Ellipse Calculator
Enter the semi-major and semi-minor axes to compute the ellipse's area, approximate circumference, focal distance and eccentricity. The calculator uses Ramanujan's approximation for the circumference, accurate to better than 1 part in 10⁷ for typical ellipse shapes.
Enter the axes
Enter the two axes and press Calculate.
Ellipse formulas
Area: A = π · a · b
Circumference: C ≈ π [ 3(a+b) − √((3a+b)(a+3b)) ] (Ramanujan)
Focal distance: c = √(a² − b²)
Eccentricity: e = c / a
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Frequently asked questions
Eccentricity measures how far the ellipse is from being a circle. It ranges from 0 (a perfect circle, a = b) to just below 1 (a very elongated ellipse). It is defined as c/a where c is the distance from the center to a focus.
The exact formula for an ellipse's circumference involves an infinite series (an elliptic integral) that has no closed form. Ramanujan's approximation is exceptionally accurate — for most practical purposes it matches the true value to 7 or more decimal places.