The pH plays an important role in many reactions in aqueous solution. In order to be able to quantitatively analyse reactions that involve shifting protonation equilibria, reaction solutions traditionally needed to be buffered to maintain constant pH. Unfortunately, buffer components can interfere with the reaction species in several ways, all of them are difficult to quantify. We propose a generally applicable computational method, which allows the quantitative analysis of reactions at non-constant pH. This circumvents the necessity to add buffer systems. The feasibility of the method is demonstrated by re-analysing the complex formation reaction between cyclam (1,4,8,11-tetraazacyclotetradecane) and Cu2+. In four spectrophotometric measurements, the reaction has been analysed at non-constant pH in the range between 6 and 1.2. Results obtained with the new method compare very well with published values.