Area of a Circle

The area of a circle follows from its radius alone, together with the constant pi, written $\pi$ and roughly equal to 3.1416.

• $S$ — the area
• $r$ — the radius
• $\pi$ — pi, the constant $3.14159\ldots$

Example

With the default radius $r = 5$:

The area is about 78.5398.

If you only know the diameter

The radius is half the diameter, so a circle 10 across has radius 5. Squaring the diameter instead of the radius gives four times the correct answer. To work straight from the diameter $d$, use $S = \dfrac{\pi d^2}{4}$.

Watch out

Area grows with the square of the radius: double the radius and the area becomes four times larger, triple it and the area is nine times larger. Do not confuse the area with the circumference $2\pi r$, which is a length (cm) rather than a length squared (cm²). Because $\pi$ cannot be written as a fraction, the answer is always an approximation.