Area of an Ellipse
Calculate the area of an ellipse using A = πab.
Learn how to find the area from the semi-major and semi-minor axes.
The Formula
A = π × a × b
This formula calculates the area of an ellipse (an oval shape).
A circle is a special case of an ellipse where a = b = r.
Variables
| Symbol | Meaning |
|---|---|
| A | Area of the ellipse |
| π | Pi, approximately 3.14159 |
| a | Semi-major axis (half the longest diameter) |
| b | Semi-minor axis (half the shortest diameter) |
Example 1
Find the area of an ellipse with semi-major axis 8 cm and semi-minor axis 5 cm
a = 8, b = 5
A = π × 8 × 5 = π × 40
A ≈ 125.66 cm²
Example 2
An oval-shaped pool is 10 m long and 6 m wide. What is its surface area?
The full length is 10 m, so a = 10 / 2 = 5 m
The full width is 6 m, so b = 6 / 2 = 3 m
A = π × 5 × 3 = π × 15
A ≈ 47.12 m²
When to Use It
Use the area of an ellipse formula when:
- Calculating the area of oval-shaped objects (pools, tracks, mirrors)
- Working with planetary orbits (which are elliptical)
- Designing elliptical features in architecture or engineering
- Any time you have an oval where you know the two axis lengths