Ellipse Calculator
Area, circumference and eccentricity from the two semi-axes.
Area is easy, circumference is not
Area is simply πab, the circle formula with both radii. The circumference has NO exact closed formula; this calculator uses Ramanujan's 1914 approximation, accurate to within a few parts per million for any ellipse you'll meet outside astronomy:
C ≈ π(3(a+b) - √((3a+b)(a+3b)))
Eccentricity
Eccentricity runs from 0 (a circle) to just under 1 (a squashed cigar). Earth's orbit is a barely-elliptical 0.017; Halley's comet rides a 0.97. The two foci sit ±c from the center, and the string-and-two-pins garden trick draws the curve exactly.