Ellipse Area and Perimeter
Area, approximate perimeter and eccentricity of an ellipse from its two semi-axes.
Results
Area
18.8496
m²
Perimeter
15.8654
m
Ratio
0.74536
What this tool does
The area of an ellipse is exact and simple: π times the two semi-axes. The perimeter has no elementary exact formula, so this uses Ramanujan's approximation, which stays within about one part in ten million for ordinary shapes.
Formula
A = π × a × b , P ≈ π[3(a+b) − √((3a+b)(a+3b))]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Semi-axis a | m |
b | Semi-axis b | m |
A | Area | m² |
P | Perimeter | m |
E | Ratio | — |
Worked example
- Semi-axis a3 m
- Semi-axis b2 m
- Area18.8496 m²
- Perimeter15.8654 m
- Ratio0.74536
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.