Ellipse Eccentricity Calculator

About this calculator

Eccentricity measures how far an ellipse deviates from a perfect circle, computed as e = √(1 − b²/a²) from the semi-major axis a and semi-minor axis b; a value of 0 is a circle, and values approaching 1 describe an increasingly elongated ellipse. The same relationship gives the focal distance c = a·e, the distance from the ellipse's center to each of its two foci.

Astronomers use orbital eccentricity to characterize how elliptical a planet's, comet's or satellite's orbit is under Kepler's first law — Earth's orbit has e ≈ 0.017, nearly circular, while many comets have e close to 1. Mechanical engineers apply the same formula when designing elliptical gears and cams, and optical designers use it for elliptical mirrors and reflectors, which focus light or sound from one focus precisely to the other.