A precision measurement of the B+c meson mass is performed using proton-proton collision data collected with the LHCb experiment at centre-of-mass energies of 7,8 and 13 TeV, corresponding to a total integrated luminosity of 9.0fb−1. The B+c mesons are reconstructed via the decays B+c→J/ψπ+, B+c→J/ψπ+π−π+, B+c→J/ψpp¯π+, B+c→J/ψD+s, B+c→J/ψD0K+ and B+c→B0sπ+. Combining the results of the individual decay channels, the B+c mass is measured to be 6274.47±0.27(stat)±0.17(syst)MeV/c2. This is the most precise measurement of the B+c mass to date. The difference between the B+c and B0s meson masses is measured to be 907.75±0.37(stat)±0.27(syst)MeV/c2.