Riemann Sum Calculator interactive tool
Approximate area under the curve on [0, 3] using 6 rectangles and a left Riemann sum:
≈ 6.8750
What Is Riemann Sum?
A Riemann sum & area under curve visualizer approximates the integral of a function over an interval by drawing rectangles and summing their areas. It supports left, right, and midpoint Riemann sums.
Connecting Sums to Integrals
Early in calculus, the definite integral is defined as the limit of Riemann sums. This tool lets you see that process visually: increasing the number of rectangles n generally narrows the sampling intervals, while left, right, and midpoint methods can produce different approximations.
How To Use the Riemann Sum Calculator
- Enter a function of x in the f(x) field using the supported math syntax (for example x*x or sin(x)).
- Set the interval [a, b] over which you want to approximate the area under the curve.
- Choose the number of rectangles n and select a method: left, right, or midpoint Riemann sum.
- The visualizer will draw rectangles under the curve and calculate the approximate area as their total area.
- Use the Example button to load a sample function and parameters, or Reset to clear everything.
Left, right, and midpoint Riemann sums
Use this Riemann sum calculator to approximate area under a curve with left-endpoint, right-endpoint, or midpoint rectangles. Change the interval and number of rectangles to see how the approximation responds.
Need the formula or convention behind this result? Read the calculator methods and assumptions.