Ellipse Calculator for Area, Circumference, Foci and Eccentricity

Updated By Unit Conversion Plus

Calculate an ellipse's area, circumference, foci and eccentricity from its two semiaxes or full axes.

Ellipse measurements

Ellipse formulas

Area = πab · c = √(a² − b²) · e = c/a

The circumference has no elementary exact formula, so this calculator uses Ramanujan's highly accurate second approximation.

Axes and foci

The major axis is the longest diameter. The two foci lie c units from the centre along it. As eccentricity approaches zero, the ellipse approaches a circle.

Frequently asked questions

Can the two semiaxes be equal?

Yes. The ellipse is then a circle with eccentricity zero.

Is ellipse circumference exact?

The displayed value is a very accurate approximation because no simple elementary exact formula exists.