Area of an Ellipse: A = πab
The area of an ellipse formula is A = πab, where a and b are the semi-axes: half the longest width and half the shortest width.
Ellipse
An ellipse is a stretched circle with a semi-major axis a and a semi-minor axis b. The perimeter has no simple exact formula, so Ramanujan’s approximation is used.
- Area
- A = πab
- Perimeter (approx.)
- P ≈ π[3(a + b) − √((3a + b)(a + 3b))]
- a semi-major axis
- b semi-minor axis
Why πab?
An ellipse is a circle stretched in one direction. Stretching a circle of radius b by a factor a ⁄ b turns its area πb² into πb² × a ⁄ b = πab. When a = b, it is a circle again and the formula becomes πr².
Worked example
An ellipse is 10 cm long and 6 cm wide.
- a = 10 ÷ 2 = 5 cm, b = 6 ÷ 2 = 3 cm
- A = π × 5 × 3 = π × 15
- A = 47.12 cm²
What about the perimeter?
There is no simple exact formula. Ramanujan’s estimate is very close: P ≈ π[3(a + b) − √((3a + b)(a + 3b))]. For a = 5, b = 3: P ≈ 25.53 cm.
Try the ellipse calculator
Try it yourself
An oval rug is 2 m long and 1.2 m wide. What is its area?
Show the answer
A = π × 1 × 0.6 = 1.88 m²
More on the ellipse formulas page.
Area of an ellipse: FAQ
What is the area of an ellipse?
A = πab, where a and b are the semi-major and semi-minor axes.
Is a circle an ellipse?
Yes. It is an ellipse with a = b = r, so A = πr².
Is there an exact formula for the perimeter of an ellipse?
Not a simple one. Ramanujan’s approximation is accurate enough for almost any use.