Iridescent colours are colours that change with viewing or illumination geometry. While they are widespread in many living organisms, most evolutionary studies on iridescence do not take into account their full complexity. Few studies try to precisely characterize what makes iridescent colours special: their angular dependency. Yet, it is likely that this angular dependency has biological functions and is therefore submitted to evolutionary pressures. For this reason, evolutionary biologists need a repeatable method to measure iridescent colours as well as variables to precisely quantify the angular dependency. In this study, we use a theoretical approach to propose five variables that allow one to fully describe iridescent colours at every angle combination. Based on the results, we propose a new measurement protocol and statistical method to reliably characterize iridescence while minimizing the required number of time-consuming measurements. We use hummingbird iridescent feathers and butterfly iridescent wings as test cases to demonstrate the strengths of this new method. We show that our method is precise enough to be potentially used at intraspecific level while being also time-efficient enough to encompass large taxonomic scales.