Add & Subtract Polynomials Calculator
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.
Free Algebra Calculators
93 toolsEquation solving, polynomial, matrix, and linear system calculators. Browse our free algebra tools below — no sign-up required.
Antilog Calculator
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.
Bessel Function Calculator
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.
Bilinear Interpolation Calculator
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.
Binary Logarithm Calculator (log₂)
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...
Binomial Coefficient Calculator
Calculate binomial coefficients C(n,k), Pascal's triangle rows, permutations P(n,k), and multinomial coefficients with step-by-step factorial breakdowns.
Characteristic Polynomial Calculator
Find the characteristic polynomial, eigenvalues, trace, and determinant of a 2×2 or 3×3 matrix with step-by-step computation and eigenvalue visualization.
Cofactor Expansion (Determinant) Calculator
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.
Cofactor Matrix & Adjugate Calculator
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.
Cofunction Calculator
Find cofunction identities for all six trigonometric functions. Calculate sin↔cos, tan↔cot, sec↔csc pairs and verify complementary angle relationships.
Condense Logarithms Calculator
Condense and combine logarithmic expressions into a single log using product, quotient, and power rules. Step-by-step solutions with rule-by-rule explanation.
Cubic Equation Solver
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.
Descartes' Rule of Signs Calculator
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.
Direct Variation Calculator
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.
Discriminant Calculator
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.
Dividing Exponents Calculator
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.
Dividing Radicals Calculator
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.
e^x Calculator (Exponential Function)
Calculate eˣ, explore the Taylor series approximation with adjustable terms, verify ln(eˣ) = x, see growth rate, doubling time, and series convergence visualization.
Equivalent Ratio Calculator
Find equivalent ratios, simplify to lowest terms, scale ratios, solve proportions, and generate comprehensive equivalent ratio tables with visual proportion bars.
Error Function Calculator (erf)
Calculate the error function erf(x), complementary error function erfc(x), inverse erf, and Taylor series convergence with reference tables and visual convergence bars.
Exact Value of Trig Functions Calculator
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.
Expanding Logarithms Calculator
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.
Exponential Form Calculator
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.
Exponential Function Calculator
Evaluate f(x) = a·bˣ + c, find growth/decay rate, doubling/halving time, asymptotes, and generate a table of values with visual bars.
Exponential Growth Calculator
Model exponential growth and decay with discrete A₀·(1+r)ᵗ or continuous A₀·eʳᵗ formulas. Find doubling time, growth factor, and timeline.
Exponential Notation Calculator
Convert numbers between standard form, scientific notation, and engineering notation. Find SI prefixes, significant figures, and order of magnitude.
Factoring Trinomials Calculator
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.
FOIL Method Calculator
Multiply two binomials step-by-step using the FOIL method. See First, Outer, Inner, Last products, simplified polynomial, area model, and term magnitude bars.
Fractional Exponent Calculator
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.
Gamma Function Calculator
Calculate Γ(x), log Γ(x), digamma ψ(x), and reciprocal gamma for any real number. Explore special values, reference tables, and magnitude visualizations.
GCF & LCM Calculator
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.
Golden Ratio Calculator
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.
Graphing Inequalities Calculator (1D Number Line)
Solve and graph one-variable linear inequalities on a number line. Supports <, >, ≤, ≥, compound AND/OR inequalities with step-by-step solutions.
Graphing Quadratic Inequalities Calculator
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.
Greatest Common Factor (GCF) Calculator
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.
Hyperbolic Functions Calculator
Calculate sinh, cosh, tanh, coth, sech, csch and their inverses for any real number. Includes value comparison bars, reference table, and identity verification.
Inequality to Interval Notation Calculator
Convert inequalities to interval notation, set-builder notation, and back. Visualize intervals on a number line with open/closed endpoints and test membership.
Interval Notation Converter
Convert between interval notation, inequality notation, set-builder notation, and number line graph. Supports open, closed, half-open, and unbounded intervals.
Inverse Variation Calculator
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.
Involute Function Calculator
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.
Lagrange Error Bound Calculator
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.
Least Common Multiple (LCM) Calculator
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.
Line Equation from Two Points Calculator
Find the equation of a line through two points. Get slope-intercept, point-slope, and standard forms plus slope, intercepts, distance, midpoint, and angle.
Linear Combination Calculator
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.
Linear Feedback Shift Register (LFSR) Calculator
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.
