Ellipse Calculator
Enter semi-major and semi-minor axes to calculate common geometric properties of an ellipse.
Area75.3982
Approx perimeter31.7309
Focal distance c4.4721
Eccentricity0.7454
How this tool works
Area A=πab. Focal distance c=√(a²−b²). Perimeter uses Ramanujan's approximation π[3(a+b)−√((3a+b)(a+3b))].
Example
For a=6 and b=4, area is about 75.398 square units and eccentricity is about 0.745.
Common questions
Why is the perimeter approximate?
Unlike a circle, an ellipse does not have a simple elementary closed-form perimeter formula; Ramanujan's expression is a highly useful approximation.
What if b is larger than a?
The interface expects a to be the semi-major axis. Swap the values if needed.