Ellipse Area Calculator
Enter the semi-major axis (a) and semi-minor axis (b) of an ellipse to get its area instantly, plus the perimeter using Ramanujan's approximation — with a step-by-step breakdown of every calculation.
How to use
- Enter the semi-major axis (a) — half of the longest width of the ellipse.
- Enter the semi-minor axis (b) — half of the shortest width — in the same unit.
- Read the result: area equals pi times a times b, plus the perimeter estimate.
- Open the steps section to see each part of the calculation worked out.
Good to know
- The area formula is pi times a times b — double either axis and the area doubles.
- A circle is just an ellipse with a equal to b.
- There is no exact simple formula for the perimeter, so Ramanujan's approximation is used.
- Keep both axes in the same unit (for example, centimetres).
Note: The famous Ramanujan approximation is used for the perimeter because there is no exact simple formula for the perimeter of an ellipse.
Frequently Asked Questions (FAQ)
What does this ellipse area calculator do?
It calculates the area and perimeter of an ellipse from the lengths of its two axes, with a step-by-step breakdown of the calculation.
Which formula does it use for the area?
The standard formula: Area = pi x a x b, where a is the semi-major axis and b is the semi-minor axis. Doubling either axis doubles the area.
What values do I enter?
The semi-major axis (a, half of the longest width) and the semi-minor axis (b, half of the shortest width), both in the same unit, such as centimetres.
How accurate is the perimeter result?
There is no exact simple formula for an ellipse perimeter, so the tool uses Ramanujan's approximation. It is very close to the true value but still an estimate.