Instant area and perimeter for any ellipse — just enter your axes
Ellipse Dimensions
The semi-major axis (a) is the longer half-axis; the semi-minor axis (b) is the shorter one. Both values must be greater than zero. If you enter b > a the calculator still works — it will automatically use whichever is larger for eccentricity.
Results
Formulas used
An ellipse calculator lets you find the area and perimeter of an ellipse in seconds. Enter the semi-major axis (a) and semi-minor axis (b) in any unit — meters, centimeters, inches, or feet — and get the exact area (π × a × b) plus Ramanujan's high-accuracy perimeter approximation, eccentricity, and a live diagram, all without leaving your browser.
The area of an ellipse is exactly π × a × b, where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter). When a = b the ellipse is a circle and the formula reduces to the familiar πr².
Unlike a circle, there is no simple closed-form formula for the exact perimeter of an ellipse — it requires an infinite series called an elliptic integral. Ramanujan's approximation [π × (3(a+b) − √((3a+b)(a+3b)))] is accurate to within 0.02% for most practical shapes and is the industry standard for engineering use.
Eccentricity (e) measures how 'stretched' an ellipse is. It ranges from 0 (a perfect circle) to just under 1 (an extremely elongated shape). It is calculated as √(1 − (b/a)²). Planets orbit in ellipses; Earth's orbit has an eccentricity of about 0.0167, making it nearly circular.
Yes — the calculator works regardless of which axis value is larger. The labels a and b are conventional names; the area and perimeter results are symmetric, so swapping a and b gives the same area and perimeter. The eccentricity calculation automatically uses the larger value as the major axis.