Average Rate of Change Calculator - Calculate the average rate of change of a function over an interval [a, b] using the difference quotient. Enter any function f(x), get the secant line slope, step-by-step solution with MathJax formulas, and an interactive graph showing the secant line and curve. New

Convolution Calculator - Calculate linear, circular, and continuous convolution of signals and functions with interactive visualizations, detailed step-by-step solutions, and comprehensive mathematical analysis. Featured

Curl Calculator - Calculate the curl ∇×F of any 2D or 3D vector field with step-by-step cross product determinant expansion. Enter component functions P, Q (and R for 3D), get symbolic curl, evaluate at a point, identify irrotational fields, and view an interactive vector field visualization with vorticity overlay. New

Curvature Calculator - Calculate the curvature (κ) of a function y=f(x) or a parametric curve at a specific point, with step-by-step derivatives, osculating circle visualization, and radius of curvature. New

Derivative Calculator - Calculate derivatives instantly with step-by-step solutions. Supports single-variable, partial, implicit, and directional derivatives with interactive visualizations.

Directional Derivative Calculator - Calculate directional derivatives of multivariable functions with step-by-step solutions, gradient computation, unit vector normalization, and interactive 3D surface visualization.

Divergence Calculator - Calculate the divergence ∇·F of any 2D or 3D vector field with step-by-step partial derivative computation. Enter component functions P, Q (and R for 3D), get symbolic divergence, evaluate at a point, identify sources and sinks, and view an interactive vector field visualization with divergence heat map. New

Double Integral Calculator - Compute double integrals with detailed step-by-step solutions and 3D surface visualization. Supports definite and indefinite integrals with polynomial, trigonometric, exponential, and hyperbolic functions.

Fourier Series Coefficients Calculator - Calculate the Fourier series coefficients a₀, aₙ, and bₙ for any periodic function. See the full integral computations, coefficient table, partial sum formula, and an interactive graph comparing the original function with its Fourier approximation. New

Gradient Calculator (Multivariable) - Calculate the gradient vector ∇f of multivariable functions. Enter any function f(x, y) or f(x, y, z), get all partial derivatives, evaluate the gradient at a specific point, see the magnitude and direction, step-by-step solution with MathJax formulas, and an interactive 2D gradient field visualization. New

Implicit Derivative Calculator - Compute derivatives of implicit functions F(x,y)=0 with detailed step-by-step solutions. Supports polynomials, trigonometric, exponential, and logarithmic functions up to 5th order derivatives.

Improper Integral Calculator - Evaluate improper integrals with infinite limits or discontinuities. Supports Type I (infinite bounds) and Type II (unbounded integrand) with step-by-step solutions, convergence analysis, animated visualizations, and comparison of truncation limits. New

Infinite Series Sum Calculator - Calculate the exact sum of convergent infinite series including geometric, telescoping, p-series, and well-known special series. Get step-by-step convergence proofs with animated partial sum visualizations. New

Instantaneous Rate of Change Calculator - Calculate the instantaneous rate of change (derivative) of any function f(x) at a specific point using the limit definition. Get step-by-step solutions with MathJax formulas, an interactive tangent line graph, and a convergence table showing how h→0 approaches the derivative. New

Integral Calculator - Calculate definite and indefinite integrals with detailed step-by-step solutions, interactive function visualization, and comprehensive explanations for calculus students and professionals.

Inverse Laplace Transform Calculator - Compute the inverse Laplace transform of F(s) to find f(t). Get step-by-step solutions, visualizations, and understand the transformation from frequency domain to time domain.

L'Hôpital's Rule Calculator - Evaluate limits of indeterminate forms (0/0, ∞/∞) using L'Hôpital's rule with step-by-step differentiation, interactive graph visualization, and detailed explanations. New

Laplace Transform Calculator - Compute Laplace transforms instantly with detailed step-by-step solutions, interactive function presets, and dual visualization of time-domain and frequency-domain functions.

Limit Calculator - Calculate limits of mathematical functions with detailed step-by-step solutions. Supports one-sided limits, indeterminate forms, and L'Hospital's Rule.

