Ellipse Area Calculator

Use $A = \pi \times a \times b$, where $a$ is the semi-major axis (half the longer diameter) and $b$ is the semi-minor axis (half the shorter diameter). When $a = b$, the ellipse is a circle and the formula reduces to $\pi r^2$.

The semi-major axis ($a$) is half the longest diameter of the ellipse. The semi-minor axis ($b$) is half the shortest diameter. Both are measured from the center to the edge. Always enter the half-lengths, not the full diameters.

Eccentricity $e = \sqrt{1 - \frac{b^2}{a^2}}$ measures how elongated an ellipse is. $e = 0$ means a perfect circle; $e$ close to 1 means a very stretched shape. Earth's orbit has $e \approx 0.017$ (nearly circular).

No. Unlike the circle, the ellipse has no closed-form perimeter formula — it requires an elliptic integral. Ramanujan's approximation $P \approx \pi\left[3(a+b) - \sqrt{(3a+b)(a+3b)}\right]$ is accurate to within 0.002% for all eccentricities.

An ellipse is a circle that has been uniformly stretched along one axis. If you scale a circle of radius $r$ by factor $k$ along one axis, you get an ellipse with semi-axes $r$ and $kr$. The area scales by the same factor: $\pi r^2$ becomes $\pi r \times kr = \pi k r^2$.