The 'spin only' magnetic moment $\mu$ (in Bohr magnetons) of a transition metal ion with $n$ unpaired d-electrons is given by:

The spin-only formula is $\mu = \sqrt{n(n + 2)}\,\text{BM}$, where $n$ is the number of unpaired electrons. It comes from the spin angular momentum quantum number $S = n/2$ and the relation $\mu = 2\sqrt{S(S+1)}\,\text{BM} = \sqrt{n(n+2)}$. The actual magnetic moment can differ slightly due to orbital contribution; this is small for first-row transition ions in octahedral fields.