Area of a Circle Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the area of a circle?

Answer

Area of a circle
A = π · r²

Here r is the radius. The result comes out in square units.

Where the formula comes from

A = π · r²

Cut the disc into many thin wedges and lay them alternately point-up and point-down: they comb together into something that gets closer and closer to a rectangle as the wedges get thinner. Its height is the radius r, and its base is half the circumference, πr. Multiply them and you have πr².

Worked examples

Let r = 5. Then the area of a circle ≈ 78.54 square units.

Let r = 3.2. Then the area of a circle ≈ 32.17 square units.

The common mistake

Putting the diameter where the radius belongs. It makes the answer four times too big, because the radius is squared: a circle 10 across has area π·5², not π·10². Halve the diameter first.

Other quantities: Circle

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a circle? (The answer is: A = π · r²). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula

If r =Area
1≈ 3.14 square units
2≈ 12.57 square units
3≈ 28.27 square units
4≈ 50.27 square units
5≈ 78.54 square units
10≈ 314.16 square units

FAQ

What is the formula for the area of a circle?

Area of a circle A = π · r²

Where does this formula come from?

Cut the disc into many thin wedges and lay them alternately point-up and point-down: they comb together into something that gets closer and closer to a rectangle as the wedges get thinner. Its height is the radius r, and its base is half the circumference, πr. Multiply them and you have πr².

What is the most common mistake here?

Putting the diameter where the radius belongs. It makes the answer four times too big, because the radius is squared: a circle 10 across has area π·5², not π·10². Halve the diameter first.

How do I use this formula?

Put your own numbers in place of the letters. With r = 3.2, for instance, the formula A = π · r² gives ≈ 32.17 square units.

See Also