivatives, zeros, a visual profile chart, and a comprehensive properties reference table.
Interpolate a value inside a 2D rectangular grid from four corner values. See the step-by-step breakdown, corner weights, partial derivatives, and a contribution table.
Calculate log base 2 of any value. Find bits needed, next power of 2, information content, and space utilization. Includes powers of 2 reference table and bit requirement visualization for CS appli...
Calculate binomial coefficients C(n,k), Pascal's triangle rows, permutations P(n,k), and multinomial coefficients with step-by-step factorial breakdowns.
Find the characteristic polynomial, eigenvalues, trace, and determinant of a 2×2 or 3×3 matrix with step-by-step computation and eigenvalue visualization.
Compute the determinant of a 2×2 or 3×3 matrix via cofactor expansion (Laplace expansion). See minors, cofactors, and a full step-by-step expansion breakdown.
Compute the cofactor matrix, adjugate (classical adjoint), determinant, and inverse of a 2×2 or 3×3 matrix with step-by-step cofactor breakdowns and visual grids.
Find cofunction identities for all six trigonometric functions. Calculate sin↔cos, tan↔cot, sec↔csc pairs and verify complementary angle relationships.
Condense and combine logarithmic expressions into a single log using product, quotient, and power rules. Step-by-step solutions with rule-by-rule explanation.
Solve any cubic equation ax³ + bx² + cx + d = 0. Find all three roots (real and complex), discriminant, and Vieta's formulas with step-by-step analysis.
Apply Descartes' Rule of Signs to any polynomial. Count sign changes in f(x) and f(−x) to determine the possible number of positive, negative, and complex roots.
Calculate the constant of variation k, predict y values, and explore direct, quadratic, cubic, and inverse variation relationships with visual proportionality bars and reference tables.
Calculate the discriminant b²−4ac of a quadratic equation, determine the number and type of roots, find vertex and axis of symmetry, and see real or complex solutions.
Simplify expressions with dividing exponents using the quotient rule, power of a quotient, negative exponents, zero exponent, and power of a power rules with step-by-step solutions.
Simplify radical divisions √a/√b, divide nth roots, rationalize denominators, and see step-by-step solutions with value comparison bars and a radical rules reference table.
Calculate eˣ, explore the Taylor series approximation with adjustable terms, verify ln(eˣ) = x, see growth rate, doubling time, and series convergence visualization.
Find equivalent ratios, simplify to lowest terms, scale ratios, solve proportions, and generate comprehensive equivalent ratio tables with visual proportion bars.
Calculate the error function erf(x), complementary error function erfc(x), inverse erf, and Taylor series convergence with reference tables and visual convergence bars.
Find exact trigonometric values for standard angles — sin, cos, tan, csc, sec, cot as fractions and radicals. Complete unit circle reference table with value comparison bars.
Expand logarithmic expressions step by step using product, quotient, and power rules. Supports any base with numeric evaluation, term breakdown bars, and a complete log rules reference table.
Convert between exponential form (b^x = y) and logarithmic form (log_b(y) = x). Solve for any variable — base, exponent, or result — with reference tables and visual comparison bars.
Evaluate f(x) = a·bˣ + c, find growth/decay rate, doubling/halving time, asymptotes, and generate a table of values with visual bars.
Model exponential growth and decay with discrete A₀·(1+r)ᵗ or continuous A₀·eʳᵗ formulas. Find doubling time, growth factor, and timeline.
Convert numbers between standard form, scientific notation, and engineering notation. Find SI prefixes, significant figures, and order of magnitude.
Factor ax² + bx + c into linear factors. Find roots, discriminant, vertex, and see the AC method step by step with a factor-pair analysis table.
Multiply two binomials step-by-step using the FOIL method. See First, Outer, Inner, Last products, simplified polynomial, area model, and term magnitude bars.
Calculate x^(m/n) — fractional and rational exponents. Convert between exponential and radical forms, see step-by-step results, and explore a reference table of common fractional powers.
Calculate Γ(x), log Γ(x), digamma ψ(x), and reciprocal gamma for any real number. Explore special values, reference tables, and magnitude visualizations.
Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 2–4 numbers using prime factorization or the Euclidean algorithm. View factor breakdown tables and step-by-step solutions.
Explore the golden ratio φ ≈ 1.618. Check if rectangles have golden proportions, generate Fibonacci sequences, view convergence to φ, and discover golden ratio properties.
