Geometry

Ellipse Area Calculator

Calculate an ellipse's area from its two semi-axes, plus its approximate circumference.

Area

47.1239

Area = π × a × b. Semi-axes of 5 and 3 give about 47.12 square units.

Circumference (approx.)

25.527

How it works

An ellipse is a stretched circle, and its area follows the same spirit: pi times the two semi-axes multiplied together. When both semi-axes are equal, it collapses neatly back into the familiar circle area.

Circumference is the trickier part — there is no simple exact formula — so the tool uses Ramanujan's well-known approximation, which is accurate to a remarkable degree for ordinary ellipses.

Enter the semi-major and semi-minor axes and you get both figures at once, useful for elliptical tables, tracks, garden beds, and machine parts.

Frequently asked questions

How do you find the area of an ellipse?

Multiply pi by the semi-major axis and by the semi-minor axis. If both are the radius of a circle, it reduces to pi r squared.

What is a semi-axis?

It is half the width or half the height of the ellipse, measured from the center. The semi-major axis is the longer one and the semi-minor the shorter.

Why is the circumference only approximate?

An ellipse's exact perimeter has no simple closed formula and involves an infinite series. Ramanujan's approximation is extremely close for typical shapes, which is why it is used here.