Line Integral Calculator - Calculate line integrals of scalar fields (∫f ds) and vector fields (∫F·dr) along parametric curves in 2D and 3D. Enter the field, parametric equations, and bounds to get symbolic results with step-by-step solutions, arc length, and an interactive curve visualization. New

Maclaurin Series Calculator - Compute the Maclaurin series expansion of common functions at x=0. Get nth-order polynomial terms, Lagrange remainder estimate, radius of convergence, and an interactive animated graph showing how partial sums converge to the original function. New

Newton's Method Calculator - Find roots of equations using the Newton-Raphson method. Enter any function f(x), set an initial guess, and see step-by-step iterations with tangent line approximations, convergence analysis, and an interactive graph showing the iteration path to the root. New

Optimization Calculator (Calculus) - Find the maximum and minimum values of any function using the first and second derivative tests. Get critical points, intervals of increase and decrease, concavity analysis, inflection points, and interactive graph visualization with step-by-step solutions. New

Partial Derivative Calculator - Compute partial derivatives of multivariable functions with detailed step-by-step solutions, interactive examples, and geometric visualization of tangent planes.

Power Series Calculator - Find the power series representation of functions centered at any point. Compute Taylor/Maclaurin coefficients, determine the radius and interval of convergence with endpoint analysis, and visualize how partial sums converge with an interactive animated graph. New

Radius of Convergence Calculator - Determine the radius and interval of convergence for power series using the Ratio Test or Root Test, with step-by-step solutions, convergence visualization, and endpoint analysis. New

Related Rates Solver - Set up and solve related rates problems step-by-step with implicit differentiation and chain rule. Supports expanding sphere, sliding ladder, filling cone, ripple in water, shadow length, approaching cars, inflating balloon, and rectangular box scenarios with animated diagrams. New

Riemann Sum Calculator - Approximate definite integrals using Riemann sums with left endpoint, right endpoint, midpoint, trapezoidal, and Simpson's rule. View animated rectangle visualizations, step-by-step solutions, and convergence analysis. New

Runge-Kutta (RK4) Method Calculator - Solve ordinary differential equations numerically using the classic 4th-order Runge-Kutta method. Enter dy/dx = f(x,y) with initial conditions and step size to see step-by-step iterations with k1, k2, k3, k4 computations, solution table, and interactive solution curve plot. New

Series Convergence Test Calculator - Test the convergence or divergence of infinite series using the Ratio Test, Root Test, Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, and p-Series Test. Get step-by-step solutions with MathJax-rendered formulas and animated partial sum graphs. New

Simpson's Rule Calculator - Approximate definite integrals using Simpson's 1/3 rule, 3/8 rule, and composite Simpson's rule. Features interactive parabolic visualization, error estimation, convergence analysis, method comparison, and detailed MathJax step-by-step solutions. New

Single Variable Derivative Calculator - Compute derivatives of any single-variable function with step-by-step solutions, differentiation rule identification, interactive graph, and critical point analysis.

Surface Integral Calculator - Evaluate surface integrals of scalar fields (∬f dS) and vector fields / flux integrals (∬F·dS) over parametric surfaces. Choose from preset surfaces (sphere, cylinder, cone, paraboloid, torus) or enter custom parametrizations. Get step-by-step solutions with normal vector computation, surface area element, and interactive 3D visualization. New

Surface of Revolution Calculator - Calculate the surface area of a solid of revolution. Enter any function f(x), set integration bounds and axis of rotation, and get step-by-step solutions with interactive 3D visualizations using the disk and shell surface area formulas. New

Taylor Series Calculator - Calculate the Taylor series expansion of any function around a point with step-by-step derivative calculations, interactive comparison graph, and educational explanations.

Trapezoidal Rule Calculator - Approximate definite integrals using the trapezoidal rule with interactive trapezoid visualization, error estimation, Richardson extrapolation, convergence analysis, and per-trapezoid area breakdown. Supports both function input and data point mode. New

Triple Integral Calculator - Compute triple integrals with detailed step-by-step solutions and 3D visualization. Supports definite and indefinite integrals with symbolic computation.

Volume of Revolution Calculator - Calculate the volume of a solid of revolution using the disk, washer, and shell methods. Enter your function, bounds, and axis of rotation to get step-by-step solutions with interactive 3D visualizations. New

Wronskian Calculator - Calculate the Wronskian determinant of a set of functions to test linear independence. See the full Wronskian matrix with derivatives, step-by-step determinant expansion, and a clear verdict on whether your functions form a fundamental set of solutions for differential equations. New