Area Under A Curve Calculator

Work out area under a curve instantly with clear inputs, formula shown and shareable results.

About Area Under A Curve Calculator

The definite integral gives the signed area, counting regions below the axis as negative. Integrating the absolute value instead gives the total geometric area, which is what a paint or material estimate needs.

Formulas

Signed area

A = ∫ₐᵇ f(x) dx

Total area

A = ∫ₐᵇ |f(x)| dx

Worked example

With the default values below, Area Under A Curve Calculator returns Area as configured of 8.66666667. Change any input above and every figure here is recalculated in your browser.

Inputs used

Polynomial coefficients, highest power first: 1, 0, 0
From x =: 1
To x =: 3
Reportone of Signed area (integral), Total unsigned area: Signed area (integral)

Results

Area as configured: 8.66666667
Signed area: 8.66666667
Total unsigned area: 8.66666667
Average height of the curve: 4.33333333

Step by step

1Values used
2Signed area
3Total area
4Area as configured= 8.66666667
5Signed area= 8.66666667
6Total unsigned area= 8.66666667
7Average height of the curve= 4.33333333

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

Area under x² from 0 to 3?

x³/3 gives 9, and since the curve is above the axis the signed and unsigned areas agree.

When do the two differ?

Whenever the curve crosses the axis. For sin x from 0 to 2π the signed area is 0 but the total area is 4.