How does the Ellipse Calculator work?

Area = π × a × b Then: Perimeter ≈ π × [3(a+b) − √((3a+b)(a+3b))] (Ramanujan) Then: Eccentricity = √(1 − (b/a)²) Then: A circle is an ellipse where a = b.

Can you give an example of how to use the Ellipse Calculator?

Example: Input a = 5, b = 3 gives a result of Area = π×5×3 = 47.12, Eccentricity ≈ 0.8.

Is the Ellipse Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Ellipse Calculator?

Our Ellipse Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Ellipse Calculator

Semi-major axis (a)

Semi-minor axis (b)

An ellipse is an oval curve defined by two focal points. It has two axes: the semi-major axis (a, longer) and semi-minor axis (b, shorter). Ellipses appear in planetary orbits, optics, and engineering.

Symbol	Name	Unit	Description
a	semi-major axis (half long axis)	length	—
b	semi-minor axis (half short axis)	length	—
e	eccentricity	—	measure of how "stretched" the ellipse is

a	b	Area	Eccentricity
5	3	47.12	0.80
10	6	188.50	0.80
8	5	125.66	0.78
7	7	153.94	0 (circle)

References

›Ellipse — Wolfram MathWorld

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Ellipse Calculator