# Ellipse Calculator

URL: https://speedycalculator.com/calculators/math/ellipse/
Last updated: 2026-10-25

> The ellipse calculator finds the area, approximate perimeter and eccentricity of an ellipse from its semi-major and semi-minor axes. The perimeter uses Ramanujan’s highly accurate approximation.

## Inputs

- Semi-major axis (a) (m, cm, mm, km, in, ft, yd, mi)
- Semi-minor axis (b) (m, cm, mm, km, in, ft, yd, mi)

## Results

- Area
- Perimeter (approx.)
- Eccentricity

## Formula

```
Area = π a b
Perimeter ≈ π[3(a + b) − √((3a + b)(a + 3b))]
```

## Explanation

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

FieldWhat to enterSemi-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)2.523.563.7535.34547.126.2558.97.570.691094.25

## 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.

## FAQ

**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.