Quick approximation for an at-the-money call price

A European call on a non-dividend stock is struck at the current price $S$. Interest rates are near zero and the time to expiry $T$ is short. Give a simple approximation for the call value in terms of $S$, $\sigma$ and $T$.

$C\approx0.4\,\sigma S\sqrt{T}$. With $r\approx0$ and $S=K$, $d_{1,2}=\pm\tfrac12\sigma\sqrt T$ are small, so $N(d_1)-N(d_2)\approx\sigma\sqrt T\,n(0)=\sigma\sqrt T/\sqrt{2\pi}$, and $1/\sqrt{2\pi}\approx0.4$.