Free math calculators with steps

Add, subtract, multiply, divide, and simplify fractions or mixed numbers with the working shown.

Find greatest common factors and least common multiples using clear factorization or Euclidean steps.

Turn a written math question into variables or equations, solve it, and explain the result in context.

Work out percentages, percentage change, increases, decreases, and reverse-percentage questions.

Rewrite quadratics in completed-square or vertex form and use that form to solve or analyze them.

Calculate the distance between coordinate points with exact radical and decimal forms when useful.

Simplify powers and solve exponential equations using exponent rules with each transformation explained.

Factor polynomial expressions and explain the pattern or method that produces the factorization.

Solve linear, polynomial, or rational inequalities while tracking sign changes and interval notation.

Solve ax² + bx + c = 0.

Combine like terms, reduce algebraic fractions, and rewrite expressions in an equivalent simpler form.

Find slope from two points or from a line equation and explain rise-over-run and sign meaning.

Solve equations for x or another variable and show the balancing operations used at each step.

Solve simultaneous equations with substitution, elimination, or row operations and verify the solution.

Determine valid inputs and possible outputs for functions, with interval or set notation where appropriate.

Compute compositions such as f(g(x)) and g(f(x)), simplify them, and discuss domain restrictions.

Find inverse functions, identify needed restrictions, and verify the result using composition.

Evaluate, expand, condense, or solve logarithmic expressions and equations with domain restrictions shown.

Perform polynomial operations, division, factoring, root finding, and remainder calculations with steps.

Simplify and combine algebraic fractions while preserving excluded values from the original expression.

Use side-angle-side or side-side-side information to find missing triangle sides or angles.

Simplify trigonometric expressions or verify identities and name the identities used at each step.

Find coterminal and reference angles, quadrants, coordinates, and exact trigonometric values.

Evaluate definite integrals from bounds and distinguish signed accumulation from geometric area when relevant.

Differentiate functions step by step and identify the power, product, quotient, or chain rules used.

Differentiate equations where y is not isolated, collect dy/dx terms, and solve for the derivative.

Find indefinite integrals, explain the integration method, and include the constant of integration.

Evaluate finite, one-sided, and infinite limits and explain when factoring, rationalizing, or other methods are needed.

Differentiate multivariable functions with respect to a chosen variable while holding the others constant.

Choose and apply an appropriate convergence test for infinite series and explain the test conditions.

Build Taylor or Maclaurin polynomials for a function at a chosen center and degree.

Find the oriented vector perpendicular to two 3D vectors and explain direction and magnitude.

Compute determinants of square matrices and explain cofactor expansion or row-operation effects.

Compute vector dot products and use the result for angles, orthogonality, or projections.

Find characteristic polynomials, eigenvalues, and eigenvectors or eigenspaces for square matrices.

Find the inverse of a nonsingular matrix using exact row operations and verify it against the identity matrix.

Perform matrix addition, multiplication, powers, row operations, and related matrix calculations with dimension checks.

Calculate common measures of center and explain how ordering, repeated values, and outliers affect them.

Count ordered arrangements or unordered selections and explain whether order matters before using factorial formulas.

Translate probability questions into the appropriate rule and calculate event probabilities without double counting.

Compute mean, variance, and sample or population standard deviation while showing the denominator choice.

Standardize a value relative to a mean and standard deviation and interpret the sign and magnitude of the z-score.

Analyze one or more functions and explain intercepts, domain, range, extrema, asymptotes, and overall graph behavior.

Calculate the five-number summary of a dataset, including the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This calculator helps students quickly analyze data distribution and understand quartiles, range, and interquartile range (IQR).

Solve tricky math riddles, number puzzles, logic questions, and mathematical brain teasers with step-by-step explanations. Enter any math riddle and get a clear answer with the reasoning behind the solution.