🥚 Ellipse Area and Circumference Calculator
Calculate the area and circumference of an ellipse from its semi-major and semi-minor axis lengths.
What this calculator finds
An ellipse is a stretched circle defined by two axes: the semi-major axis (a), the longer half-axis, and the semi-minor axis (b), the shorter half-axis. This calculator finds both the area and the circumference (perimeter) of an ellipse.
The formulas
Area = π · a · b — this is exact, a direct extension of the circle area formula.
Circumference has no simple exact formula, so this calculator uses Ramanujan’s second approximation, which is accurate to within a fraction of a percent for almost any ellipse shape: C ≈ π(a+b)[1 + 3h / (10 + √(4 − 3h))], where h = (a−b)² / (a+b)².
When a and b are equal, the ellipse becomes a circle and both formulas reduce to the familiar circle formulas. This tool is for general math and educational purposes.