In this paper, a mathematical description of the voltage response of a pyroelectric detector to a single rectangular pulse of optical radiation is presented. Mathematical procedures leading to the derivation of the dependencies describing the detector response for the cases, taking into account the duration of the radiation pulse absorbed by the detector and the relations between values of the electrical and thermal time constants of the detector, are shown in detail. The analytical results are compared and verified by experimental studies carried out using a commercially available pyroelectric detector (model PE10-S-Q) manufactured by the company Ophir. Comparison of the experimentally obtained data with analytical calculations showed good agreement.