Equations describing the optical throughput of a monochromator are used as a basis for modeling the dependency of the signal-to-noise ratio on the monochromator parameters and the limiting noise. In-depth evaluation is made for the detector noise-limited case with multiple detectors, i.e. a linear photodiode array detector. The model shows that the detection limit improves with the square root of the spectral bandpass and with the square root of the pixel width. A high resolution echelle monochromator and a low resolution (200 mm focal length) monochromator are both accurately described by the model. The two monochromators have comparable detection limits when the limiting noises are the same.