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Area of a Circle Using the Diameter

(KS3, Year 7)

The area of a circle is found using the formula: area_circle_diameter_formula

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

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? area circle diameter example

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.

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:

area circle formula

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

circle radius1

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: area_of_a_circle_mini

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

Substitute ^d⁄₂ for r: derive_area_using_diameter_1

The ^d⁄₂ in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared: derive_area_using_diameter_2

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.