∫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.
About the Numerical Integration Calculator
Features
Three methods compared
Trapezoidal, Simpson's, and Midpoint rules shown side by side.
Function or data table
Works from a symbolic function or pasted (x, y) sample points.
Error estimate
Compares each method against a high-resolution reference value.
Visual geometry
Graph draws the trapezoids, parabolic arcs, or rectangles used.
Frequently Asked Questions
How does the numerical integration calculator work?
Enter a function and interval, or a table of data points, choose a method, and it computes the approximation with every step shown.
What methods are supported?
Trapezoidal Rule, Simpson's Rule, and the Midpoint (Rectangle) Rule.
Is it free?
Completely free, no sign-up, downloads, or limits.
Can I use it without a formula, just data points?
Yes, switch to table mode and enter your (x, y) pairs directly.
Does it show how accurate the approximation is?
When a function is given, yes — it computes a high-precision reference value and shows the error.
Why does Simpson's Rule need an even number of subintervals?
It's a requirement of the method; the calculator auto-adjusts n if needed and tells you.
Does it show the geometry of each method?
Yes, a graph draws the trapezoids, parabolic arcs, or rectangles used, directly over the function.
Which method is most accurate?
Generally Simpson's Rule for smooth functions; the side-by-side comparison shows this for your specific input.
Is my input stored anywhere?
No; everything runs in your browser and isn't stored or sent anywhere.
Does it work on mobile?
Yes, fully responsive, including the graph and step-by-step panel.