Solve and graph one-variable linear inequalities on a number line. Supports <, >, ≤, ≥, compound AND/OR inequalities with step-by-step solutions.
Solve and graph quadratic inequalities of the form ax²+bx+c > 0, < 0, ≥ 0, or ≤ 0. Find roots, vertex, solution intervals, and visualize solution regions on a number line.
Find the GCF and LCM of 2-4 numbers using the Euclidean algorithm and prime factorization. View step-by-step solutions, Bézout coefficients, and factor comparison visuals.
Calculate sinh, cosh, tanh, coth, sech, csch and their inverses for any real number. Includes value comparison bars, reference table, and identity verification.
Convert inequalities to interval notation, set-builder notation, and back. Visualize intervals on a number line with open/closed endpoints and test membership.
Convert between interval notation, inequality notation, set-builder notation, and number line graph. Supports open, closed, half-open, and unbounded intervals.
Calculate inverse variation (y = k/x), inverse square (y = k/x²), and inverse cube (y = k/x³). Find the constant k, predict new values, and compare with direct variation.
Calculate the involute function inv(α) = tan(α) − α for gear design. Find involute values, tooth thickness, base pitch, and gear dimensions from pressure angle and module.
Calculate the Lagrange remainder (Taylor polynomial error bound) |Rₙ(x)| ≤ M·|x−a|ⁿ⁺¹/(n+1)!. Find the maximum error, number of terms needed for desired accuracy, and convergence rate.
Calculate the LCM (Least Common Multiple) of 2–4 numbers using prime factorization. Also shows GCF, LCM×GCF relationship, prime factor breakdown, and multiples comparison table.
Find the equation of a line through two points. Get slope-intercept, point-slope, and standard forms plus slope, intercepts, distance, midpoint, and angle.
Express a target vector as a linear combination of basis vectors in 2D or 3D. Find scalar coefficients, verify the solution, and visualise component contributions.
Generate pseudo-random bit sequences using linear feedback shift registers. Configure register length, tap positions, and seed to analyze LFSR period, feedback polynomial, and sequence properties.
Test whether a set of vectors is linearly independent. Enter 2–4 vectors in 2D or 3D, compute determinant, rank, row reduction (RREF), and find dependency relations if dependent.
Interpolate a y-value for a given x between two known points using linear interpolation (LERP). Supports extrapolation, multi-point error analysis, and shows slope, equation, and interpolation para...
Calculate logarithms with any base. Enter a base b and value x to find log_b(x), natural log, common log, and binary log. Includes change of base, reference tables, and magnitude comparison.
Calculate x raised to the power n for any base and exponent including integers, fractions, negatives, and zero. View scientific notation, digit count, powers table, and growth visualization.
Raise a 2×2 or 3×3 matrix to any positive integer power. View the result matrix, determinant, eigenvalues, trace, powers sequence table, and element growth visualization.
Evaluate mathematical expressions step by step with correct PEMDAS/BODMAS order of operations including modulo (%). See each step, compare with left-to-right evaluation, and understand operator pre...
Multiply two binomials using the FOIL method. Expand (ax+b)(cx+d), compute perfect squares (ax+b)², and difference of squares (ax+b)(ax−b). Step-by-step breakdown with area model visualization.
Simplify exponent expressions using all five rules: product (aⁿ·aᵐ), power of power ((aⁿ)ᵐ), power of product ((ab)ⁿ), quotient (aⁿ/aᵐ), and power of quotient ((a/b)ⁿ). Step-by-step with verification.
Multiply two polynomials up to degree 4 with step-by-step distribution, product expansion, and coefficient analysis. See the full FOIL and distribution grid.
Multiply radical expressions with same or different indices. Simplify √a·√b, ⁿ√a·ⁿ√b, and mixed-index radicals with step-by-step simplification.
Calculate the natural logarithm ln(x) = logₑ(x). See ln value, e^ln(x) verification, derivative 1/x, integral, and a full reference table of common ln values.
Calculate −log₁₀(x) and −ln(x) for pH, pKa, pOH, and general use. Includes pH scale interpretation, concentration ↔ pH conversion, and reference tables.
Decompose rational expressions into partial fractions. Handles distinct/repeated linear and irreducible quadratic factors with step-by-step solutions.
Divide polynomials using long division or synthetic division. See quotient, remainder, step-by-step work, and factor verification.
Analyze polynomials up to degree 5 for graphing — find roots, y-intercept, end behavior, critical points, inflection points, and generate a table of values.
