Discoveries of ratios whose values are constant within broad classes of materials have led to many deep physical insights. The Kadowaki-Woods ratio (KWR; refs 1, 2) compares the temperature dependence of a metal's resistivity to that of its heat capacity, thereby probing the relationship between the electron-electron scattering rate and the renormalization of the electron mass. However, the KWR takes very different values in different materials(3,4). Here we introduce a ratio, closely related to the KWR, that includes the effects of carrier density and spatial dimensionality and takes the same (predicted) value in organic charge-transfer salts, transition-metal oxides, heavy fermions and transition metals-despite the numerator and denominator varying by ten orders of magnitude. Hence, in these materials, the same emergent physics is responsible for the mass enhancement and the quadratic temperature dependence of the resistivity, and no exotic explanations of their KWRs are required.