Algebra Calculators
Equations, powers and roots without the guesswork. Solve quadratics and cubics, simplify radicals, evaluate huge exponents and rearrange logarithms — with each step written out.
36 calculators
Most used
- Exponent CalculatorCalculate b to the power n for whole, negative, decimal or fractional exponents, with exact answers and the rules behind them.
- Logarithm CalculatorFind the logarithm of any positive number in any base, with natural, common and binary logs side by side and the change-of-base steps.
- Quadratic Formula CalculatorSolve any quadratic equation ax² + bx + c = 0 and get exact roots, the discriminant, the vertex and a graph of the parabola.
- Square Root CalculatorFind the square root of any number in simplest radical form and as a decimal, with the prime factorization steps shown.
Equations & polynomials 9
- Completing the Square CalculatorRewrite a quadratic as a(x − h)² + k by completing the square, then solve it, with every algebra step written out.
- Cubic Equation CalculatorFind all three roots of a cubic equation, exact when a rational root exists, with the discriminant, the method used and a graph.
- Difference of Two Squares CalculatorFactor an expression of the form a² − b² into (a − b)(a + b), pulling out common factors and repeating the pattern until nothing more factors.
- FOIL Method CalculatorExpand the product of two binomials (ax + b)(cx + d) with the FOIL method and see each of the four products and the combined result.
- Linear Inequality CalculatorSolve linear and compound inequalities step by step and see the answer in inequality, interval and set-builder notation on a number line.
- Polynomial Long Division CalculatorDivide any polynomial by another and see every long-division step, the quotient and remainder, and a check that multiplies the answer back out.
- Quadratic Formula CalculatorSolve any quadratic equation ax² + bx + c = 0 and get exact roots, the discriminant, the vertex and a graph of the parabola.
- Synthetic Division CalculatorDivide a polynomial by a linear factor such as x − 2 or 2x + 1 using synthetic division, with the full table, quotient and remainder.
- System of Linear Equations CalculatorSolve two or three linear equations at once, with exact fractions, elimination or Cramer's rule steps and a graph of the lines.
Exponents & logarithms 9
- Cube Number CalculatorFind the cube of any number, x³, exactly, with the repeated multiplication and a place-value shortcut shown.
- Exponent CalculatorCalculate b to the power n for whole, negative, decimal or fractional exponents, with exact answers and the rules behind them.
- Large Exponents CalculatorRaise a whole number to a large whole-number power and get the exact result with every digit, plus its length and scientific notation.
- List of Perfect CubesBuild a table of perfect cubes for any range of n, including negative numbers, or list every perfect cube below a chosen value.
- List of Perfect SquaresGenerate a table of perfect squares for any range, or list every perfect square below a chosen number, with the gaps between them.
- Logarithm CalculatorFind the logarithm of any positive number in any base, with natural, common and binary logs side by side and the change-of-base steps.
- Logarithm Equation CalculatorSolve the logarithmic equation log_b(x) = y for whichever of the base, the number or the log value is unknown, with every step.
- Solve for Exponent CalculatorFind the exponent x that makes b^x equal a given number, using logarithms, with an exact answer whenever one exists.
- Square Number CalculatorFind the square of any number, x², exactly, with the multiplication shown and a shortcut for squaring numbers in your head.
Roots & radicals 6
- Cube Root CalculatorFind the cube root of any real number, negative ones included, as a simplified radical and as a decimal.
- Fifth Root CalculatorFind the fifth root of a positive or negative number, exactly when possible and as a decimal, with the factor grouping explained.
- Fourth Root CalculatorFind the fourth root of a number, the value that gives x when raised to the fourth power, exactly or as a decimal.
- Nth Root CalculatorCalculate the root of any index n, from square and cube roots to the 1,000th root, exactly or as a decimal.
- Simplify Radicals CalculatorRewrite a radical in simplest form, with a coefficient, any index and fractions, showing exactly which factors come out of the radical.
- Square Root CalculatorFind the square root of any number in simplest radical form and as a decimal, with the prime factorization steps shown.
Vectors & absolute value 4
- Absolute Difference CalculatorFind how far apart two numbers are, |a − b|, or compare two lists pair by pair and get the mean absolute difference.
- Absolute Value CalculatorFind the absolute value of a number, solve absolute value equations and inequalities, or find the modulus of a complex number.
- Cross Product CalculatorCompute the cross product of two 3D vectors, with the determinant steps, the area it represents and a unit normal vector.
- Dot Product CalculatorFind the dot product of two vectors of any dimension, plus their lengths, the angle between them and the projection of one onto the other.
Matrices 3
- Matrix CalculatorAdd, subtract or multiply two matrices, multiply by a scalar, transpose, or raise a square matrix to a power, with exact fractions.
- Matrix Determinant CalculatorFind the exact determinant of any square matrix up to 6 × 6, with cofactor-expansion or row-reduction steps and an invertibility check.
- Matrix Inverse CalculatorFind the inverse of a square matrix up to 6 × 6 in exact fractions, with Gauss–Jordan or adjugate steps and a built-in check.
Functions & calculus 5
- Definite Integral CalculatorIntegrate a function of x between two limits numerically with Simpson's rule, with an error estimate, rule comparison and shaded graph.
- Function Table CalculatorGenerate a table of values for any function of x, with first and second differences, pattern detection, sign changes and a graph.
- Linear Interpolation CalculatorEstimate an in-between value from two points or a data table with linear interpolation, or work backward to find x from a known y.
- Polynomial Derivative CalculatorDifferentiate a polynomial term by term with the power rule, then get its value, slope and tangent line at any x, plus critical points.
- Riemann Sum CalculatorApproximate the area under f(x) with left, right, midpoint or trapezoidal Riemann sums, drawn as rectangles and compared with the integral.
Guides
- Exponent Rules: The Laws of Exponents With ExamplesThe seven laws of exponents, why each one works, and how to combine them to simplify expressions with negative and fractional powers.
- How to Factor Trinomials: x² + bx + c and ax² + bx + cFind two numbers that multiply to one value and add to another. The product-sum and AC methods, sign patterns, and how to tell when a trinomial will not factor.
- How to Simplify Square Roots and Other RadicalsPull the largest perfect-square factor out from under the root sign. Step-by-step examples for square roots, cube roots, variables and denominators.
- How to Solve Quadratic Equations: Factoring, Completing the Square and the FormulaThree methods solve every quadratic equation. Learn when each one is fastest, how the discriminant predicts the answers, and how to check your roots.
- How to Solve a System of Equations: Substitution, Elimination and Cramer's RuleFour ways to solve two or three linear equations at once, how to choose between them, and how to spot systems with no solution or infinitely many.
- Logarithm Rules: Product, Quotient, Power and Change of BaseEvery logarithm rule in one place, why each works, and how to use them to expand and condense logs and solve exponential and log equations.