Explore power functions f(x) = axⁿ: compute values, analyze domain, range, symmetry, end behavior, and growth rate. Compare powers with a table and growth bars.
Compute aⁿ mod m using modular exponentiation. See the result, step-by-step binary exponentiation, repeated squaring table, and binary decomposition of the exponent.
Calculate 10ⁿ for any integer or decimal exponent. See the result, scientific notation, SI prefix, number of digits, and a full reference table from 10⁻¹² to 10¹².
Calculate 2ⁿ for any exponent. See the result, binary representation, nearest power, storage-unit context (KB, MB, GB), and a full reference table from 2⁰ to 2⁶⁴.
Simplify and evaluate (aⁿ)ᵐ using the power-of-a-power rule. See combined exponents, verify results, and explore exponent growth with visual bars and a rules reference table.
Generate the power set P(S) of any set with up to 6 elements. See all subsets organized by size, cardinality 2ⁿ, size distribution bars, and a complete subset listing.
Evaluate power-reducing trig identities for sin², cos², tan², sin⁴, and cos⁴. Compare original and reduced values with visual bars, a formulas reference table, and common angle values.
Calculate iⁿ for any integer n, see the repeating 4-cycle (1, i, −1, −i), and extend to complex number powers. Visual cycle indicator, sequence table, and unit circle position.
Solve a/b = c/d for any missing value using cross multiplication. See step-by-step solution, cross products, scaling factor, equivalent ratios table, and ratio comparison bars.
Solve any quadratic equation with the quadratic formula. Find both roots, discriminant, vertex, axis of symmetry, and factored form with step-by-step solutions.
Simplify radicals, add/subtract like radicals, and multiply radical expressions. Shows simplified form, prime factorization, decimal value, and step-by-step work.
Simplify the ratio of three numbers. Find percentages, distribute a total, scale the ratio, and view a distribution table with visual proportion bars.
Simplify the ratio of two numbers. See the simplified ratio, fraction, decimal, percentage split, scale to a target total, and a table of equivalent ratios.
Calculate rational exponents x^(p/q). Convert between exponential and radical form, simplify exponents, and review exponent rules with step-by-step solutions.
Find all possible rational zeros of a polynomial using the Rational Root Theorem. Test ±p/q candidates, identify actual zeros, and see step-by-step analysis.
Rationalize denominators containing square roots, cube roots, or binomial radicals. See step-by-step conjugate multiplication, before/after comparison, and simplified results.
Find the point that divides a directed line segment AB in a given ratio m:n. Supports internal and external division with section formula, distance calculations, and visual segment diagrams.
Factor quadratic expressions ax² + bx + c using the reverse FOIL (AC) method. See factor pair analysis, step-by-step grouping, and visual sum comparison for every factor pair.
Calculate slope (rise/run) from two points. Find angle of inclination, parallel and perpendicular slopes, line equations, distance, and midpoint with an interactive graph.
Simplify radical expressions by extracting perfect square, cube, or nth-root factors. See prime factorization, step-by-step extraction, and visual grouping of prime factors.
Simplify ratios to lowest terms using GCD. Handles two-part (a:b) and three-part (a:b:c) ratios with step-by-step simplification, decimal equivalents, and visual comparison bars.
Evaluate y = A·sin(Bx + C) + D with full wave analysis. Compute amplitude, period, frequency, phase shift, key points, and visualize wave properties with interactive bars.
Work with equations in y = mx + b form. Enter slope and y-intercept or two points to find the equation, x-intercept, slope angle, parallel/perpendicular slopes, and generate sample points.
Convert linear equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Shows step-by-step conversion, both forms side-by-side, intercepts, and verification table.
Solve systems of two linear equations using the substitution method. Step-by-step solution, intersection graph, verification, and comparison with elimination method.
Calculate the sum of an arithmetic sequence using S = n/2·(a₁ + aₙ). Enter first term, common difference, and number of terms. Shows sum, last term, average, partial sums, term table, and growth bars.
Divide polynomials using synthetic division. Enter coefficients and divisor to get quotient, remainder, step-by-step layout, factor theorem test, and rational root candidates.
Solve 2×2 and 3×3 linear systems using Cramer's Rule, elimination, substitution, or matrix methods. Shows solution, determinants, verification, and method comparison.
Calculate the tangent ratio (tan θ = opposite/adjacent) for any angle or triangle sides. Find missing values, view SOH-CAH-TOA reference, common tangent values table, and side ratio visualization.
