Area of a circle

What the symbols mean

$A$

the area inside the circle

$r$

the radius: centre to edge (half the diameter)

$\pi$

pi, about 3.14159: the ratio of any circle's circumference to its diameter

When to use it

Use it for anything round and flat: pizzas, pipes in cross-section, circular gardens, the area a sprinkler covers. Working backwards gives the radius needed for a given area. If you are given the diameter, halve it first.

Why it works

Cut a circle into many thin slices and lay them top to tail: they form a shape close to a rectangle whose height is r and whose length is half the circumference, $\pi r$. Its area is $\pi r\times r$. The more slices, the closer the fit.

Common mistakes

• Using the diameter as r. A 30 cm pizza has r = 15 cm; using 30 gives four times the area.
• Squaring π as well: it is $\pi \times r^2$, not $(\pi r{)}^2$.
• Thinking doubling the radius doubles the area. It multiplies the area by 4.