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:

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.

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

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See Also

What is an ellipse? Find the area of an ellipse ( interactive widget)