Numerical Integration Calculator (Simpson's Rule)
Approximate a definite integral of a list of function values.
Enter your values
Enter the function values (comma-separated, odd count) you are working with.
Enter the step size h you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Approximate integral
- 72
- Number of intervals
- 6
- Step size
- 1
Quick answer
Simpson's rule fits parabolas through pairs of intervals for a more accurate approximation than the trapezoidal rule.
∫≈(h/3)[f0+4f1+2f2+...+4f(n-1)+fn]
At a glance
| What it does | Approximate a definite integral of a list of function values. |
|---|---|
| Category | Math |
| Inputs needed | Function values (comma-separated, odd count), Step size h |
| Main output | Approximate integral |
| Formula | ∫≈(h/3)[f0+4f1+2f2+...+4f(n-1)+fn] |
| Cost | Free — no sign-up, no download |
How to use the Numerical Integration Calculator (Simpson's Rule)
- 1List an odd number of evenly spaced function values.
- 2Enter the step size h between consecutive x values.
- 3Simpson's rule weights the values 1-4-2-4-...-4-1 and scales by h/3.
Inputs explained
- Function values (comma-separated, odd count)
- Enter the function values (comma-separated, odd count) you are working with.
- Step size h
- Enter the step size h you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Function values (comma-separated, odd count)0,1,4,9,16,25,36
- Step size h1
Results
- Approximate integral72
- Number of intervals6
- Step size1
Frequently asked questions
Why does it need an odd count of points?
Simpson's rule pairs points into parabolic segments, requiring an even number of intervals (odd number of points).
How accurate is it?
Much more accurate than the trapezoidal rule for smooth functions, with error shrinking as h^4.
What do I need to enter into the Numerical Integration Calculator (Simpson's Rule)?
Just 2 values: function values (comma-separated, odd count), step size h. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Numerical Integration Calculator (Simpson's Rule) work out the answer?
Simpson's rule fits parabolas through pairs of intervals for a more accurate approximation than the trapezoidal rule. It applies the formula ∫≈(h/3)[f0+4f1+2f2+...+4f(n-1)+fn] and shows the working so you can check each step by hand.
Is the Numerical Integration Calculator (Simpson's Rule) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.