About the Riemann Sum Calculator
Approximate the area under a curve with left, right, midpoint or trapezoidal Riemann sums, with a table of subintervals.
Also known as: left riemann sum, right riemann sum, midpoint rule, trapezoidal rule, riemann sums.
How to use this calculator
- Enter f(x), a, b, subintervals n and the other fields.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
Σ f(xᵢ*)·Δx, Δx = (b − a)/n
Worked example
Using the values pre-filled in the calculator above:
- f(x): x^2
- a = 0
- b = 2
- Subintervals n = 8
- Method: Midpoints
the calculator returns:
- Riemann sum: 2.65625
- Exact integral: 2.6666666667
- Error: -0.010417
- Δx: 0.25