Area Between Two Curves Calculator

Work out area between two curves instantly with clear inputs, formula shown and shareable results.

About Area Between Two Curves Calculator

The area between two curves integrates the vertical gap: ∫(upper − lower) dx. Using the absolute difference handles intervals where the curves swap places.

Formula

Area between curves

A = ∫ₐᵇ |f(x) − g(x)| dx

Worked example

With the default values below, Area Between Two Curves Calculator returns Area between the curves of 0.83333333. Change any input above and every figure here is recalculated in your browser.

Inputs used

Upper curve coefficients: 0, 1, 0
Lower curve coefficients: 1, 0, 0
From x =: 1
To x =: 2

Results

Area between the curves: 0.83333333
Signed integral of the difference: -0.83333333
Vertical gap at the start: 0.000000
Vertical gap at the end: -2.000000

Step by step

1Values used
2Area between curves
3Area between the curves= 0.83333333
4Signed integral of the difference= -0.83333333
5Vertical gap at the start= 0.000000
6Vertical gap at the end= -2.000000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Between y = x and y = x² from 0 to 1?

∫(x − x²) dx = 1/2 − 1/3 = 1/6 ≈ 0.1666667.

What if the curves cross?

Split the interval at the crossing points, or integrate the absolute difference as done here.