Ellipse Perimeter Calculator

About this calculator

Unlike a circle, an ellipse has no simple closed-form formula for its perimeter — the exact answer requires an elliptic integral that can't be written with elementary functions, so calculators instead rely on very accurate approximations. The one used most often today is Ramanujan's second approximation, published by the Indian mathematician Srinivasa Ramanujan in 1914: perimeter ≈ π[3(a + b) − √((3a + b)(a + 3b))], where a and b are the semi-major and semi-minor axes. It stays within about 0.04% of the true value even for fairly elongated ellipses, which is why it remains the standard shortcut in engineering software rather than the more cumbersome infinite-series or numerical-integration methods.

Engineers and designers reach for an ellipse perimeter calculation whenever they need to size elliptical hardware or trim material to length — the edge of an elliptical running track, the rim of an oval architectural window, gear and cam profiles, or the fabric border of an elliptical tabletop or mirror — while the area formula (π × a × b) is exact and used alongside it for material or coverage estimates.

This calculator takes the semi-major and semi-minor axis lengths and returns both the Ramanujan-approximated perimeter and the exact area.