Evaluate any trigonometric function (sin, cos, tan, csc, sec, cot) for any angle. Shows value, quadrant, reference angle, sign, all 6 function values, quadrant sign chart, and identity verification.
Complete trigonometric reference: compute all 6 trig functions for any angle in degrees or radians. Unit circle table, identity verification, cofunction values, double-angle formulas, and function...
Convert between standard form (ax² + bx + c) and vertex form (a(x − h)² + k). Find the vertex, axis of symmetry, direction, focus, directrix, and parabola properties in one view.
Find the y-intercept of linear, quadratic, cubic, exponential, and logarithmic functions. Also shows x-intercepts, slope at origin, domain, and range with visual comparison bars.
Midpoint, slope, distance, and coordinate transformation calculators.
Calculators coming soon.
Fraction simplification, common denominator, and ratio calculators.
Compare 2 or 3 fractions using simplification, common denominators, decimals, and cross products. Rank fractions, find the LCD, and visualize which value is largest at a glance.
Solve or verify proportions of the form a/b = c/d with cross multiplication. Find a missing term, compare cross products, reduce both fractions, and inspect equivalent ratio tables.
Divide proper fractions, improper fractions, or mixed numbers. Convert to improper form, flip the divisor, simplify the quotient, and view the result as a decimal and mixed number.
Decompose fractions into sums of distinct unit fractions with greedy-method steps, improper-fraction handling, term visuals, and exact checks.
Generate equivalent fractions, target a new denominator, and verify equivalence with cross multiplication, fraction strips, and step-by-step scaling tables.
Convert improper fractions to mixed numbers with simplification, decimal checks, nearby-whole comparisons, and whole-plus-remainder visuals.
Find the Least Common Denominator (LCD) of 2–5 fractions. Shows prime factorization method, equivalent fractions, visual fraction bars, and step-by-step work.
Convert mixed numbers to improper fractions with sign handling, simplification, decimal checks, equivalent forms, and step-by-step breakdowns.
Reduce fractions to lowest terms with GCF steps, prime-factor detail, divisor lists, equivalent forms, and decimal or mixed-number checks.
Reduce any fraction to its lowest terms. Shows GCD calculation via Euclidean algorithm, step-by-step reduction, cross-multiplication verification, and batch mode.
Prime numbers, GCD, LCM, and divisibility calculators.
Compute logical AND and bitwise AND for up to 4 inputs — see truth tables, bit-by-bit visualization, binary/hex output, and Boolean algebra laws.
Convert decimal numbers to Babylonian base-60 (sexagesimal) notation with cuneiform symbols, positional breakdown, and conversion tables showing the legacy of base-60 in modern time and angles.
Perform left shift, logical right shift, and arithmetic right shift with bit-by-bit visualization, shift tables, sign extension, and multiply/divide equivalences.
Perform all bitwise operations (AND, OR, XOR, NOT, NAND, NOR, XNOR, shifts) on two numbers with step-by-step binary breakdown, bit grid visualization, and operations comparison table.
Solve systems of 2 or 3 congruences with the Chinese Remainder Theorem. Normalize residues, merge non-coprime systems, verify every modulus, and list the full solution family.
Calculate chord length, arc length, sagitta, segment area, and sector area from radius and central angle, with circle diagram, reference table, and visual comparison bars.
Explore the Collatz conjecture (3n+1 problem) for any starting number. See total steps, max value, stopping time, full sequence table, step chart visual, and preset examples.
Find the common denominator for two or more fractions, convert to equivalent fractions, compare values, and see step-by-step LCD solutions with visual fraction bars.
Perform operations on complex numbers in a+bi form — add, subtract, multiply, divide, conjugate, modulus, and argument with an interactive Argand diagram.
Convert complex numbers between rectangular (a+bi), polar (r∠θ), Euler (re^iθ), and trigonometric forms with step-by-step conversion and a unit-circle diagram.
Plot points on a coordinate grid, calculate distances, midpoints, slopes, areas, and identify quadrants. Includes SVG grid display, pairwise distance table, and presets.
Find corner points of a feasible region from a system of linear inequalities, evaluate an objective function at each vertex, and identify the optimal solution for linear programming problems.
Convert between cylindrical (r, θ, z) and Cartesian (x, y, z) coordinates with step-by-step solutions, reference angle table, and top-down projection visual.
Test divisibility of any number by 2–12 and custom divisors. See rules, digit sum method, remainder, comprehensive rules table, visual divisibility grid, and presets.
