Simpson’s Rule Calculator (Free, Step-by-Step)

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.

Original price was: $109.99.Current price is: $54.99.

How to use it

  1. Enter f(x), the interval a and b, and an even n.
  2. 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.

Original price was: $109.99.Current price is: $54.99.

How accurate is it?

Very accurate for smooth functions — it is exact for polynomials up to degree three.

Original price was: $109.99.Current price is: $54.99.

Does it show the error?

Yes — it compares the estimate to a fine-grid value of the integral.

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