Area of an Ellipse
Area enclosed by an ellipse.
Formula
Variables
Example
Semi-axes a=5, b=3: A = π·5·3 ≈ 47.1 square units.
How it works
An ellipse is like a stretched circle, and its area depends on how far it stretches in two perpendicular directions. The formula A = πab comes from scaling a circle: if a circle of radius r has area πr², then stretching it to semi-axes a and b multiplies the area by those two scale factors, giving πab. Here, a and b must be the semi-major and semi-minor axes, not the full widths.
When to use it
Use this formula whenever you need the area of an ellipse-shaped region, such as an oval garden, lens, stadium end, or any ellipse in geometry and physics problems. It is also useful for approximating areas of shapes that are close to elliptical.
Worked example, step by step
Suppose an ellipse has semi-major axis a = 8 cm and semi-minor axis b = 4 cm. A = πab A = π × 8 × 4 A = 32π A ≈ 100.5 cm² So, the area of the ellipse is about 100.5 square centimetres.
Common mistakes to avoid
- Using the full axis lengths instead of the semi-axes
- Forgetting to multiply both a and b before applying π
- Mixing up ellipse area with the circle formula πr² and using only one radius
Did You Know?
An ellipse's area is πab — collapse it to a circle (a=b=r) and it becomes the familiar πr².
Share this formula
More in Geometry & Trigonometry
View allPythagorean Theorem
BasicRelates the sides of a right triangle.
Area of a Circle
BasicThe area enclosed by a circle.
Circumference of a Circle
BasicThe perimeter (boundary length) of a circle.
Equation of a Circle
IntermediateThe standard form of the equation of a circle with centre (h, k) and radius r.
Area of a Rectangle
BasicArea of a rectangle.
Area of a Triangle
BasicArea of a triangle from base and height.