Star formation rates (SFRs) of galaxies are commonly calculated by converting the measured Hα luminosities (LHα) into current SFRs. This conversion is based on a constant initial mass function (IMF) independent of the total SFR. As was recently recognized, the maximum stellar mass in a star cluster is limited by the embedded total cluster mass and, in addition, the maximum embedded star cluster mass is constrained by the current SFR. The combination of these two relations leads to an integrated galactic initial stellar mass function (IGIMF, the IMF for the whole galaxy) which is steeper in the high-mass regime than the constant canonical IMF, and is dependent on the SFR of the galaxy. Consequently, the LHα-SFR relation becomes nonlinear and flattens for low SFRs. Especially for dwarf galaxies, the SFRs can be underestimated by up to 3 orders of magnitude. We revise the existing linear LHα-SFR relations using our IGIMF notion. These are likely to lead to a revision of cosmological star formation histories. We also demonstrate that in the case of the Sculptor dwarf irregular galaxies, the IGIMF formalism implies a linear dependence of the total SFR on the total galaxy gas mass. A constant gas depletion timescale of a few Gyr results independently of the galaxy gas mass, with a reduced scatter compared to the conventional results. Our findings are qualitatively independent of the explicit choice of the IGIMF details, and challenge current star formation theory in dwarf galaxies.