Implying sigma from an at-the-money price in a normal model

In a model where the stock's terminal value is normal, centred on the current spot with standard deviation $\sigma$, you observe the market price $C$ of an at-the-money call (ignore discounting). How can you estimate $\sigma$ quickly?

$\sigma\approx\sqrt{2\pi}\,C\approx2.5\,C$. In this model the at-the-money call is worth exactly $\sigma/\sqrt{2\pi}$, so inverting gives $\sigma$ directly; with non-zero rates, first undo the discount factor.