Equation solving, polynomial, matrix, and linear system calculators. Browse our free algebra tools below — all calculators are instant, accurate, and require no sign-up.
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.
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.
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.
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.
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 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.
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.
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.
Cofunction Calculator — Find cofunction identities for all six trigonometric functions. Calculate sin↔cos, tan↔cot, sec↔csc pairs and verify complementary angle relationships.
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.
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.
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.
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.
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 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.
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.
Equivalent Ratio Calculator — Find equivalent ratios, simplify to lowest terms, scale ratios, solve proportions, and generate comprehensive equivalent ratio tables with visual proportion 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.
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.
Exponential Notation Calculator — Convert numbers between standard form, scientific notation, and engineering notation. Find SI prefixes, significant figures, and order of magnitude.
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.
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.
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.
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.
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...
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.
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 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-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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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 instantly.