Ellipse Area Calculator

Work out ellipse area instantly with clear inputs, formula shown and shareable results.

About Ellipse Area Calculator

An ellipse is a circle stretched by a along one axis and b along the other, so its area is πab. When a = b it reduces to the circle area πr².

Formulas

Ellipse area

A = π·a·b

Equal-area circle

r = √(ab)

Worked example

With the default values below, Ellipse Area Calculator returns Area of 125.6637. Change any input above and every figure here is recalculated in your browser.

Inputs used

Semi-major axis aminimum 0: 8
Semi-minor axis bminimum 0: 5

Results

Area: 125.6637
Equal-area circle radius: 6.3246
Aspect ratio a:b: 1.6000
a × b: 40.0000

Step by step

1Values used
2Ellipse area
3Equal-area circle
4Area= 125.6637
5Equal-area circle radius= 6.3246
6Aspect ratio a:b= 1.6000
7a × b= 40.0000

Assumptions and limits

The result is derived only from the 2 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 4 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

Do I use the full axes or the semi-axes?

Semi-axes. If you measured the full width and height, halve them first.

Is there a simple exact perimeter formula?

No. The perimeter needs an elliptic integral, which is why Ramanujan's approximation is used instead.