Romberg Integration Calculator

About this calculator

Romberg integration is a numerical method for estimating a definite integral that starts with the trapezoidal rule at increasingly fine subdivisions, then applies Richardson extrapolation to cancel out lower-order error terms and converge on a far more accurate result than the trapezoid rule alone. Each added level roughly squares the accuracy of the previous one.

This calculator lets you pick a function, set the integration interval, and choose how many Romberg levels to compute, building the full triangular table of trapezoidal estimates and their extrapolated refinements. It's a standard technique taught in numerical analysis courses and used by engineers and scientists to integrate functions that don't have a clean closed-form antiderivative.