The Simons Observatory (SO) is an upcoming experiment that will study temperature and polarization fluctuations in the cosmic microwave background (CMB) from the Atacama Desert in Chile. SO will field both a large aperture telescope (LAT) and an array of small aperture telescopes (SATs) that will observe in six bands with center frequencies spanning from 27 to 270 GHz. Key considerations during the SO design phase are vast, including the number of cameras per telescope, focal plane magnification and pixel density, in-band optical power and camera throughput, detector parameter tolerances, and scan strategy optimization. To inform the SO design in a rapid, organized, and traceable manner, we have created a Python-based sensitivity calculator with several state-of-the-art features, including detector-to-detector optical white-noise correlations, a handling of simulated and measured bandpasses, and propagation of low-level parameter uncertainties to uncertainty in on-sky noise performance. We discuss the mathematics of the sensitivity calculation, the calculator's object-oriented structure and key features, how it has informed the design of SO, and how it can enhance instrument design in the broader CMB community, particularly for CMB-S4.