  We find a formula that relates the Fourier transform of a radial function on
$\mathbf{R}^n$ with the Fourier transform of the same function defined on
$\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the
Fourier transform of any radial function $f(r)$ in any dimension, provided one
knows the Fourier transform of the one-dimensional function $t\to f(|t|)$ and
the two-dimensional function $(x_1,x_2)\to f(|(x_1,x_2)|)$. We prove analogous
results for radial tempered distributions.
