Ellipse Calculator (Area & Perimeter)
Ellipse calculator: area, perimeter (Ramanujan’s approximation) and eccentricity from the semi-major and semi-minor axes.
A = π · a · b
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Area = π a b. The perimeter has no simple exact formula; Ramanujan’s approximation is accurate to a few parts per million.
Formula
A = π · a · b
| Symbol | Quantity | Units |
|---|---|---|
| a | Semi-major axis | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| b | Semi-minor axis | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| A | Area | m², km², cm², mm², ha, ft², in², yd², ac, mi² |
Worked example
Given: a = 5 cm · b = 3 cm
A = π a b
Result: A = 47.1239 cm²
Area for different values of Semi-major axis
| a · Semi-major axis | A · Area |
|---|---|
| 2.5 cm | 23.562 cm² |
| 3.75 cm | 35.343 cm² |
| 4.5 cm | 42.412 cm² |
| 5 cm | 47.124 cm² |
| 5.5 cm | 51.836 cm² |
| 6.25 cm | 58.905 cm² |
| 7.5 cm | 70.686 cm² |
| 10 cm | 94.248 cm² |
Other values as in the worked example.
Frequently asked questions
Ellipse with a = 5 cm, b = 3 cm?
Area ≈ 47.12 cm², perimeter ≈ 25.53 cm.
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