Calculus Calculators
Last updated: September 2026
Critical Points Calculator
Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero.
Area Under Curve Calculator
Computes the exact area between a parabola f(x) = ax² + bx + c and the x-axis over an interval [x₁, x₂].
Riemann Sum Calculator
Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums.
Optimization Calculator
Find the largest area a rectangle can enclose with a fixed perimeter — a classic quadratic optimization: the area A(x) = x(P/2 − x) peaks at its vertex x = P/4, a square.
Numerical Derivative Calculator
Compute the derivative of a power function f(x) = c·x^n + k at a chosen point using either the analytical power rule or a numerical finite-difference approximation.
Rectangular Rule Strip Area Calculator
Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value.
Surface Area of Revolution Calculator
Calculates the surface area generated when the curve y = ax^n is revolved around the x-axis or y-axis between two bounds.
Limit Calculator
Compute the limit of a rational function (numerator_coeff · x^numerator_power) / (denominator_coeff · x^denominator_power) as x approaches a given value via direct substitution.
Related Rates Calculator
Compute the rate of area change of a circle whose radius grows at a constant rate, evaluated after a given elapsed time.