ใฐ๏ธArc 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.