Math Calculators

Ellipse Area Calculator

Calculate an ellipse's area and approximate perimeter from its semi-major and semi-minor axes, each in the unit of your choice.

Area —

Approximate perimeter —

About the Ellipse Area Calculator

An ellipse's area follows a simple exact formula, but its perimeter has no elementary closed form and is instead estimated using Ramanujan's highly accurate approximation. The semi-major and semi-minor axes each have their own unit selector, and so do the area and perimeter results.

Formulas: Area = πab · Perimeter ≈ π(a+b)(1 + 3h/(10+√(4−3h))), where h = ((a−b)/(a+b))²