Area of an Ellipse Calculator
Calculate the area and approximate circumference of an ellipse from its semi-major and semi-minor axes. See also Area of Circle Calculator and Area of Sector Calculator.
How to Calculate the Area of an Ellipse
An ellipse is an oval shape defined by two axes: the semi-major axis (a) — the longer radius — and the semi-minor axis (b) — the shorter radius. To find the area, multiply π by both axes: A = π × a × b. When a = b, the ellipse becomes a circle and the formula reduces to A = πr². The circumference of an ellipse has no simple exact formula, so this calculator uses Ramanujan's approximation, which is accurate to within 0.01% for most ellipses.
Ellipse Area Formula
A = π × a × b
Circumference ≈ π(a + b)(1 + 3h/(10 + √(4 − 3h)))
where h = ((a − b)/(a + b))²
Example
Find the area of an ellipse with a = 8 and b = 5:
A = π × a × b
A = π × 8 × 5
A = 40π
A ≈ 125.6637 square units
Ellipse Area Reference Table
| a | b | Area | Circumference |
|---|---|---|---|
| 2 | 1 | 6.2832 | 9.6884 |
| 3 | 2 | 18.8496 | 15.8654 |
| 4 | 3 | 37.6991 | 22.1035 |
| 5 | 3 | 47.1239 | 25.5270 |
| 6 | 4 | 75.3982 | 31.7309 |
| 8 | 5 | 125.6637 | 41.3863 |
| 10 | 6 | 188.4956 | 51.0540 |
| 10 | 8 | 251.3274 | 56.7233 |
| 12 | 8 | 301.5929 | 63.4618 |
| 15 | 10 | 471.2389 | 79.3272 |
| 20 | 12 | 753.9822 | 102.1080 |
| 25 | 15 | 1178.0972 | 127.6350 |
Frequently Asked Questions
What is the difference between an ellipse and a circle?
A circle is a special case of an ellipse where both axes are equal (a = b = r). An ellipse has two different axis lengths, making it oval-shaped.
What is the eccentricity of an ellipse?
Eccentricity (e) measures how elongated an ellipse is: e = √(1 − b²/a²). A circle has e = 0, and as the ellipse gets more elongated, e approaches 1.
Why is the circumference approximate?
Unlike a circle, there is no simple closed-form formula for the exact circumference of an ellipse. It requires an elliptic integral. Ramanujan's approximation used here is extremely accurate for practical purposes.
What are the foci of an ellipse?
The foci are two special points inside the ellipse. The sum of distances from any point on the ellipse to both foci is constant and equals 2a. The distance from center to each focus is c = √(a² − b²).