The voltage response of a water electrolyzer at low frequencies is characterized by a combination of a static polarization curve and dynamic, capacitive effects. In this paper, a model combining these two phenomena is created, which incorporates the Butler–Volmer equation in parallel with a capacitance in order to produce differential equations for the activation overpotentials separately on both electrodes. A parameter fitting methodology is then developed for obtaining the seven model parameters from a set of low-frequency, high-amplitude dynamic waveform measurements. The method is further implemented in an electrolyzer modeling toolbox for MATLAB. The model built in this study is proven to predict well both static and dynamic voltage responses down to the 1Hz frequency. At higher frequencies and at small amplitudes the model reduces to the Randles equivalent circuit, and in a static case to the polarization curve of the cell. The proposed methodology can be used for probing individual electrode properties with full-cell measurements and providing a reliable tool for simulating water electrolyzer voltage responses with arbitrary waveforms and amplitudes.