Ellipse Area Calculator

A = pi x 5 x 3 = 47.12 square units. This is 60% of a circle with radius 5 (78.54 sq units), because the ratio b/a = 3/5 = 0.6 directly scales the area relative to a circle.

The semi-major axis (a) is half the longest diameter of the ellipse. The semi-minor axis (b) is half the shortest diameter. The semi-major axis is always greater than or equal to the semi-minor axis. If they are equal, the shape is a circle.

If the oval is a true ellipse (mathematically defined), use A = pi x a x b where a and b are the half-lengths of the long and short diameters. Measure the longest distance across (major diameter), divide by 2 for a. Measure the shortest distance across (minor diameter), divide by 2 for b.

Unlike the area, ellipse perimeter has no simple exact formula. The best approximation is Ramanujan's: P = pi x (3(a+b) - sqrt((3a+b)(a+3b))). For a=5, b=3: P = pi x (24 - sqrt(23x18)) = pi x (24 - 20.35) = 11.46. Exact value is about 25.53.

When the semi-major axis equals the semi-minor axis (a = b), the ellipse is a perfect circle. The eccentricity becomes 0. The area formula pi x a x b reduces to pi x r^2, and the perimeter becomes 2 x pi x r.

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