How to Find the Area of a Circle

The area of a circle is the space inside it, measured in square units. It depends only on the radius (the distance from the center to the edge) and the number π (pi, about 3.14159).

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The steps

Find the radius. If you are given the diameter (all the way across), the radius is half of it.
Write the formula: A = π × r².
Square the radius: multiply it by itself.
Multiply by π. Leave the answer as a multiple of π (exact), or use 3.14159 or the π key for a decimal.
Write the units as square units, such as cm² or square feet.

A worked example

Find the area of a circle with radius 5 cm.

The radius is r = 5.
Square it: 5² = 25.
Multiply by π: A = π × 25 = 25π.
As a decimal: 25 × 3.14159 ≈ 78.54.

The area is 25π cm², which is about 78.54 cm².

Why it works

Why the radius is squared: double the radius and the circle is twice as wide and twice as tall, so it covers four times the area. That "times 4" is what r² does. The number π is what makes the squares fit the curve: a circle's area is a little more than 3 squares built on its radius (3.14159 of them).

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Common mistakes

Using the diameter as the radius. A circle 10 cm across has radius 5.
Doubling instead of squaring. r² means r × r, not r × 2.
Mixing up area and circumference. Circumference (the distance around) is 2πr and is measured in plain units; area uses r² and is in square units.
Forgetting the units are squared. Write cm², not cm.

Questions people ask

What if I know the diameter?

Halve it to get the radius, then use A = πr². Or use A = π × d²/4.

What is the circumference of this circle?

2 × π × 5 = 10π ≈ 31.42 cm.

Why does π appear?

π is the ratio of any circle's circumference to its diameter. It is the same for every circle.

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