Free Algebra Calculators

Quadratic Equation Solver

Solve quadratic equations (ax² + bx + c = 0) and find both real and complex roots.

Cubic Equation Solver | ax³+bx²+cx+d=0

Solve cubic equations (ax³ + bx² + cx + d = 0) and find all three roots with step-by-step working, graph, and factored form.

Polynomial Evaluator | Compute f(x)

Evaluate any polynomial at a given value of x using Horner method.

Logarithm Calculator | Log & Ln

Calculate logarithms with any base. Supports natural log (ln), log base 10, and custom bases.

Absolute Value Equation Solver

Solve |ax + b| = c and |ax + b| = |cx + d| with step-by-step case analysis, verification, and formatted solutions.

Linear Equation Solver | Solve ax+b=c

Solve linear equations in one variable (ax + b = c) with step-by-step solutions.

Systems of Equations Solver 2×2

Solve systems of two linear equations with two unknowns using Cramer's rule.

Inequality Solver | Linear & Quadratic

Solve linear and quadratic inequalities with step-by-step solutions.

Summation Calculator | Sigma Notation

Evaluate summation expressions with custom formulas, bounds, and step values.

Complex Number Calculator | a+bi

Add, subtract, multiply, divide, and apply powers and logs to complex numbers. Shows Argand diagram, polar form, modulus, and step-by-step working.

Completing the Square Calculator

Convert ax² + bx + c to vertex form a(x−h)² + k step by step. Find the vertex, axis of symmetry, and roots of any quadratic.

Synthetic Division Calculator

Divide polynomials using synthetic division and find quotient and remainder.

Rational Root Theorem Calculator

Find all possible rational roots of a polynomial using the Rational Root Theorem.

Exponent Rules Calculator | All 8 Laws

Apply all 8 laws of exponents, product, quotient, power of a power, zero, negative, fractional, and multiple-base rules, with step-by-step working and numerical verification for any base and exponents.

Logarithm Laws Calculator

Apply logarithm laws: product, quotient, power, change of base, and natural log rules.

Arithmetic Sequence Calculator

Find the nth term, partial sum, and common difference of any arithmetic sequence. Solve for any unknown and generate up to 1,000 terms.

Geometric Sequence Calculator | nth Term & Sum

Find the nth term, partial sum, and infinite sum of any geometric sequence. Solve for the common ratio or number of terms. Determine convergence with first 12 terms shown.

Simplify Radicals Calculator

Simplify radical expressions by extracting perfect square (or nth-power) factors. Converts √72 → 6√2, ∛54 → 3∛2, and handles variables.

Exponential Growth & Decay Calculator | y = aeʳᵗ

Calculate exponential growth or decay using y = ae^(rt). Solve for any unknown: initial value, growth/decay rate, time, or final value. Covers population growth, bacterial cultures, radioactive decay, investment compounding, and any continuous growth model. Doubling and half-life shown automatically.

Polynomial Long Division Calculator | Step-by-Step Quotient & Remainder

Divide any polynomial P(x) by any divisor Q(x) using full long-division notation. Shows every multiply-subtract step exactly as you would write it by hand, outputs the quotient and remainder, reconstructs the original polynomial for verification, and checks if Q(x) is an exact factor.