Follow a worked example.
Every example below can be loaded using its calculator’s Reset example button. Inputs use centimetres, square centimetres or cubic centimetres as labelled, while angles use degrees.
Two semi-axes
Given: Semi-major axis a = 6; Semi-minor axis b = 4.
A = πab; e = √(1−b²/a²)
| Measurement | Calculated value |
|---|---|
| Area | 75.398224 cm² |
| Perimeter (Ramanujan approximation) | 31.730879 cm |
| Eccentricity | 0.74535599 |
| Distance between foci | 8.9442719 cm |
Full axis lengths
Given: Major axis length = 12; Minor axis length = 8.
a = major axis/2; b = minor axis/2
| Measurement | Calculated value |
|---|---|
| Area | 75.398224 cm² |
| Perimeter (Ramanujan approximation) | 31.730879 cm |
| Eccentricity | 0.74535599 |
| Distance between foci | 8.9442719 cm |
Area and semi-major axis
Given: Area A = 75.3982236862; Semi-major axis a = 6.
b = A/(πa)
| Measurement | Calculated value |
|---|---|
| Area | 75.398224 cm² |
| Perimeter (Ramanujan approximation) | 31.730879 cm |
| Eccentricity | 0.74535599 |
| Distance between foci | 8.9442719 cm |
Semi-major axis and eccentricity
Given: Semi-major axis a = 6; Eccentricity e = 0.6.
b = a√(1−e²)
| Measurement | Calculated value |
|---|---|
| Area | 90.477868 cm² |
| Perimeter (Ramanujan approximation) | 34.034001 cm |
| Eccentricity | 0.6 |
| Distance between foci | 7.2 cm |
Check the answer’s dimensions
An area contains a product of two lengths, while volume contains three. A perimeter or radius is still a length. If your input measurements are mixed between metres and centimetres, convert them to a common unit first. A realistic-looking number can still be wrong if the units were inconsistent.