Ellipse Perimeter Calculator

How it is calculated

You enter the two semi-axes, a (semi-major) and b (semi-minor), each half of the full width and full height of the ellipse, in the same length unit. The perimeter uses the second Ramanujan approximation P ≈ π × [ 3(a + b) − √( (3a + b)(a + 3b) ) ], and the area is exact: A = π × a × b. Both are rounded to two decimals.

Both axes must be greater than zero. The formula is symmetric, so entering the shorter axis first gives the same answer. When a = b the ellipse is a circle and the formula returns 2πr. The perimeter is in the unit you typed and the area in its square; the result is labelled only as units.

Common mistakes

• Entering the full length and width instead of the semi-axes; the inputs are half of those, so a 10 by 6 ellipse needs 5 and 3.
• Averaging the axes and using the circle formula 2π × (a + b) / 2; for an elongated ellipse this noticeably misses the perimeter.
• Treating the perimeter as exact; Ramanujan's formula is a very close approximation, not the elliptic integral itself.
• Mixing units, such as 5 metres and 300 centimetres, which gives a meaningless shape.
• Reading the second output as a length: the area is in square units and is not interchangeable with the perimeter.