Ellipse Area Calculator

Reviewed by CalcMulti Editorial Team·Last updated: ·Geometry Hub

An ellipse is an oval shape defined by two axes: the semi-major axis a (longest radius) and the semi-minor axis b (shortest radius). The area is A = π × a × b. When a = b, the ellipse becomes a circle with area πr².

Unlike the circle, there is no simple exact formula for the perimeter of an ellipse. This calculator uses Ramanujan's approximation: P ≈ π × [3(a+b) − √((3a+b)(a+3b))], which is accurate to within 0.0001% for most ellipses.

Formula

A = π × a × b

A
area of the ellipse
a
semi-major axis (longest radius, a ≥ b)
b
semi-minor axis (shortest radius)

Ellipse Area Calculator

Semi-major axis a ≥ semi-minor axis b (if b > a, they will be swapped)

Ellipse Reference Table (a = 10)

b (semi-minor)AreaPerimeterEccentricity
262.8342.020.9798
4125.6646.030.9165
5157.0848.440.8660
6188.5051.050.8000
7219.9153.820.7141
8251.3356.720.6000
9282.7459.730.4359
10314.1662.830.0000

Disclaimer

This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.

Frequently Asked Questions