Ellipse Area and Perimeter Calculator

Online calculator to calculate the area \( A \) and the circumference \( C \) of an ellipse, given by the formulas:

Diagram of an ellipse with semi-major axis a and semi-minor axis b
Ellipse with semi-major axis \(a\) and semi-minor axis \(b\)
\[ A = \pi a b \] \[ C = \pi (a + b)\left[ 1 + \sum_{n=1}^{\infty} \left(\frac{(2n-1)!!}{n!\,2^n}\right)^2 \frac{h^n}{(2n-1)^2} \right] \] \[ \text{where} \quad h = \frac{(a-b)^2}{(a+b)^2} \]

Note: The circumference is given by an infinite series and therefore cannot be calculated exactly. By increasing the number of terms \(N\) in the series, you improve accuracy. The calculator below lets you adjust \(N\) to observe convergence.

How to Use the Calculator

Enter the semi-axes \(a\) and \(b\) (positive numbers), the number of series terms \(N\) (integer, ≥ 1), and the desired decimal places. Then press "Calculate".

Ellipse Calculator

Semi-axes a, b > 0 | Terms N ≥ 1

-- sq units
-- units
Try this: Keep a=5, b=4 and increase N from 5 to 10 to 20. Watch how the circumference value converges (changes less and less). The decimal places control lets you see more precise values!

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