∫Numerical Integration Calculator
Approximate a definite integral with the Trapezoidal, Simpson's, or Midpoint rule.
Free Numerical Integration Calculator
Need to approximate a definite integral — whether from a function or a table of measured data points? Our free numerical integration calculator applies the Trapezoidal Rule, Simpson's Rule, and the Midpoint Rule side by side. Enter a function and interval (or paste in data points), choose your number of subintervals, and see each sample point, the formula substitution, and the final approximation.
When a function is provided, the calculator also computes a high-precision reference value and reports the error of each approximation, so you can see which method converges fastest. A graph draws the actual trapezoids used directly over the curve.
Enter your function or data to get started. No sign-up, no downloads, no limits.