Finding the Diameter from the Area
(KS3, Year 7)

The Lesson

The diameter of a circle is found from the area of a circle using the formula:

diameter equals two times square root of area divided by pi In this formula, A is the area of the circle. The image below shows what we mean by finding the diameter from the circumference:

area and diameter on a circle

How to Find the Diameter from the Area

Finding the diameter from the area is easy.

Question

What is the diameter of the circle, with area 50 cm2, below?

Step-by-Step:

1

Start with the formula:
Diameter = 2√ (Aπ)
Don't forget: √ means square root, / means ÷ and π is pi (≈ 3.14)

2

Substitute the area into the formula. In our example, A = 50.
Diameter = √ (50π) Diameter = √ (50 ÷ π) Diameter = √ (50 ÷ 3.14) Diameter = √ 16 cm Diameter = 4 cm

Answer:

The diameter of the circle is 4 cm.

Lesson Slides

The slider below shows another real example of how to find the diameter of a circle from the area. Open the slider in a new tab

Interactive Widget

Here is an interactive widget to help you learn about finding the diameter of a circle from its area.

Equivalent Formula for Finding the Diameter of a Circle from the Area

An equivalent formula for how to find the diameter of a circle from the area is:

This is equivalent as the square root of 4 is 2.
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See Also

What is the diameter? What is a circle? Finding the area of a circle Finding the area of a circle using the diameter Find the diameter from the area of a circle ( interactive widget)