Ellipse Calculator (Area, Perimeter, Eccentricity)
By Santaji GadepatilinUpdated October 27, 2026
An ellipse is a stretched circle defined by two axes. Its area is simple to calculate, but its perimeter needs an approximation such as Ramanujan's formula.
How to use the ellipse calculator
Enter the semi-major axis (half the longest width) and the semi-minor axis (half the shortest width). You get the area, perimeter, eccentricity and the distance from the centre to each focus.
Ellipse formulas
| Quantity | Formula |
|---|---|
| Area | π a b |
| Perimeter (Ramanujan) | π [3(a + b) − √((3a + b)(a + 3b))] |
| Eccentricity | √(1 − b² ÷ a²) |
| Focus distance | √(a² − b²) |
Example
a = 10 cm, b = 6 cm:
- Area = π × 10 × 6 = 188.50 cm²
- Perimeter ≈ 51.05 cm
- Eccentricity = 0.8000
Ellipse table (a = 10)
| b | Area | Perimeter | Eccentricity |
|---|---|---|---|
| 10 | 314.2 | 62.83 | 0.000 |
| 8 | 251.3 | 56.72 | 0.600 |
| 6 | 188.5 | 51.05 | 0.800 |
| 4 | 125.7 | 46.03 | 0.917 |
| 2 | 62.8 | 42.01 | 0.980 |
| 1 | 31.4 | 40.61 | 0.995 |
When b = a, the ellipse is a circle and the eccentricity is 0.
Planet orbits
Planets move in ellipses with the Sun at one focus. Earth’s orbit has an eccentricity of about 0.017 — almost a circle. Halley’s Comet has about 0.967, a long, thin ellipse.
Drawing an ellipse
Push two pins into a board at the foci, loop a string of length 2a around them and trace with a pencil keeping the string tight. This is the gardener’s method for oval flower beds.
Frequently asked questions
What is the area of an ellipse?
π × a × b, where a and b are the semi-axes (half the longest and shortest widths).
Is there an exact formula for the perimeter of an ellipse?
No simple exact formula exists. Ramanujan’s approximation used here is accurate to within a tiny fraction of a percent for most shapes.
What is eccentricity?
A measure of how stretched the ellipse is, from 0 (a circle) to nearly 1 (very flat).
How do I measure an oval table?
Measure the full length and width, then halve each to get a and b.