Triangle, circle, polygon, 3D shape, area, perimeter, and volume calculators. Browse our free geometry tools below — no sign-up required.
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...
