Ellipses describe planetary orbits, oval tables and stretched circles.
How to use the Ellipse Calculator
- Semi-major axis (a)
- Semi-minor axis (b)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Area is exact. The perimeter has no simple exact formula, so Ramanujan’s approximation is used.
Inputs explained
| Field | What to enter |
|---|---|
| Semi-major axis (a) | Units: m, cm, mm, km, in, ft … |
| Semi-minor axis (b) | Units: m, cm, mm, km, in, ft … |
What each result means
- Area = pi×[Semi-major axis (a)]×[Semi-minor axis (b)]
- Perimeter (approx.) = pi×(3×([Semi-major axis (a)] + [Semi-minor axis (b)]) – sqrt((3×[Semi-major axis (a)] + [Semi-minor axis (b)])×([Semi-major axis (a)] + 3×[Semi-minor axis (b)])))
- Eccentricity = sqrt(1 – (min([Semi-major axis (a)],[Semi-minor axis (b)])÷max([Semi-major axis (a)],[Semi-minor axis (b)]))^2)
Example values
How the main result changes when Semi-major axis changes and everything else stays at the example values above:
| Semi-major axis (a) (m) | Area (m²) |
|---|---|
| 2.5 | 23.56 |
| 3.75 | 35.34 |
| 5 | 47.12 |
| 6.25 | 58.9 |
| 7.5 | 70.69 |
| 10 | 94.25 |
Formula
Area = π a bPerimeter ≈ π[3(a + b) − √((3a + b)(a + 3b))]Worked example
Inputs — Semi-major axis (a): 5 m; Semi-minor axis (b): 3 m.
Results — Area = 47.12 m²; Perimeter (approx.) = 25.53 m; Eccentricity = 0.8.
Frequently asked questions
What is eccentricity?
A measure of how stretched the ellipse is: 0 is a circle, close to 1 is very flat.
How accurate is the perimeter?
Ramanujan’s formula is accurate to a tiny fraction of a percent for most ellipses.
What formula does the Ellipse Calculator use?
Area = π a b.