Find all divisors of a number, count them (τ), sum them (σ), classify as perfect/abundant/deficient, visualize factor pairs, and explore presets with a comprehensive divisors table.
Compute GCD via the Euclidean algorithm with step-by-step division, extended Euclidean algorithm, Bézout coefficients, LCM, presets, steps table, and visual representation.
Write any number in expanded form, factored form, scientific notation, and word form with place value breakdown tables, visual blocks, and reference charts.
Verify Fermat's little theorem, compute a^(p-1) mod p, perform modular exponentiation, check primality, view computation steps, and explore theorem properties with presets.
Compute the nth Fibonacci number, generate a sequence of terms, explore golden ratio convergence, Binet's formula, presets, sequence table, and ratio convergence visual.
Find the GCD of fraction denominators, simplify fractions, explore prime factorizations, and visualize the relationship between GCD and LCD with step-by-step solutions.
Calculate the GCD using the Euclidean algorithm and prime factorization. See Bézout identity, coprimality check, factor Venn diagram, and step-by-step solutions.
Calculate the LCD for fractions using prime factorization or listing multiples. Convert fractions, compare visually, and see step-by-step solutions with factor tables.
Find the lowest common denominator, add or subtract fractions, compare with visual fraction strips, and follow step-by-step solutions for any pair of fractions.
Compute logical NOR and bitwise NOR, see truth tables, universal gate proofs (build AND/OR/NOT from NOR), bit-by-bit visualization, and multi-input NOR.
Compute inclusive OR and exclusive OR (XOR) for up to 4 inputs — see truth tables, bit-by-bit visualization, binary/hex output, and Boolean algebra laws.
Convert between point-slope, slope-intercept, and standard form. Find the equation of a line from two points, parallel lines, and perpendicular lines with visual plots and comparison tables.
Multiply, divide, raise to powers, and extract roots of complex numbers in polar form using De Moivre's theorem with an interactive polar plot.
Analyze queueing systems with M/M/1, M/M/c, and M/M/1/K models. Calculate utilization, average queue length, wait time, system time, probability of empty system, and more. Includes preset...
Check if two or more numbers are relatively prime (coprime), see Euclidean algorithm steps, prime factorizations, totient values, and coprimality grids.
Convert between spherical (ρ, θ, φ), Cartesian (x, y, z), and cylindrical (r, θ, z) coordinates with step-by-step solutions, convention toggle, and projection diagrams.
Compute the tensor (Kronecker) product of two matrices with step-by-step block decomposition, heatmap visualization, dimension analysis, and property verification table.
Generate truth tables for logical expressions with up to 4 variables — AND, OR, NOT, XOR, NAND, NOR, IMPLIES, and XNOR — with tautology/contradiction detection and a visual result grid.
Explore the Ugly Duckling Theorem with binary feature vectors. Compare objects using Hamming distance, shared features, Jaccard similarity, and matching coefficients. Includes preset examples, feat...
Compute logical XOR and bitwise XOR for up to 4 inputs — see truth tables, parity checks, bit-by-bit visualization, binary/hex output, and swap tricks.
Exponent rules, logarithm properties, and power calculators.
Calculate the fifth root of any number. Compare with other roots, view perfect fifth powers, verify results, and explore fractional exponents.
Calculate the fourth root of any number. View perfect fourth powers, compare with square root, explore all complex roots, and verify results step by step.
Calculate any nth root of any number. Supports square, cube, and higher roots. Shows radical simplification, fractional exponents, verification, and comparison tables.
Arithmetic, geometric, and Fibonacci sequence calculators.
Calculate the nth triangular number, check if a number is triangular, explore the sequence with dot patterns, and learn properties and identities.
Percentage calculation, change, error, and comparison calculators.
Calculators coming soon.
Determinant, cross product, dot product, and eigenvalue calculators.
Compute the classical adjoint (adjugate) matrix with cofactors, minors, sign pattern visualization, inverse connection, and verification that A·adj(A) = det(A)·I.
Find the angle between two vectors in 2D–6D using the dot product formula. Get degrees, radians, cos/sin/tan θ, perpendicularity and parallelism checks, computation steps, and a visual angle gauge.
Factor a symmetric positive definite matrix A = LLᵀ with step-by-step Cholesky algorithm, positive definiteness check, solve Ax=b, and verification display.
Solve 2×2, 3×3, and 4×4 systems of linear equations using Cramer's Rule with determinant calculations, step-by-step Dx/Dy/Dz display, solution verification, and determinant comparison visualization.
