Ellipse Calculator
Calculate area, circumference, eccentricity and foci of an ellipse from its semi-axes.
Inputs
Area
188.4956sq units
Circumference (approx)
51.0540units
Eccentricity
0.800000
Focal Distance (c)
8.0000units
Step by step
Area
A = π × 10 × 6
= 188.4956
Eccentricity
e = √(1 − (6/10)²)
= 0.800000
Focal distance from center
c = √(10² − 6²)
= 8.0000
Circumference (Ramanujan)
= 51.0540
How it works
An ellipse is defined by its semi-major axis a and semi-minor axis b. The area is πab. The circumference has no elementary closed form; this uses Ramanujan's approximation. Eccentricity measures how elongated the ellipse is (0 = circle, approaching 1 = very flat).
Formulas
Area
A = π × a × b
- a
- Semi-major axis
- b
- Semi-minor axis
Eccentricity
e = √(1 − b²/a²)
- a
- Semi-major axis
- b
- Semi-minor axis
Frequently Asked Questions
What if a equals b?
Then the ellipse is a circle with radius a, eccentricity 0, and circumference 2πa.
How accurate is the circumference approximation?
Ramanujan's formula is accurate to within 0.05% for all eccentricities. The exact value requires an elliptic integral.