This article describes a predictive model of explosive detonation velocity and pressure based on first-order approximation of the detonation velocity equation. Detonation pressure was calculated from equations derived from the ideal detonation theory since that pressure is functionally related to detonation velocity. In the model calibration process, several product formation hierarchies were explored, with the best results yielded by the Kamlet and Jacobs (KJ) hierarchy. The predictive capacity of our model (labelled DEoS) was tested using different experimental databases, and was compared with predictions by thermochemical models (BKW-RR, JCZ3-J and JCZS) and by the empirical KJ method. The prediction values obtained using an experimental database of 238 explosive substances (75 singles and 163 composites), for a range of densities (1 g cc-1 to 2 g cc-1), were excellent in terms of both velocity and pressure, with root mean square error values of 1.7% (519 data items) and 6.0% (263 data items), respectively. We analysed results, broken down by explosive type, in detail, finding that the model residuals did not correlate with the predictor variables and also that the model predicts reasonable values for other parameters in the detonation state, such as density, the Jones parameter, and the Grüneisen parameter.