Q10 Temperature Coefficient

Q10 answers a single question: by what factor does a rate grow for every 10 K of warming? A rate that doubles over 10 K has a Q10 of 2 by definition, so this page is a definition and a way to describe two measurements, not a physical law. Biological rates such as respiration, enzyme activity and decomposition typically run a Q10 of 2 to 3, so 10 K of warming roughly doubles or triples such a rate. The formula does not explain why a rate responds to temperature; it only puts a number on how much.

The formula turns two measurements into that factor. The ratio $R_2/R_1$ says how many times faster the rate is at $T_2$ than at $T_1$, and the exponent $10/(T_2 - T_1)$ rescales that ratio to a step of 10 K. A rate that grows 4 times over 20 K has $4^{10/20} = 2$, a doubling for each 10 K. Only the temperature difference enters, so °C and K give the same answer, and the two rates can be in any unit as long as both use the same one.

For the worked example, a rate that goes from 1 to 2 between 20 °C and 30 °C has a Q10 of 2. A rate that goes from 1.5 to 6 between 10 °C and 30 °C also has a Q10 of 2, over a wider span. Run forward, a Q10 of 3 and a rate of 2 at 15 °C give a rate of 6 at 25 °C. Solved for temperature, a Q10 of 2 and a rate that grows 8-fold (three doublings) from 10 °C needs 30 K of warming, so it reaches 40 °C.

Q10 assumes the same factor for every 10 K step, which is exponential growth with temperature. The Arrhenius equation is the exponential law that Q10 approximates over a limited range, so a Q10 measured between two temperatures should be quoted with them and not carried far beyond them. The Arrhenius two-temperature page gives the chemistry version of the same rate ratio, with an activation energy in place of the per-10-K factor. Dolbear's law, a cricket's chirp rate against temperature, is an example of a rate that follows temperature.