How do I find an ellipse's area?
Multiply pi by the two semi-axes: pi times a times b. It is the exact equivalent of a circle's pi r squared, but with two different radii instead of one.
// maths › 2D Shapes
Ellipse Area Calculator
Find an ellipse's area exactly from its semi-major and semi-minor axes, plus a very accurate approximate circumference (Ramanujan's formula).
area = πab ; circumference ≈ π[3(a+b) − √((3a+b)(a+3b))] (Ramanujan)
Frequently asked questions
What are the semi-major and semi-minor axes?
Half of the longest diameter (semi-major, a) and half of the shortest diameter (semi-minor, b). When a equals b, the ellipse is just a circle.
Why is the circumference only approximate?
Because an ellipse's perimeter has no simple exact formula. This calculator uses Ramanujan's approximation, which is astonishingly accurate for almost all ellipses.
What happens if a equals b?
You get a circle. The area becomes pi r squared and the circumference approximation collapses to the exact 2 pi r. The ellipse formulas generalise the circle ones.
Where do ellipses appear?
Planetary orbits, whispering galleries, elliptical tracks and tables, and the cross-section of many tanks and tunnels.