Ellipse Calculator
Enter semi-axes to calculate area, circumference, and eccentricity.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter the two semi-axis lengths to get the area and approximate circumference of an ellipse.
- Enter semi-axis a. This is half the length of the longest diameter.
- Enter semi-axis b. This is half the length of the shortest diameter.
- Read results. Area, circumference approximation, and eccentricity appear instantly.
The circumference uses Ramanujan's approximation, which is highly accurate for most ellipses.
About Ellipses
An ellipse is a closed curve where the sum of distances from any point on the curve to two fixed points (foci) is constant. The area is exactly pi * a * b. Unlike a circle, the circumference of an ellipse has no closed-form solution and must be approximated. The eccentricity measures how elongated the ellipse is, ranging from 0 (a circle) to nearly 1 (very elongated).
Frequently Asked Questions
What is the formula for ellipse area?
The area of an ellipse is pi * a * b, where a and b are the semi-major and semi-minor axes.
How is ellipse circumference calculated?
There is no exact formula. This calculator uses Ramanujan's approximation: C is approximately pi * (3(a+b) - sqrt((3a+b)(a+3b))).
What is eccentricity?
Eccentricity measures how much an ellipse deviates from being circular. It ranges from 0 (perfect circle) to values approaching 1 (very elongated).