Ellipse Calculator
Enter the two semi-axes of an ellipse to find its area and approximate perimeter.
units
units
31.7309
Formula
Examples
| Input | Result |
|---|---|
| a = 6, b = 4 | Area ≈ 75.3982, Perimeter ≈ 31.7269 |
About this calculator
An ellipse is the set of points where the sum of distances to two fixed foci is constant; it looks like a stretched circle defined by two semi-axes, a (semi-major) and b (semi-minor). Its area is exactly π × a × b, generalizing the circle area πr² (where a = b = r).
Unlike the area, the exact perimeter has no simple closed form, so this tool uses Ramanujan’s celebrated approximation, which is accurate to a tiny fraction of a percent for most ellipses. The more elongated the ellipse, the slightly larger any approximation error becomes.
Frequently asked questions
Area = π × a × b, where a and b are the semi-major and semi-minor axes. When a equals b, this reduces to the circle area πr².
The exact perimeter requires an elliptic integral with no elementary closed form. Ramanujan’s approximation is extremely accurate and is used here.
A semi-axis is half of the full axis, measured from the center to the edge. Enter the semi-major and semi-minor values, not the full widths.
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