Circle Area Calculator

The formula is $A = \pi r^2$, where $r$ is the radius. If you know the diameter $d$ instead, use $A = \frac{\pi d^2}{4}$. Both formulas give the same result since $r = \frac{d}{2}$.

Because area depends on $r^2$. If the radius becomes $2r$, the area becomes $\pi(2r)^2 = 4\pi r^2$, which is 4 times the original area. This quadratic scaling is why a 16-inch pizza has more than twice the area of an 8-inch pizza.

Use $A = \frac{C^2}{4\pi}$. First square the circumference, then divide by $4\pi$. For example, if $C = 31.42$, then $A = \frac{31.42^2}{4\pi} = \frac{987.2}{12.57} \approx 78.54$.

The derivative of area with respect to radius equals the circumference: $\frac{dA}{dr} = 2\pi r = C$. This means adding a thin ring of width $dr$ to a circle adds area equal to the circumference times $dr$.

Subtract the inner circle area from the outer: $A = \pi(R^2 - r^2)$, where $R$ is the outer radius and $r$ is the inner radius. This can also be factored as $A = \pi(R + r)(R - r)$.