Ellipse Calculator

Enter the semi-major and semi-minor axes to calculate an ellipse's area, circumference, and eccentricity.

How to Use the Ellipse Calculator

Enter the semi-major axis (half the longest diameter) and semi-minor axis (half the shortest). Area, circumference, and eccentricity all update together.

area = π × a × b
eccentricity = √(1 − (b² ÷ a²))

Area has a clean formula — it's just a circle's πr² with the single radius split into two different axes. Circumference doesn't get off so easily: unlike a circle, there's no exact elementary formula for it, only approximations. This calculator uses Ramanujan's second approximation, accurate to within a fraction of a percent for almost any ellipse:

circumference ≈ π × [3(a + b) − √((3a + b)(a + 3b))]

Eccentricity measures how stretched the ellipse is, from 0 (a perfect circle, a equals b) up toward 1 (a sliver flattened almost to a line) — it's the same number astronomers quote for how elliptical a planet's orbit is.