Calculus Calculators

Calculus studies change and accumulation. The derivative measures how fast a quantity changes; the integral adds up small pieces to find areas and totals. These calculators show which rule is applied at every step and verify each result.

Calculators

Derivative Calculator

See which differentiation rule applies at each stage, from the outermost operation inward.

Integral Calculator

Indefinite and definite integrals with the technique named at every step, and each antiderivative verified before it is shown.

Definite Integral Calculator

Enter a function and two limits of integration to get the exact value of the definite integral, with the antiderivative, the evaluation F(b) − F(a) and, for improper integrals, the limit that decides convergence.

Double Integral Calculator

Enter f(x, y), choose the order of integration and type the limits. Inner limits may be curves such as x² or √(1 − x²). Get the exact value where one exists, the inner integral written out, and a numerical cross-check.

Differential Equation Solver

Choose the equation type, enter its parts and, if you have them, the initial conditions. Get the general or particular solution with the separation, integrating factor or characteristic equation shown, and the answer substituted back as a check.

Limit Calculator

Enter a function and the value x approaches to find the limit, with the indeterminate form identified, the rule that resolves it and a numerical check that the answer is right.

Partial Derivative Calculator

Enter a function of several variables and the variable or sequence of variables to differentiate with respect to, and get the partial derivative with every rule shown, plus its value at a point if you want one.

Implicit Differentiation Calculator

Enter an equation in x and y to find dy/dx by implicit differentiation, with the chain rule applied to every y term, the algebra that isolates y′ and, optionally, the slope and tangent line at a point.

Taylor Series Calculator

Enter a function, a center and an order to build its Taylor polynomial, with every derivative evaluated at the center, exact coefficients and, if you give an x-value, the approximation compared with the true value.

Series Convergence Calculator

Enter the general term of an infinite series to find out whether it converges or diverges, which test decides it and why, with the exact sum whenever the series is geometric.

Topics covered

Differentiation: Power, product, quotient and chain rules, higher-order derivatives and evaluation at a point.
Integration: Antiderivatives, substitution, integration by parts, partial fractions and definite integrals.
Limits: Direct substitution, L'Hôpital's rule, one-sided limits and limits at infinity.
Multivariable and implicit: Partial derivatives, mixed partials and dy/dx from an implicit equation.
Series: Taylor and Maclaurin polynomials and convergence tests for infinite series.

How the calculus tools show their work

Each derivative is broken down into the rules that produce it. The calculator identifies the outermost operation, applies the matching rule, and then works inward, so a chain rule problem shows both the outer and inner derivatives before they are multiplied. Integrals name the technique used, whether a basic antiderivative, substitution, integration by parts or partial fractions, and every antiderivative is checked by differentiating it back.

Limits are solved by direct substitution when possible, and otherwise by simplifying, applying L'Hôpital's rule or comparing growth rates at infinity. Definite integrals give an exact value when an antiderivative exists and a clearly labeled numerical approximation when it does not.

Building intuition

Calculus is easier when you connect symbols to pictures. A derivative is the slope of a tangent line, a definite integral is a signed area, and a Taylor polynomial is a curve that hugs the original function near one point. Use the graphing calculator alongside these tools to see what each result means, then check that the sign and size of your answer match the picture.

Courses and topics

Topic explainers with worked examples, common mistakes and practice questions in Calculus.

Guides

Derivative Rules Explained with Worked Examples
Computing derivatives from the limit definition is slow. A small set of rules, each proved once from that definition, lets you differentiate almost any formula in a few lines. This guide explains each rule, why it works and how to combine them.