We present distance scale measurements from the baryon acoustic oscillation signal in the constant stellar mass and low-redshift sample samples from the Data Release 12 of the Baryon Oscillation Spectroscopic Survey. The total volume probed is 14.5 Gpc3, a 10 per cent increment from Data Release 11. From an analysis of the spherically averaged correlation function, we infer a distance to z = 0.57 of $D_V(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 2028\pm 21$  Mpc and a distance to z = 0.32 of $D_V(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 1264\pm 22$  Mpc assuming a cosmology in which $r^{\rm fid}_{\rm d} = 147.10$  Mpc. From the anisotropic analysis, we find an angular diameter distance to z = 0.57 of $D_{\rm A}(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 1401\pm 21$  Mpc and a distance to z = 0.32 of 981 ± 20 Mpc, a 1.5 and 2.0 per cent measurement, respectively. The Hubble parameter at z = 0.57 is $H(z)r_{\rm d}/r^{\rm fid}_{\rm d} = 100.3\pm 3.7$  km s−1 Mpc−1 and its value at z = 0.32 is 79.2 ± 5.6 km s−1 Mpc−1, a 3.7 and 7.1 per cent measurement, respectively. These cosmic distance scale constraints are in excellent agreement with a Λ cold dark matter model with cosmological parameters released by the recent Planck 2015 results.