Ellipse Calculator
Enter the two semi-axes of an ellipse to find its area and approximate perimeter.
units
units
- 1
Product of the semi-axes
6 × 4 = 24 - 2
Area = π × a × b
π × 24 = 75.3982Generalises the circle area πr² — when a = b it reduces to πr².
Formula
How this is calculated
You provide two numbers: the semi-major axis a (half of the longest diameter, measured from the center to the farthest edge) and the semi-minor axis b (half of the shortest diameter). Both are lengths in the same unit you choose, so the area comes out in that unit squared and the perimeter in that unit. The inputs must be positive; if either is zero or negative the shape collapses and no result is shown.
The area is computed exactly as π × a × b. This generalizes the circle formula: when a equals b the ellipse is a circle of radius r and the area becomes πr². The perimeter, however, has no exact elementary formula — it is technically a complete elliptic integral — so the tool uses Ramanujan's approximation, π × (3(a + b) − √((3a + b)(a + 3b))).
That approximation is accurate to well under a hundredth of a percent for near-circular shapes; the error only grows noticeably for extremely elongated ellipses. The shape meter reports b ÷ a, where 1 is a perfect circle and values near 0 indicate a long, thin ellipse.
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.
Also known as
TG we-Calculate Editorial Team. (2026). Ellipse Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ellipse-calculator
TG we-Calculate Editorial Team. "Ellipse Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/ellipse-calculator.
TG we-Calculate Editorial Team, "Ellipse Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ellipse-calculator
@misc{wecalculate_ellipse_calculator, title = {Ellipse Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ellipse-calculator}}, year = {2026}, note = {TG we-Calculate} }
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