Results. The total infrared luminosity (LIR), dust mass (Mdust), and dust temperature of the cold component (Tcold) form a plane that we refer to as the dust plane. A galaxy's sSFR drives its position on the dust plane: starburst (high sSFR) galaxies show higher LIR, Mdust, and Tcold compared to main sequence (typical sSFR) and passive galaxies (low sSFR). Starburst galaxies also show higher specific dust masses (Mdust/M-circle dot) and specific gas masses (Mgas/M-circle dot). We confirm earlier findings of an anti-correlation between the dust to stellar mass ratio and M-circle dot . We also find di ff erent anti-correlations depending on sSFR; the anti-correlation becomes stronger as the sSFR increases, with the spread due to di ff erent cold dust temperatures. The dust mass is more closely correlated with the total gas mass (atomic plus molecular) than with the individual atomic and molecular gas masses. Our comprehensive multiwavelength data allows us to define several equations to accurately estimate LIR, Mdust, and Tcold from one or two monochromatic luminosities in the infrared and/or sub-millimeter. Conclusions. It is possible to estimate the dust mass and infrared luminosity from a single monochromatic luminosity within the Rayleigh-Jeans tail of the dust emission, with errors of 0.12 and 0.20 dex, respectively. These errors are reduced to 0.05 and 0.10 dex, respectively, if the dust temperature of the cold component is used. The dust mass is better correlated with the total ISM mass (M-ISM/M-dust 0 : 7). For galaxies with stellar masses 8.5 < log(M-circle dot/M-circle dot) < 11.9, the conversion factor between the single monochromatic luminosity at 850 mu m and the total ISM mass (alpha 850 mu m) shows a large scatter (rms = 0.29 dex) and a weak correlation with the LIR. The star formation mode of a galaxy shows a correlation with both the gas mass and dust mass: the dustiest (high Mdust/M-circle dot) galaxies are gas-rich and show the highest SFRs.