Calculus Tools
Derivative calculators, integral solvers, limit evaluators, and series tools.
Derivative Calculator
Differentiate algebraic, trigonometric, exponential, and logarithmic functions with step-by-step rule breakdowns (power, product, quotient, chain) and live tangent line plots.
Integral Calculator
Evaluate definite integrals (∫ₐᵇ f(x) dx) and indefinite antiderivatives (F(x) + C) step-by-step with live 2D Riemann area under the curve shading.
Limit Calculator
Evaluate two-sided limits, left-hand limits (x→c⁻), right-hand limits (x→c⁺), limits at infinity, and L'Hôpital's rule indeterminate forms (0/0, ∞/∞).
Taylor Series Calculator
Compute Taylor and Maclaurin series polynomial approximations ∑ [f⁽ⁿ⁾(a)/n!] (x - a)ⁿ with convergence intervals and dynamic polynomial overlays.
Riemann Sum Calculator
Approximate definite integrals using Left, Right, Midpoint, and Trapezoidal Riemann sums with interactive partition visualizers.
Double Integral Calculator
Evaluate iterated double integrals ∬ f(x, y) dA over rectangular and general 2D regions in Cartesian and polar coordinates.
Arc Length Calculator
Calculate the exact curve length L = ∫ √(1 + [f'(x)]²) dx of algebraic, trigonometric, and parametric functions across intervals.
Laplace Transform Calculator
Compute unilateral Laplace transforms ℒ{f(t)} = ∫₀^∞ e^(-st) f(t) dt and inverse Laplace transforms with step-by-step table lookups.
Series Calculator
Calculate the sum of geometric, arithmetic, and power series.
Definite Integral Solver
Compute the definite integral value over a specific interval [a, b].
Beta Function Calculator - Online Tool
Evaluate derivatives, integrals, series approximations, and functional transforms for Beta Function - Online with complete mathematical derivations.
Average Rate of Change Calculator
Free online Average Rate of Change Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Composite Function Range Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Composite Function Range with complete mathematical derivations.
Curl Calculator | Vector Field Analysis Tool
Evaluate derivatives, integrals, series approximations, and functional transforms for Curl | Vector Field Analysis with complete mathematical derivations.
Complementary Error Function (erfc) Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Complementary Error Function (erfc) with complete mathematical derivations.
Continuous Exponential Decay Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Continuous Exponential Decay with complete mathematical derivations.
Contour Integral Calculator
Free online Contour Integral Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Hessian Matrix Calculator
Free online Hessian Matrix Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Gradient Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Gradient with complete mathematical derivations.
Directional Derivative Calculator
Free online Directional Derivative Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Hyperbolic Cosine Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Hyperbolic Cosine with complete mathematical derivations.
Composite Function Calculator: f(g(h(x)))
Evaluate derivatives, integrals, series approximations, and functional transforms for Composite Function: f(g(h(x))) with complete mathematical derivations.
Improper Integral Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Improper Integral with complete mathematical derivations.
Jacobian Matrix Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Jacobian Matrix with complete mathematical derivations.
Lagrange Multipliers Solver - Find Optimal Points
Evaluate derivatives, integrals, series approximations, and functional transforms for Lagrange Multipliers - Find Optimal Points with complete mathematical derivations.
Inflection Point Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Inflection Point with complete mathematical derivations.
Inverse Function Checker
Evaluate derivatives, integrals, series approximations, and functional transforms for Inverse Function Checker with complete mathematical derivations.
Inverse Function Calculator: Find f⁻¹(x) Easily
Evaluate derivatives, integrals, series approximations, and functional transforms for Inverse Function: Find f⁻¹(x) Easily with complete mathematical derivations.
Multivariable Chain Rule Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Multivariable Chain Rule with complete mathematical derivations.
Iterated Function Calculator
Free online Iterated Function Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Multivariable Integral Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Multivariable Integral with complete mathematical derivations.
