Latus Rectum Calculator

The formula

A = πab, perimeter ≈ Ramanujan’s approximation

Why the perimeter is hard

An ellipse’s area is exactly πab, but its perimeter has no elementary closed form — it needs an elliptic integral, which is where those functions got their name. Ramanujan’s approximation used here is accurate to better than one part in a billion for ordinary shapes, and reduces exactly to 2πr when the axes are equal.

Area scales with the square

Double every length in a flat shape and the area quadruples; triple them and it grows ninefold. Perimeter, being a length, scales in step with the sides. That mismatch is why bigger shapes enclose proportionally more area per unit of edge — and why a circle, having no corners at all, encloses the most area for a given perimeter of any shape.

Units

Whatever unit you enter, the area comes out in that unit squared and the perimeter in the unit itself. The calculator is unit-agnostic — enter centimetres and read cm and cm², or feet and read ft and ft². Just do not mix units between fields.