Ellipse Area Calculator
Enter the semi major and semi minor axes of an ellipse to find its area, circumference and eccentricity using the exact area formula and the Ramanujan perimeter approximation.
How to find the area of an ellipse
- Enter the semi major axis a, the longer half axis.
- Enter the semi minor axis b, the shorter half axis.
- Read the area, circumference and eccentricity instantly.
Examples
Axes a = 5, b = 3
a = 5, b = 3
area = 47.1239, circumference = 25.527, eccentricity = 0.8
Circle a = b = 4
a = 4, b = 4
area = 50.2655, circumference = 25.1327, eccentricity = 0
Frequently asked questions
What is the formula for the area of an ellipse?
The area equals pi times the semi major axis times the semi minor axis. When both axes are equal it reduces to the area of a circle.
How is the circumference of an ellipse calculated?
There is no simple exact formula, so this tool uses the Ramanujan second approximation. It is accurate to many decimal places for typical ellipses.
What does eccentricity mean?
Eccentricity measures how stretched an ellipse is. It is zero for a circle and approaches one as the ellipse becomes long and thin.
How is eccentricity computed here?
It equals the square root of one minus the squared ratio of the shorter axis to the longer axis, so it never depends on which axis you label major.
What units does this use?
It is unit free. Enter both axes in the same unit and the area is in square units while the circumference is in the same length unit.
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