A mathematical model from which detection range may be predicted is developed. The model is specific to systems that base detection upon the exceeding of a threshold voltage by signal plus noise voltage. It is not restricted to a particular electromagnetic wavelength region. The model is applied to a passive infrared detection system. Normalized detection range is given in graphical form as a function of a wide range of values of normalized closure between scans, normalized range at initiation of scan, false alarm rate parameter, and degree of target scintillation, for probabilities of detection of 0.9, 0.7 and 0.5. Specification of the characteristics of a particular system-target-environment complex will allow rapid calculation of detection range for a prescribed probability of detection.