How to Find the Area of an Ellipse

Finding the Area of an Ellipse

The area of an ellipse is found using the formula:

In this formula, a is the semi-minor axis and b is the semi-major axis. The image below shows what we mean by the semi-minor and semi-major axis:

Interactive Widget

Use this interactive widget to create an ellipse and then calculate its area. Start by clicking in the shaded area.




Oops, it's broken!

Turn your phone on its side to use this widget.

How to Find the Area of an Ellipse

Finding the area of an ellipse is easy.

Question

What is the area of an ellipse with a semi-minor axis of 3 cm and a semi-major axis of 5 cm, as shown below?

Step-by-Step:

1

Start with the formula:

Area = πab

Don't forget: π is pi (≈ 3.14) and πab = π × a × b

2

Substitute the semi-minor and semi-major axis into the formula. In our example, a = 3 and b = 5.

Area = π × 3 × 5 = 47.1 cm2

Answer:

The area of the ellipse with a semi-minor axis of 3 cm and a semi-major axis of 5 cm is 47.1 cm2.

Slider

The slider below shows another real example of how to find the area of an ellipse.

Open the slider in a new tab

See Also

What is an ellipse?