Algebra Calculators
Last updated: September 2026
System of Linear Equations Solver
Solve a system of two linear equations in two unknowns (x and y) using Cramer's Rule.
Quadratic Equation Solver
Finds real roots of any quadratic equation ax² + bx + c = 0 using the quadratic formula.
Vertex Form Calculator
Find the vertex of any quadratic function in standard form ax² + bx + c.
Quadratic Expression Factoring Calculator
Factors any quadratic expression ax² + bx + c into two linear factors.
2×2 Matrix Operations Calculator
Find the determinant and inverse of a 2×2 matrix in one step.
Linear Equation Solver
Solve any single-variable linear equation of the form ax + b = 0 for the unknown x.
Polynomial Evaluator
Evaluate a cubic polynomial ax³ + bx² + cx + d at any value of x.
Matrix Operations Calculator
Computes the determinant and inverse of a 2×2 matrix.
2x2 System of Equations Solver
Solve a 2×2 system of linear equations in the form a₁x + b₁y = c₁ and a₂x + b₂y = c₂ using Cramer's rule.
Polynomial Factoring Calculator
Factor a quadratic polynomial and instantly find its discriminant, roots, and factored form.
Quadratic Formula Solver
Solve any quadratic equation of the form ax² + bx + c = 0 instantly.
Geometric Sequence Calculator
Calculate the sum of a finite or infinite geometric series given a first term and common ratio.
Linear Inequality Solver
Solve linear inequalities of the form ax + b < c (or ≤, >, ≥) and express the answer as an interval or number line.
Matrix Determinant Calculator (2×2 and 3×3)
Calculates the determinant of a 2×2 or 3×3 matrix from its elements.
Arithmetic and Geometric Sequence Calculator
Find the nth term or partial sum of arithmetic and geometric sequences instantly.
Arithmetic & Geometric Series Calculator
Find the nth term and sum of arithmetic or geometric sequences instantly.
Arithmetic Sequence Calculator
Calculate the nth term, sum of n terms, or position of a term in an arithmetic sequence.
System of Linear Equations Solver (2×2)
Solves a 2×2 system of linear equations (a₁x + b₁y = c₁ and a₂x + b₂y = c₂) using Cramer's Rule.
Rational Function Analyzer
Analyze a rational function of the form (num_a·x + num_b) / (den_a·x + den_b) to find its vertical asymptote, horizontal asymptote, domain, and intercepts.
Polynomial Roots Calculator
Find every real root of a three-term polynomial a·xⁿ + b·xⁿ⁻¹ + c of degree 2, 3, or 4 (for example x² − 3x + 2, x³ − 2x² + 1 or x⁴ + x³ − 3).
Midpoint Calculator
Finds the exact midpoint coordinates between two points on a plane by averaging their x- and y-values.
Rational Expression Calculator
Simplify, add, subtract, multiply, or divide two fractions and reduce the answer to lowest terms — the same arithmetic rational expressions follow.
Function Composition Calculator
Evaluate the composite function (f∘g)(x) = f(g(x)) for linear, quadratic, exponential, or logarithmic f and linear g at any x value.
Arithmetic & Geometric Sequence Calculator
Find the nth term of either an arithmetic or geometric sequence side by side.
Function Domain & Range Calculator
Determines the domain and range of rational, radical, and logarithmic functions from their coefficients.
Logarithm Calculator
Compute the logarithm of any positive number in any positive base using the change-of-base formula.
Exponential Growth Calculator
Project the future value of any quantity that grows by a fixed percentage each period using A = P(1 + r)ᵗ.
Polynomial Synthetic Division Calculator
Divides a polynomial by a linear factor (x − r) using synthetic division, returning the quotient coefficients and remainder.
Partial Fraction Decomposition Calculator
Decomposes a rational function with a factorable denominator into a sum of simpler partial fractions.
Exponential Growth and Decay Calculator
Computes a final amount after exponential growth or decay using A = Pe^(rt).
Radical Expression Simplifier
Simplifies radical expressions of the form c·ⁿ√radicand by extracting perfect nth-power factors.
Quadratic Formula Calculator
Solve a quadratic equation ax² + bx + c = 0 for its real root using the quadratic formula.
Slope Calculator
Calculate the slope of a line between two points using (y₂ − y₁) / (x₂ − x₁).
Distance Formula Calculator
Calculate the straight-line distance between two points on a coordinate plane using √((x₂−x₁)² + (y₂−y₁)²).