The current-voltage (I-V) curves of solar photovoltaic (PV) systems have been widely used as a tool to determine their electrical operation. Usually, I-V curves are described employing three cardinal points: the short-circuit point (0, I sc), the open-circuit point (V oc , 0), and the maximum power point (V mp , I mp). In this context, to study the I-V curves, the single-diode model (SDM) is often used. In this manuscript, we present a practical approach for determining the parameters domain of the SDM given a set of cardinal points. An in-depth mathematical analysis showed that the SDM must satisfy the following inequalities Voc /2 < V mp < V oc and Isc /2 < I mp < I sc. Then, it is possible to implicitly represent the SDM by a single parameter and, consequently, to determine its domain. For this purpose, a fast open-source computational algorithm for the single parameter domain of the SDM is presented. The algorithm has been computer-tested using 40 000 synthetically generated maximum power points which are processed in about one minute of the CPU time on a standard laptop computer. Moreover, as practical applications, the databases from the California Energy Commission and the NREL are analyzed using the presented algorithm.