\[S = \frac{\pi d^{2}}{4}\ \ \ \ \ \ \ \ \ \ \ \ | \cdot 4\ \ \ \ \ \]
\[4S = \pi d^{2}\ \ \ \ \ \ \ \ \ \ |\ :\pi\ \ \ \ \]
\[d^{2} = \frac{4S}{\pi}\text{\ \ \ }\]
\[d = \sqrt{\frac{4S}{\pi}\ } = 2\sqrt{\frac{S}{\pi}}.\]