Understanding Ellipse
The ellipse calculator computes the area, circumference, and eccentricity of an ellipse from its semi-major and semi-minor axes. An ellipse is an oval shape defined as the set of all points where the sum of distances from two fixed points called foci is constant. Ellipses are remarkably common in nature and engineering. Planetary orbits are elliptical, as described by Kepler's laws. Stadiums, racetracks, mirrors, and many mechanical components use elliptical shapes. The area of an ellipse equals pi times the semi-major axis times the semi-minor axis, a natural extension of the circle area formula. The circumference is more complex and has no exact algebraic formula, so the calculator uses Ramanujan's approximation which provides excellent accuracy. Eccentricity measures how elongated the ellipse is, ranging from zero for a perfect circle to values approaching one for highly elongated ellipses. This calculator takes the two semi-axis lengths as input and provides all three measurements instantly with the formulas used. Understanding ellipse properties is important for astronomy, optics, engineering, architecture, and mathematics. Use this free ellipse calculator for academic studies, engineering design, astronomical calculations, or any application involving elliptical geometry.