algebra Calculators
Last updated: May 2026
Quadratic Formula Calculator
Finds all real solutions to any quadratic equation of the form ax² + bx + c = 0.
Slope Calculator
Calculates the slope (steepness) of a straight line passing through any two coordinate points.
Linear Equation Solver
Solve any single-variable linear equation of the form ax + b = 0 for the unknown x.
Distance Formula Calculator
Finds the straight-line distance between two points (x₁, y₁) and (x₂, y₂) on a coordinate plane.
Midpoint Calculator
Finds the exact midpoint coordinates between two points on a plane by averaging their x- and y-values.
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.
Vertex Form Calculator
Find the vertex of any quadratic function in standard form ax² + bx + c.
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 Evaluator
Evaluate a cubic polynomial ax³ + bx² + cx + d at any value of x.
Logarithm Calculator
Compute the logarithm of any positive number in any positive base using the change-of-base formula.
Quadratic Equation Solver
Finds real roots of any quadratic equation ax² + bx + c = 0 using the quadratic formula.
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.
Polynomial Synthetic Division Calculator
Divides a polynomial by a linear factor (x − r) using synthetic division, returning the quotient coefficients and remainder.
Exponential Growth and Decay Calculator
Computes a final amount after exponential growth or decay using A = Pe^(rt).
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.
Rational Expression Calculator
Simplify, add, subtract, multiply, or divide rational expressions (fractions with polynomial numerators and denominators) in one step.
Linear Inequality Solver
Solve linear inequalities of the form ax + b < c (or ≤, >, ≥) and express the answer as an interval or number line.
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.
System of Linear Equations Solver
Solve a system of two linear equations in two unknowns (x and y) using Cramer's Rule.
Polynomial Factoring Calculator
Factor a quadratic polynomial and instantly find its discriminant, roots, and factored form.
Function Composition Calculator
Compute the composite function (f∘g)(x) for two linear functions and evaluate it at any point x.
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.
Arithmetic & Geometric Series Calculator
Find the nth term and sum of arithmetic or geometric sequences instantly.
2×2 Matrix Operations Calculator
Perform addition, multiplication, determinant, and inverse operations on 2×2 matrices.
Quadratic Formula Solver
Solve any quadratic equation of the form ax² + bx + c = 0 instantly.
Polynomial Roots Calculator
Find the primary real root of a polynomial of degree 2, 3, or 4 from its leading coefficient, second coefficient, and constant term.
Arithmetic Sequence Calculator
Calculate the nth term, sum of n terms, or position of a term in an arithmetic sequence.
Geometric Sequence Calculator
Calculate the sum of a finite or infinite geometric series given a first term and common ratio.
Arithmetic & Geometric Sequence Calculator
Find the nth term of either an arithmetic or geometric sequence side by side.
Quadratic Expression Factoring Calculator
Factors any quadratic expression ax² + bx + c into two linear factors.
Radical Expression Simplifier
Simplifies radical expressions of the form c·ⁿ√radicand by extracting perfect nth-power factors.
Matrix Operations Calculator
Computes determinant, inverse, and multiplication for 2×2 and 3×3 matrices.
Function Domain & Range Calculator
Determines the domain and range of rational, radical, and logarithmic functions from their coefficients.
Partial Fraction Decomposition Calculator
Decomposes a rational function with a factorable denominator into a sum of simpler partial fractions.