The solar photospheric carbon abundance has been determined from [C I], C I, CH vibration-rotation, CH A-X electronic and C2 Swan electronic lines by means of a time-dependent, 3D, hydrodynamical model of the solar atmosphere. Departures from LTE have been considered for the C I lines. These turned out to be of increasing importance for stronger lines and are crucial to remove a trend in LTE abundances with the strengths of the lines. Very gratifying agreement is found among all the atomic and molecular abundance diagnostics in spite of their widely different line formation sensitivities. The mean value of the solar carbon abundance based on the four primary abundance indicators ([C I], C I, CH vibration-rotation, C2 Swan) is log ɛC = 8.39 ± 0.05, including our best estimate of possible systematic errors. Consistent results also come from the CH electronic lines, which we have relegated to a supporting role due to their sensitivity to the line broadening. The new 3D based solar C abundance is significantly lower than previously estimated in studies using 1D model atmospheres.