The relationship between $A$, the area of a circle, and $r$, its radius, is $A=\pi r^2$. We can use this to find the area of a circle if we know the radius. For example, if a circle has a radius of 10 cm, then the area is $\pi \boldcdot 10^2$, or $100\pi$ cm². We can also use the formula to find the radius of a circle if we know the area. For example, if a circle has an area of $49 \pi$ m² then its radius is 7 m and its diameter is 14 m.

Sometimes instead of leaving $\pi$ in expressions for the area, a numerical approximation can be helpful. For the examples above, a circle of radius 10 cm has an area of about 314 cm². In a similar way, a circle with an area of 154 m² has a radius of about 7 m.

We can also figure out the area of a fraction of a circle. For example, the figure shows a circle divided into 3 pieces of equal area. The shaded part has an area of $\frac13 \pi r^2$.

A circle divided into three equal sections. From the center of the circle three line segments extend to a point on the circle. The line segment extending downward and to the right is labeled “r”. The upper left region of the circle is shaded.