Ellipse Area Calculator
The area and approximate perimeter of an ellipse from its two semi-axes.
Result
Area
47.12
Perimeter (approx.)
25.53
How it works
An ellipse is a stretched circle, described by two radii: the semi-major axis a and the semi-minor axis b. Its area is beautifully simple — π·a·b — which collapses to πr² when a and b are equal and the ellipse becomes a circle. The perimeter is the opposite: it has no exact formula in elementary functions. This calculator uses Ramanujan's approximation, which is accurate to a fraction of a percent for ordinary shapes — a rare case where a famous constant hides an unsolvable problem behind an easy one. Ellipses are the natural shape of orbits: Kepler showed planets travel on ellipses with the Sun at one focus, not at the centre. They also appear whenever a circle is viewed at an angle, which is why a round plate looks elliptical from across the table.
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Frequently asked questions
What are a and b?
The semi-axes — half of the longest and shortest diameters of the ellipse.
Is the perimeter exact?
No exact elementary formula exists; this uses Ramanujan’s approximation, accurate to a tiny fraction of a percent.
How do I draw an accurate ellipse?
Use the gardener's method: push two pins into the two foci, loop a length of string around them, and trace with a pencil held taut against the loop. The constant string length is exactly the property that defines an ellipse.
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