Compute the cross product of two 3D vectors, find the parallelogram area, unit normal direction, angle between vectors, and scalar triple product with step-by-step breakdowns.
Compute the dot product of two vectors in 2D–6D, find the angle between them, check orthogonality and parallelism, and visualize component contributions with an interactive calculator.
Compute eigenvalues and eigenvectors for 2×2 and 3×3 matrices with characteristic polynomial, diagonalization check, spectrum visualization, and detailed calculation steps.
Solve systems of linear equations Ax=b via augmented matrix Gauss-Jordan elimination with step-by-step row operations, back substitution display, and solution visualization.
Apply the Gram-Schmidt process to 2–4 vectors in R², R³, or R⁴. View step-by-step projections, orthonormal results, dot-product verification matrix, and norm comparison bars.
Calculate the Hadamard (element-wise) product of two matrices. Compare with standard multiplication, view properties, and explore visual breakdowns.
Factor a square matrix into lower and upper triangular matrices A=LU with step-by-step Doolittle method, solve Ax=b via forward/back substitution, and verification display.
Add or subtract matrices up to 5×5 with element-wise breakdown, scalar combination mode, Frobenius norms, comparison heat map, and detailed result tables.
Perform matrix operations including addition, subtraction, multiplication, transpose, determinant, inverse, and scalar multiplication for matrices up to 5×5.
Compute the determinant for 2×2 through 5×5 matrices with cofactor expansion steps, minor matrix display, term contribution bars, and comprehensive properties table.
Find the inverse of a matrix up to 5×5 using the cofactor/adjugate method, with step-by-step cofactor table, verification A×A⁻¹=I, condition number analysis, and singular detection.
Multiply matrices up to 5×5 with dimension compatibility check, partial products breakdown, Strassen complexity comparison, and result magnitude visualization.
Compute Frobenius, spectral, 1-norm, infinity-norm, and max-norm of a matrix with comparison bars, relationship verification, and breakdown tables.
Compute the rank of a matrix up to 5×5 via row echelon form with nullity, rank-nullity theorem verification, pivot visualization, and step-by-step row reduction.
Multiply a matrix by a scalar with element-wise display, property verification, chain operations, determinant/trace scaling, and before/after visualization.
Compute the trace of a square matrix with property verification, eigenvalue connection, diagonal contribution bars, and two-matrix mode for cyclic property testing.
Transpose a matrix up to 5×5 with symmetry checks, skew-symmetric detection, double transpose verification, before/after display, and properties table.
Find the null space of a matrix via RREF with basis vectors, dimension, solution verification, step-by-step reduction, and component visualization.
Determine the order of magnitude of any number, convert to scientific notation, compare magnitudes, see the SI prefix region, and explore a logarithmic scale with real-world examples.
Decompose a matrix A = UP into a unitary factor U and positive semi-definite factor P. View singular values, condition number, and geometric interpretation.
Compute the Moore-Penrose pseudoinverse of rectangular or singular matrices via SVD. Verify all four Moore-Penrose conditions with step-by-step details.
Compute QR decomposition via Gram-Schmidt. View orthogonal Q and upper triangular R with step-by-step process, verification, and application reference.
Transform any matrix to Row Echelon Form and Reduced Row Echelon Form with step-by-step row operations, pivot identification, rank determination, and visual pivot highlighting.
Compute the Singular Value Decomposition A = UΣVᵀ. View singular values, rank, condition number, matrix norms, energy distribution, and low-rank approximation.
Compute the unit vector (normalization) of any vector from 2D to 6D. Verify ‖û‖ = 1, see direction angles, component contributions, scaling, and compare original vs unit vector visually.
Add or subtract 2–5 vectors in 2D or 3D. View resultant magnitude, direction, component-wise breakdown table, magnitude comparison bars, and component contribution visuals.
Compute vector magnitude, unit vector, scalar multiplication, direction angles, and negation for 2D and 3D vectors with component visualization bars and properties table.
Compute direction angles α, β, γ from a 2D or 3D vector, direction cosines, azimuth/elevation, compass visualization, angle bars, and direction cosine identity verification.
Compute vector magnitude for 2D to 6D vectors using L1 (Manhattan), L2 (Euclidean), L∞ (Chebyshev), and custom Lp norms with unit vector, component contribution bars, and norm comparison.
Project vector a onto vector b: scalar projection, vector projection, rejection, angle between vectors, decomposition table, visual breakdown, and orthogonality verification.
Mathematical concepts, functions, and applied math calculators.
