Area Between Two Curves Calculator
This calculator finds the area of the region trapped between two curves f(x) and g(x) across an interval by numerically integrating their absolute difference.
Function f(x)
Function g(x)
Integral of |f(x) − g(x)| over the interval
How does this calculator work?
The area between two curves is the integral of their absolute difference, ∫ₐᵇ |f(x) − g(x)| dx. Choose functions f and g and the interval [a, b], and this tool evaluates that integral with composite Simpson's rule to return the enclosed area, plotting both curves and the shaded region.
Formula
How this is calculated
Pick two functions f(x) and g(x) from the menus and set the interval endpoints a and b. The area between the curves equals the definite integral of the absolute difference |f(x) − g(x)| from a to b. Taking the absolute value guarantees a non-negative area even where the curves cross or swap which one is on top.
The integral is evaluated with composite Simpson's rule using n = 1000 subintervals, which fits parabolas through successive triples of points for high accuracy on smooth functions. The endpoints are ordered automatically, so entering a > b gives the same positive result; if a = b the width is zero and the calculator asks for distinct limits.
Results assume both functions are real and finite over the whole interval. Functions such as √x, ln(x), and 1/x are only defined on part of the real line, so choosing an interval outside their domain produces undefined samples and no result. Because the method is numerical, sharp corners or many oscillations within [a, b] can introduce small approximation error.
Frequently asked questions
The geometric area between curves is always positive. Using |f(x) − g(x)| ensures regions where g rises above f still add to the total instead of subtracting from it.
No. Because the integrand is the absolute difference, swapping f and g gives the identical area.
Composite Simpson's rule with 1000 panels is highly accurate for smooth functions, typically matching the exact area to several decimal places.
Also known as
TG we-Calculate Editorial Team. (2026). Area Between Two Curves Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-between-curves-calculator
TG we-Calculate Editorial Team. "Area Between Two Curves Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-between-curves-calculator.
TG we-Calculate Editorial Team, "Area Between Two Curves Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-between-curves-calculator
@misc{wecalculate_area_between_curves_calculator, title = {Area Between Two Curves Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-between-curves-calculator}}, year = {2026}, note = {TG we-Calculate} }
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