About this calculator
Enter both axes.
How to use it
- Enter the semi-major axis.
- Enter the semi-minor axis.
- Read the results.
The formula
Area = πab; perimeter ≈ π(a + b)(1 + 3h ÷ (10 + √(4 − 3h))), h = ((a − b) ÷ (a + b))²
- a, b
- semi-axes
Worked example
a = 5, b = 3
- Area = 15π ≈ 47.12.
- Perimeter ≈ 25.53; eccentricity 0.8; foci 4 from the centre.
What the result means
When a = b, the ellipse is a circle and the eccentricity is 0.
Assumptions
- All lengths in the same unit.
Limitations
- Results are rounded to 10 significant figures.
Frequently asked questions
What is the area of an ellipse?
π × a × b.
Why is the perimeter approximate?
It has no simple exact formula; Ramanujan’s is very close.
What is eccentricity?
How stretched the ellipse is, from 0 to nearly 1.
Last reviewed on 3 October 2026. Found a mistake? Tell us.