Area of a Circle Using the Diameter
(KS3, Year 7)

The Lesson

The area of a circle is found using the formula:

In this formula, d is the diameter of the circle. The image below shows what we mean by diameter:

Interactive Widget

Use this interactive widget to draw a circle and then calculate its area from the diameter. Start by clicking in the shaded area.
Diameter
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Radius (diameter ÷ 2)
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How to Find the Area of a Circle Using the Diameter

Finding the area of a circle using the diameter is easy.

Question

What is the area of a circle with a diameter of 10 cm, as shown below?

Step-by-Step:

1

Start with the formula:
Area = πd2⁄4
Don't forget: π is pi (≈ 3.14) and d2 = d × d (d squared) and / means ÷.

2

Substitute the diameter into the formula. In our example, d = 10.

Area = π × 102⁄4

Area = π × 10 × 10 ÷ 4

Area = π × 100 ÷ 4

Area = π × 25

Area = 3.14 × 25

Area = 78.5 cm2

Answer:

The area of the circle with a diameter of 10 cm is 78.5 cm2.

Lesson Slides

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

How to Find the Area of a Circle Using the Radius

The area of a circle can be found using the radius rather than the diameter. The area of a circle, using the radius, is found using the formula:

In the formula, r is the radius of the circle. The image below shows what we mean by radius:

Read more about how to find the area of a circle using the radius

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

Why Does This Formula Work?

The formula for the area of a circle is better known in terms of the radius:

The radius can be found from the diameter. The radius is half the length of the diameter:

Substitute d2 for r:

The d2 in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared:

This is is formula for the area of a circle using the diameter.

A Note on Units

The area of a circle is a length times a length, so we say its dimension is length2. (All areas are lengths squared). This affects the units used. If the diameter is in cm, the area is in cm2. If it is in inches, the area is in inches2.
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See Also

What is a circle? What is pi? What is the diameter? Find the area of a circle using the radius How to find the radius from the diameter The exponent where the base is a fraction What is the numerator? What is the denominator?