We show how to use on-shell unitarity methods to calculate renormalisation group coefficients such as beta functions and anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is equal to minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond. Based on arXiv:1607.06448.