Linear Independence Calculator
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.
Linear Interpolation Calculator
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...
Logarithm Calculator (log base b)
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.
Math Power Calculator — Exponentiation (xⁿ)
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.
Matrix Power Calculator — Compute Aⁿ for 2×2 & 3×3 Matrices
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.
Modulo & Order of Operations Calculator — PEMDAS with Mod
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...
Multiplying Binomials Calculator — FOIL, Special Products & Area Model
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.
Multiplying Exponents Calculator — Product, Power & Quotient Rules
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.
Multiplying Polynomials Calculator
Multiply two polynomials up to degree 4 with step-by-step distribution, product expansion, and coefficient analysis. See the full FOIL and distribution grid.
Multiplying Radicals Calculator
Multiply radical expressions with same or different indices. Simplify √a·√b, ⁿ√a·ⁿ√b, and mixed-index radicals with step-by-step simplification.
Natural Log (ln) Calculator
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.
Negative Log Calculator (−log x)
Calculate −log₁₀(x) and −ln(x) for pH, pKa, pOH, and general use. Includes pH scale interpretation, concentration ↔ pH conversion, and reference tables.
Partial Fraction Decomposition Calculator
Decompose rational expressions into partial fractions. Handles distinct/repeated linear and irreducible quadratic factors with step-by-step solutions.
Polynomial Division Calculator
Divide polynomials using long division or synthetic division. See quotient, remainder, step-by-step work, and factor verification.
Polynomial Graphing Calculator
Analyze polynomials up to degree 5 for graphing — find roots, y-intercept, end behavior, critical points, inflection points, and generate a table of values.
Power Function Calculator — f(x) = axⁿ
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.
Power Modulo Calculator — aⁿ mod m
Compute aⁿ mod m using modular exponentiation. See the result, step-by-step binary exponentiation, repeated squaring table, and binary decomposition of the exponent.
Power of 10 Calculator — 10ⁿ
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.
Power of 2 Calculator — 2ⁿ
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.
Power of a Power Calculator
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.
Power Set Generator
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.
Power-Reducing Formulas Calculator
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.
Powers of i Calculator
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.
Proportion Calculator
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.
Quadratic Formula Calculator — Solve ax² + bx + c = 0
Solve any quadratic equation with the quadratic formula. Find both roots, discriminant, vertex, axis of symmetry, and factored form with step-by-step solutions.
Radical Simplification Calculator — Simplify ⁿ√x
Simplify radicals, add/subtract like radicals, and multiply radical expressions. Shows simplified form, prime factorization, decimal value, and step-by-step work.
Ratio of Three Numbers Calculator — Simplify a:b:c
Simplify the ratio of three numbers. Find percentages, distribute a total, scale the ratio, and view a distribution table with visual proportion bars.
Ratio of Two Numbers Calculator — Simplify a:b
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.
Rational Exponents Calculator — Evaluate x^(p/q)
Calculate rational exponents x^(p/q). Convert between exponential and radical form, simplify exponents, and review exponent rules with step-by-step solutions.
Rational Zeros Calculator
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 the Denominator Calculator
Rationalize denominators containing square roots, cube roots, or binomial radicals. See step-by-step conjugate multiplication, before/after comparison, and simplified results.
Ratios of Directed Line Segments Calculator
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.
Reverse FOIL Calculator
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.
Rise Over Run Calculator — Slope from Two Points
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 Radicals Calculator
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 Ratio Calculator
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.
Sine Function Calculator
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.
Slope-Intercept Form Calculator
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.
Standard Form to Slope-Intercept Form Calculator
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.
Substitution Method Calculator — Systems of Equations
Solve systems of two linear equations using the substitution method. Step-by-step solution, intersection graph, verification, and comparison with elimination method.
Sum of Linear Number Sequence Calculator
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.
Synthetic Division Calculator
Divide polynomials using synthetic division. Enter coefficients and divisor to get quotient, remainder, step-by-step layout, factor theorem test, and rational root candidates.
Systems of Equations Calculator
Solve 2×2 and 3×3 linear systems using Cramer's Rule, elimination, substitution, or matrix methods. Shows solution, determinants, verification, and method comparison.
Tangent Ratio Calculator
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.
Trig Function Calculator
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.
Trigonometric Functions Calculator
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...
Vertex Form Calculator
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.
Y-Intercept Calculator
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.