We present a self-consistent cross-calibration of the three main molecular gas mass tracers in galaxies, namely the ^12^CO(1-0), [CI](^3^P_!_-^3^P_0_) lines,and the submm dust continuum emission, using asample of 407 galaxies, ranging from local disks to submillimetre-selected galaxies (SMGs) up to z~6. A Bayesian statistical method is used to produce galaxy-scale universal calibrations of these molecular gas indicators that hold over 3-4 orders of magnitude in infrared luminosity, L_IR_. Regarding the dust continuum, we use a mass-weighted dust temperature, T_mw_, determined using new empirical relations between temperature and luminosity. We find the average L/M_mol_ gas mass conversion factors (including He) to be {alpha}_850_=6.9x10^12^mW/Hz/M_{sun}_, {alpha}_CO_=4.0M_{sun}_/(K.(km/s)/pc^2^} and {alpha}_CI_=17.0M_{sun}/(K.(km/s)/pc^2^), based on the assumption that the mean dust properties of the sample ({kappa}_H_= gas-to-dust ratio/dust emissivity) will be similar to those of local metal rich galaxies and the Milky Way. The tracer with the least intrinsic scatter is CI(1-0), while CO(1-0) has the highest. The conversion factors show a weak but significant correlation with L_IR_ which is not apparent when T_mw_ is held constant. Assuming dust properties typical of metal-rich galaxies, we infer a neutral carbon abundance X_CI_=[C^0^/H_2_]=1.6x10^-5^, similar to that in the Milky Way. We find no evidence for bi-modality of aco between main- sequence (MS) galaxies and those with extreme star-formation intensity, i.e. ultraluminous infrared galaxies (ULIRGs) and SMGs. The means of the three conversion factors are found to be similar between MS galaxies and ULIRGs/SMGs, to within 10-20 per cent. The overarching conclusion of our work is that, for metal-rich galaxies, near-universal average values for aco, X_CI_ and kh are adequate for global molecular gas estimates within the expected uncertainties. The 1{sigma} scatter in our optimised values for {alpha}_CO_, X_CI_ and {kappa}_H_ are 0.14, 0.11 and 0.15dex respectively.