Line Integral Calculator
Free online Line Integral Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Critical Point Finder | Multivariable Calculus Tool
Evaluate derivatives, integrals, series approximations, and functional transforms for Critical Point Finder | Multivariable Calculus with complete mathematical derivations.
Laplacian Calculator
Free online Laplacian Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Partial Fraction Decomposition Integrator
Evaluate derivatives, integrals, series approximations, and functional transforms for Partial Fraction Decomposition Integrator with complete mathematical derivations.
Local Extrema Classifier: Find Minima, Maxima & Saddle Points
Evaluate derivatives, integrals, series approximations, and functional transforms for Local Extrema Classifier: Find Minima, Maxima & Saddle Points with complete mathematical derivations.
Reduction Formula Integrator
Evaluate derivatives, integrals, series approximations, and functional transforms for Reduction Formula Integrator with complete mathematical derivations.
Integration by Parts Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Integration by Parts with complete mathematical derivations.
Numerical Integration Calculator
Free online Numerical Integration Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Partial Derivative Calculator
Free online Partial Derivative Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Second Derivative Calculator | Find Concavity
Free online Second Derivative Calculator | Find Concavity with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Rational Function Continuity Checker | Easy Function Test
Evaluate derivatives, integrals, series approximations, and functional transforms for Rational Function Continuity Checker | Easy Function Test with complete mathematical derivations.
Natural Logarithm (ln) Calculator
Free online Natural Logarithm (ln) Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Local Maxima and Minima Finder
Evaluate derivatives, integrals, series approximations, and functional transforms for Local Maxima and Minima Finder with complete mathematical derivations.
Rational Function Integral Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Rational Function Integral with complete mathematical derivations.
Surface Integral Calculator
Free online Surface Integral Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Trigonometric Substitution Integrator
Evaluate derivatives, integrals, series approximations, and functional transforms for Trigonometric Substitution Integrator with complete mathematical derivations.
Rational Function Derivative Calculator
Free online Rational Function Derivative Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Vector Divergence Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for Vector Divergence with complete mathematical derivations.
Triple Integral Calculator: Solve 3D Integrals Online
Evaluate derivatives, integrals, series approximations, and functional transforms for Triple Integral: Solve 3D Integrals Online with complete mathematical derivations.
Mass to Weight Conversion
Free online Mass to Weight Conversion with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Trigonometric Equation Solver | Find Solutions to Trig Equations
Evaluate derivatives, integrals, series approximations, and functional transforms for Trigonometric Equation | Find Solutions to Trig Equations with complete mathematical derivations.
U-Substitution Integral Calculator
Evaluate derivatives, integrals, series approximations, and functional transforms for U-Substitution Integral with complete mathematical derivations.
Calculus Calculators: Derivatives, Integrals, and Limits
Calculus is the mathematical study of continuous change, developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century. It provides the tools to analyze rates of change (differential calculus) and accumulation of quantities (integral calculus), making it essential for physics, engineering, economics, and computer science.
Solve Calculus Problems Step by Step
Our calculus calculators help you work through derivatives, definite and indefinite integrals, limits, and series expansions. Each solution is broken down into individual steps so you can follow the mathematical reasoning and learn the techniques, not just get the final answer.
Tools for Every Calculus Student
- Derivative Calculator: Compute first, second, and higher-order derivatives of polynomial, trigonometric, exponential, and logarithmic functions using standard differentiation rules (power rule, chain rule, product rule, quotient rule).
- Integral Calculator: Evaluate definite and indefinite integrals with step-by-step application of integration techniques including substitution and integration by parts.
- Limit Calculator: Find one-sided and two-sided limits of functions, including indeterminate forms solved via L'Hôpital's Rule.
- Series Calculator: Expand functions as Taylor and Maclaurin series and test for convergence.
Calculus concepts appear everywhere in the real world: engineers use derivatives to optimize designs, economists calculate marginal cost and revenue, physicists model motion and gravity, and biologists analyze population growth. Our free tools make these powerful techniques accessible to anyone with a web browser.