Simpson’s Rule Calculator (Free, Step-by-Step)
Use this free Simpson’s rule calculator to approximate a definite integral. Enter the function, the interval, and an even number of subintervals to get the estimate, the step size, the error, and a graph.
How Simpson’s rule works
It fits parabolas through groups of points, weighting endpoints by 1, odd points by 4, and even points by 2, then scales by h/3. n must be even.
How to use it
- Enter f(x), the interval a and b, and an even n.
- Press Approximate.
Related: the Riemann Sum Calculator and the Integral Calculator.
Frequently asked questions
Why must n be even?
Simpson’s rule pairs subintervals into parabolic arcs, so it needs an even number of them.
How accurate is it?
Very accurate for smooth functions — it is exact for polynomials up to degree three.
Does it show the error?
Yes — it compares the estimate to a fine-grid value of the integral.
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