๐Riemann Sum Calculator
Enter a function, interval [a, b], and number of subintervals to approximate the area under the curve. All four methods โ left, right, midpoint, and trapezoidal โ are computed simultaneously, with the selected method's rectangles drawn on the graph and step-by-step working shown below.
Working
Riemann Sum Calculator Online
Approximating the area under a curve? Our free Riemann sum calculator computes and visualises it the moment you enter your function. As a fast and reliable riemann sum calculator online, it takes any function over an interval [a, b] with your chosen number of subintervals and returns the left, right, midpoint, and trapezoidal approximations โ so you can compare methods side by side.
But it does more than a number. It plots your function and overlays the rectangles or trapezoids used in the approximation, so you can actually see how the estimate is built and how it tightens as you increase n. A clear breakdown shows the width ฮx, sample points, and summed area behind the result. Whether you're a student learning integration, checking homework, or teaching the concept, the maths and the picture are right in front of you.
Simply enter your function and interval to see the results instantly. No sign-up, no downloads, no limits โ just clear calculus whenever you need it.
The Four Methods
Left Riemann Sum samples f at the left edge of each subinterval. It underestimates increasing functions and overestimates decreasing ones.
Right Riemann Sum samples f at the right edge. Its bias is the mirror image of the left sum on monotone functions.
Midpoint Riemann Sum samples f at the centre of each subinterval and is typically more accurate than left or right for the same n.
Trapezoidal Rule averages the left and right values, drawing trapezoids instead of rectangles. It gives the exact answer for any linear function and equals the average of the left and right sums.
Supported Functions
- Polynomials:
x^2,3*x^3 - 2*x + 1 - Trigonometric:
sin(x),cos(x),tan(x) - Exponential & log:
e^x,log(x),log(x, 10) - Roots:
sqrt(x),x^(1/3) - Combinations:
x * sin(x),e^(-x^2)
All calculations run entirely in your browser using math.js for safe function evaluation. No data is sent to a server. Results are numerical approximations โ increase n to approach the true integral value.