Home › Geometry › Ellipse Calculator
Ellipse Calculator
Enter semi-axes a and b — area and perimeter update instantly.
Formula
Area = π·a·b | Perimeter ≈ π[3(a+b) − √((3a+b)(a+3b))] (Ramanujan)
Example
a = 50, b = 30 mm → Area = 4712.4 mm², perimeter ≈ 256.5 mm.
FAQ
Why is there no exact ellipse perimeter formula?
The perimeter is an elliptic integral with no closed elementary form. Ramanujan's approximation is accurate to better than 0.001% for most shapes.
What are the semi-axes?
a and b are half the longest and shortest diameters of the ellipse, measured from the center.