For infrared FPA detectors applied to a low-temperature background, the first aspect that must be confirmed in the design stage is whether the performance of the detectors at low temperatures meets the application requirements. Using the basic theoretical formula of the unit detector, from the perspective of testing, the main performance parameters of the theoretical calculation formula for FPA detectors were deduced, including the peak responsivity, noise, peak detectivity, and dynamic range. In addition, flowchart of the calculation design for the detectors was proposed. The main parameters of the long-wave infrared FPA detector at low temperatures were designed, calculated, and verified using an example, and the results are in good agreement with the theoretical calculations. Thus, the theoretical formula and design calculation flow are practical and can provide a reference for designing infrared FPA detectors.