Free Calculus Calculators

Derivative Calculator | Find f′(x) Instantly

Compute 1st through 4th numerical derivatives of any function at any point. Shows tangent line equation, derivative table, and interactive chart.

Second Derivative Calculator

Compute the second derivative and determine concavity at a given point.

Integral Calculator | Numerical

Compute definite integrals numerically using Simpson's rule and the trapezoidal rule.

Limit Calculator | Evaluate Limits

Evaluate limits of functions numerically as x approaches a value from left, right, or both sides.

Riemann Sum Calculator

Approximate definite integrals using left, right, midpoint, and trapezoidal Riemann sums.

Tangent Line Calculator

Find the equation of the tangent line to a function at a given point.

Newton's Method Calculator

Find roots of equations using Newton's iterative method with step-by-step convergence.

Arc Length Calculator | Curves & Circle Arcs

Calculate arc length for any function f(x) over an interval using numerical integration, or compute a circle arc length from radius and angle. Also shows sector area, chord length, and step-by-step working.

Partial Derivative Calculator

Compute partial derivatives of multivariable polynomial functions.

Taylor Series Calculator

Compute Taylor/Maclaurin series expansions for common functions.

Differential Equation Solver | ODE

Solve first-order ODEs numerically using Euler, Heun, and RK4. Compare method accuracy step by step.

Area Between Curves Calculator | Two Functions

Calculate the exact area enclosed between two functions f(x) and g(x) over any interval. Automatically detects intersection points, splits the integral correctly, and shows a sub-region breakdown.

Volume of Revolution Calculator

Calculate volumes of solids of revolution using disc and shell methods.

Laplace Transform Calculator

Find Laplace transforms and inverse transforms for common functions.

Fourier Series Calculator | aₙ, bₙ & Spectrum

Compute Fourier coefficients aₙ and bₙ for any periodic function using 2000-point Simpson's rule. Supports square wave, sawtooth, triangle, rectifiers, and custom expressions. Shows amplitude spectrum, coefficient table, partial sum, and Gibbs phenomenon detection.

Improper Integral Calculator

Evaluate improper integrals with infinite limits or discontinuities.

Series Convergence Calculator

Test if an infinite series converges or diverges using ratio, root, and comparison tests.

Interpolation Calculator | Lagrange, Newton & Divided Differences

Construct an interpolating polynomial through any set of data points using Lagrange interpolation or Newton's divided difference method. Displays the full divided difference table, polynomial in expanded form, and evaluates at any x — with error bound estimation between data points.

ODE Numerical Solver | Euler, Heun & Runge-Kutta RK4

Numerically solve first-order ordinary differential equations y′ = f(x, y) using three methods side-by-side: Euler's method, Heun's method (improved Euler), and the 4th-order Runge-Kutta (RK4). Shows all intermediate k₁–k₄ values for RK4 and a full step-by-step comparison table.

Numerical Differentiation Calculator | Forward, Central & Richardson

Approximate the derivative of any function f(x) at a given point using forward difference, backward difference, central difference (O(h²) accurate), and Richardson extrapolation (O(h⁴) accurate). Also computes the second derivative via the central second-difference formula and shows the truncation error for each method.

Numerical Integration Calculator | Simpson, Gaussian & Trapezoid

Integrate any function f(x) over an interval [a, b] using five methods side-by-side: Trapezoid rule, Simpson's 1/3 rule, Simpson's 3/8 rule, Boole's rule, and 5-point Gaussian quadrature. Compares all results, shows step-by-step working for the selected method, and estimates truncation error.

Wronskian Calculator | Linear Independence & Fundamental Solution Sets

Compute the Wronskian determinant W(f₁, f₂) or W(f₁, f₂, f₃) by evaluating derivatives numerically. Tests linear independence of function sets, identifies fundamental solution sets for linear ODEs, and displays the full derivative matrix evaluated at multiple points.