MihsabaHow to use
An ellipse is described by two semi-axes. Area is exact; circumference has no simple elementary closed form, so this tool uses Ramanujan’s approximation and also reports eccentricity and focal distance.
- Enter the two semi-axes.
- They may be entered in either order; the tool identifies major and minor automatically.
- Choose the unit.
- Review area, approximate circumference, eccentricity and focal distance.
How it is calculated
A=πab; e=√(1−b²/a²); circumference by Ramanujan approximation
Example
For semi-axes 5 and 3: area=15π≈47.124, eccentricity=0.8 and focal distance=4.
Important notes
When the semi-axes are equal, the ellipse is a circle and eccentricity is zero. Circumference is an approximation.
Frequently asked questions
Is the circumference exact?
Area is exact; circumference uses a highly accurate Ramanujan approximation.
What is eccentricity?
A value from 0 to below 1 describing how stretched the ellipse is.
What is focal distance?
Distance from center to each focus: c=a√(1−b²/a²).
Is this calculator free?
Yes. It is free to use and requires no account.