Reviewed by CalcMulti Editorial Team·Last updated: ·← Geometry Hub
An ellipse is an oval shape defined by two axes: the semi-major axis a (longest radius) and the semi-minor axis b (shortest radius). The area is A = π × a × b. When a = b, the ellipse becomes a circle with area πr².
Unlike the circle, there is no simple exact formula for the perimeter of an ellipse. This calculator uses Ramanujan's approximation: P ≈ π × [3(a+b) − √((3a+b)(a+3b))], which is accurate to within 0.0001% for most ellipses.
A = π × a × b
Semi-major axis a ≥ semi-minor axis b (if b > a, they will be swapped)
| b (semi-minor) | Area | Perimeter | Eccentricity |
|---|---|---|---|
| 2 | 62.83 | 42.02 | 0.9798 |
| 4 | 125.66 | 46.03 | 0.9165 |
| 5 | 157.08 | 48.44 | 0.8660 |
| 6 | 188.50 | 51.05 | 0.8000 |
| 7 | 219.91 | 53.82 | 0.7141 |
| 8 | 251.33 | 56.72 | 0.6000 |
| 9 | 282.74 | 59.73 | 0.4359 |
| 10 | 314.16 | 62.83 | 0.0000 |
A = πr² — special ellipse where a = b
Sector Area CalculatorArea and arc length of a circular sector
Polygon Area CalculatorArea of regular polygons 3–12 sides
Perimeter CalculatorPerimeter of rectangles, triangles, circles
Surface Area Calculator3D shapes surface area — sphere, cylinder, cone
Sphere Volume CalculatorV = (4/3)πr³ — volume and surface area
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.