ใ€ฐ๏ธArc Length Calculator

Find the arc length of a curve y=f(x) or a parametric curve, with step-by-step setup and a highlighted graph.

Calculations run entirely in your browser using math.js for derivatives and Simpson's rule for the integral. No data is sent to a server.

Free Arc Length Calculator

Need the length of a curve between two points, not just its equation? Our free arc length calculator applies the arc length integral instantly and shows the full setup. Choose an explicit function y = f(x) or a parametric curve x(t), y(t), enter your interval, and see the derivative, the integrand, and the final length computed step by step.

When the resulting integral has no elementary antiderivative โ€” which is common for arc length problems โ€” the calculator uses numerical integration (Simpson's rule) and clearly labels the result, so you always get an answer. A graph highlights the exact segment of the curve being measured, making it easy to sanity-check the result visually.

Enter your curve and interval to get started. No sign-up, no downloads, no limits โ€” just clear, worked-out calculus whenever you need it. See the About page or the FAQ for more.