Area of an Ellipse
(KS3, Year 7)
The area of an ellipse is found using the formula:

area ellipse 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:

ellipse radius2

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? ellipse radius1

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.

"Find the Area" Widget

Here is a widget to help you learn the formulas to find the areas of different shapes.
  • Click on the shape you're learning about.
  • Click on the pad to start.
  • Follow the instructions in the bottom-left corner.
  • On the last click, the formula, workings, and answer will appear in the yellow box.
  • Enjoy!
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Lesson Slides

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

What Is an Ellipse?

An ellipse is a squashed circle. It is symmetrical about its longest axis (called the major axis) and its shortest axis (called the minor axis).

ellipse explained Half of the major axis is the semi-major axis. Half of the minor axis is the semi-minor axis.

ellipse explained1
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This page was written by Stephen Clarke.