The mass–luminosity relation for late-type stars has long been a critical tool for estimating stellar masses. However, there is growing need for both a higher-precision relation and a better understanding of systematic effects (e.g., metallicity). Here we present an empirical relationship between M K and M * spanning 0.075 M ⊙ < M * < 0.70 M ⊙. The relation is derived from 62 nearby binaries, whose orbits we determine using a combination of Keck/NIRC2 imaging, archival adaptive optics data, and literature astrometry. From their orbital parameters, we determine the total mass of each system, with a precision better than 1% in the best cases. We use these total masses, in combination with resolved K S magnitudes and system parallaxes, to calibrate the M K–M * relation. The resulting posteriors can be used to determine masses of single stars with a precision of 2%–3%, which we confirm by testing the relation on stars with individual dynamical masses from the literature. The precision is limited by scatter around the best-fit relation beyond measured M * uncertainties, perhaps driven by intrinsic variation in the M K–M * relation or underestimated uncertainties in the input parallaxes. We find that the effect of [Fe/H] on the M K–M * relation is likely negligible for metallicities in the solar neighborhood (0.0% ± 2.2% change in mass per dex change in [Fe/H]). This weak effect is consistent with predictions from the Dartmouth Stellar Evolution Database, but inconsistent with those from MESA Isochrones and Stellar Tracks (at 5σ). A sample of binaries with a wider range of abundances will be required to discern the importance of metallicity in extreme populations (e.g., in the Galactic halo or thick disk).