Perform complex number arithmetic — add, subtract, multiply, divide, raise to powers via De Moivre, find modulus, argument, polar form, and conjugate.
Explore Galileo's paradox interactively — compare counting numbers with perfect squares, visualize bijections, and understand infinite set cardinality.
Simulate Hilbert's Hotel thought experiment — accommodate new guests in a fully-occupied infinite hotel and explore cardinal arithmetic interactively.
Validate credit card numbers, IMEI codes, and other IDs using the Luhn checksum algorithm. Generate check digits with step-by-step visualization.
Convert between decimal and Mayan vigesimal (base-20) numeral system. See dots-and-bars glyphs, Long Count notation, and place-value breakdowns.
Calculate the probability of "miraculous" events — birthday paradox, lottery odds, coincidence probability, and Littlewood's Law of Miracles.
Convert between decimal and one's complement binary representation. View bit flipping, sign detection, range tables, and comparison with two's complement.
Explore pi — view digits, approximate with Leibniz/Machin/Monte Carlo methods, calculate circle area, circumference, and annulus area interactively.
Convert between infix, prefix (Polish), and postfix (Reverse Polish) notation. Evaluate RPN expressions with step-by-step stack traces.
Explore the Potato Paradox — see how 100 kg of 99% water potatoes become 50 kg at 98% water. Generalize with any weight and water percentage.
Explore the Prisoner's Dilemma — payoff matrices, Nash equilibrium, iterated games with Tit-for-Tat, Grim Trigger, Pavlov, and more strategies.
Explore RSA encryption with small primes — generate keys, encrypt and decrypt messages, see modular exponentiation step by step.
Plot data points, compute Pearson correlation, linear regression, R², residuals, standard error, and outlier detection interactively.
Convert between set-builder and roster notation, perform union/intersection/difference, test membership, and explore set theory interactively.
Count significant figures in any number, round to N sig figs, and perform arithmetic with proper significant figure rules. Digit-by-digit analysis.
Generate all subsets (power set) of a set, count by size with C(n,k), view binary encodings, and solve subset-sum problems interactively.
Convert between decimal and two's complement binary for 8, 16, 32, 64-bit widths. View hex, octal, range, overflow detection, and arithmetic operations.
Complex numbers, vectors, and applied mathematics calculators.
Calculate catenary curve properties including sag, arc length, tension, slope, and curvature using the equation y = a·cosh(x/a).
Calculate the center of mass for 2D or 3D point mass systems with weighted averages, moment of inertia, and position diagrams.
Calculate the centroid of a triangle or polygon from vertex coordinates, with area, perimeter, interior angles, and polygon diagram.
Perform complex number operations: add, subtract, multiply, divide, conjugate, and power with rectangular and polar forms, Argand diagram.
Find all nth roots of a complex number, roots of unity, plot on unit circle, with rectangular and polar forms.
Compute discrete convolution of two sequences with step-by-step computation, signal visualization, and output analysis.
Divide complex numbers step by step using the conjugate method, with polar division, verification, and Argand diagram.
Explore imaginary numbers: powers of i, operations with imaginary numbers, square roots of negatives, cycle visualization.
Multiply complex numbers with FOIL method steps, polar multiplication, Argand diagram, and detailed breakdown.
Quaternion operations: add, multiply, conjugate, inverse, normalize, axis-angle conversion, rotation matrix, and 3D rotation representation.
Derivatives, integrals, limits, and gradient calculators.
Compute the gradient vector, directional derivative, gradient magnitude, and visualize the gradient field for multivariable functions f(x,y).
Polar coordinates, parabolas, and coordinate system calculators.
Convert Cartesian (x, y) coordinates to polar (r, θ) and back, with batch mode, coordinate plot, and conversion reference table.
Analyze parabolas in vertex or standard form — find vertex, focus, directrix, axis of symmetry, latus rectum, and x/y-intercepts with interactive graph.
Find a parallel line through a point, compute distance between parallel lines, and compare slopes, intercepts, and angles with visualization.
Convert polar (r, θ) coordinates to Cartesian (x, y) and back, with batch mode, coordinate plot, and complete conversion reference.
Calculate slope from two points or slope-intercept form, find angle of inclination, parallel and perpendicular slopes, and graph the line.
Miscellaneous math tools and specialty calculators.
Calculate arc length, sector area, chord length, and arc-to-chord ratio from radius and central angle. Includes preset common angles, a properties table, and an arc diagram.
