From 21 independent Baryon Acoustic Oscillation (BAO) measurements we obtain the following sum of masses of active Dirac or Majorana neutrinos: $sum m_ u = 0.711 - 0.335 cdot delta h + 0.050 cdot delta b pm 0.063 textrm{ eV,}$ where $delta h equiv (h - 0.678) / 0.009$ and $delta b equiv (Omega_b h^2 - 0.02226) / 0.00023$. This result may be combined with independent measurements that constrain the parameters $sum m_ u$, $h$, and $Omega_b h^2$. For $delta h = pm 1$ and $delta b = pm 1$, we obtain $m_ u < 0.43$ eV at 95% confidence.