Demonstrate and verify the associative property for addition and multiplication. See counterexamples for subtraction and division with custom numbers, presets, and grouping visuals.
Calculate the average rate of change (f(b)−f(a))/(b−a) for common functions. Includes secant line slope, comparison with instantaneous rate, interval table, and visual diagram.
Multiply polynomials using the box/area model method. Displays a visual grid, collects like terms, shows the expanded and simplified result with presets and step-by-step breakdown.
Calculate the central angle from arc length and radius. Find inscribed angle relationships, sector area, and segment properties with presets, properties table, and circle visual.
Apply the logarithm change of base formula to convert between any bases. Compare natural, common, and binary logarithms with a conversion table and visual comparison.
Calculate the angle between the hour and minute hands of an analog clock. Shows reflex angle, hand positions, and a clock face visual with a full-day angles table.
Explore the coin rotation paradox: how many times does a coin rotate when rolling around another? Handles inner/outer rolling, different radii, path length, and demonstrates the paradox with visuals.
Find the column space of a matrix including basis vectors, rank, nullity, and RREF steps. Supports matrices up to 6×6 with presets and step-by-step row reduction.
Find the LCM, GCD, and first N common multiples of two or more numbers. Includes prime factorization table, multiples overlap visualization, and preset number sets.
Find compatible number pairs for mental math estimation. Compare rounding strategies, see error percentages, and discover the most accurate estimation approach for any arithmetic operation.
Compute the matrix condition number κ(A) in 1-norm, ∞-norm, and Frobenius norm. Checks if a matrix is well or ill-conditioned with sensitivity visualization.
Find the complex conjugate or radical conjugate of a number. Computes modulus, argument, product z·z̄, rationalization, and displays an Argand diagram.
Calculate cycloid curve properties: arc length, area under arch, cusps, parametric points, surface of revolution. Includes interactive curve plot and properties table.
Calculate all properties of a regular decagon: perimeter, area, apothem, circumradius, interior angles, diagonals. Input by side, radius, apothem, area, or perimeter.
Convert between diameter, radius, circumference, and area of a circle. Batch mode for multiple values, circle diagram, and complete conversion table.
Solve diamond factoring puzzles: find two numbers given their product and sum, or reverse. Visual diamond shape, presets for common problems, solutions table, and step-by-step factoring breakdown.
Compute the digital root (repeated digit sum) of any number. Shows iteration steps, divisibility-by-9 connection, multiplicative digital root, additive persistence, and digit frequency analysis.
Demonstrate and verify the distributive property a(b+c) = ab + ac with numbers. Expand expressions, see step-by-step verification, area model visual, and comparison table for multiple examples.
Calculate regular dodecagon (12-sided polygon) properties: perimeter, area, diagonals, interior/exterior angles, apothem, inradius, circumradius. Presets, properties table, and polygon visual.
Calculate doubling time from a growth rate using the Rule of 72, exact formula, and continuous compounding. Also tripling time, comparison table across rates, and exponential growth curve visual.
Solve 2×2 and 3×3 systems of linear equations by elimination. Step-by-step multiply-and-add operations, presets for common systems, elimination steps table, and solution coordinate visual.
Find a missing endpoint given a midpoint and the other endpoint in 2D or 3D. Distance verification, calculation steps, presets for common problems, coordinate visualization, and formulas.
Convert numbers to engineering notation (exponents that are multiples of 3), SI prefix lookup, comparison with scientific notation, magnitude scale visual, presets for common values.
Arithmetic sequences, geometric series, harmonic numbers, and sum calculators.
Calculate the nth term, sum of n terms, common difference, and generate arithmetic sequences with visual growth charts and partial sums.
Calculate nth term, finite and infinite sums, common ratio, and visualize exponential growth or decay in geometric sequences.
Calculate the harmonic mean of any set of numbers, compare with arithmetic and geometric means, and verify the AM-GM-HM inequality.
Compute the nth harmonic number H(n), partial sums, approximations using the Euler-Mascheroni constant, and generalized harmonic numbers.
Calculate the digital sum, digital root, iteration steps, and divisibility properties of any number in multiple bases.
Compute partial sums of arithmetic, geometric, telescoping, p-series, and power sum series with convergence analysis and visualization.
Permutations, combinations, and counting principle calculators.
Apply the multiplication principle for multi-stage counting problems, connect to permutations, and visualize the tree diagram structure.
Calculate P(n,r) and C(n,r), with and without repetition, compare all four variants, visualize Pascal's triangle, and explore the computation table.
