  Metallicity is a fundamental parameter that contributes to the physical
characteristics of a star. However, the low temperatures and complex molecules
present in M dwarf atmospheres make it difficult to measure their metallicities
using techniques that have been commonly used for Sun-like stars. Although
there has been significant progress in developing empirical methods to measure
M dwarf metallicities over the last few years, these techniques have been
developed primarily for early- to mid-M dwarfs. We present a method to measure
the metallicity of mid- to late-M dwarfs from moderate resolution (R~2000)
K-band (2.2 microns) spectra. We calibrate our formula using 44 wide binaries
containing an F, G, K, or early M primary of known metallicity and a mid- to
late-M dwarf companion. We show that similar features and techniques used for
early M dwarfs are still effective for late-M dwarfs. Our revised calibration
is accurate to 0.07 dex for M4.5-M9.5 dwarfs with -0.58<[Fe/H]<+0.56 and shows
no systematic trends with spectral type, metallicity, or the method used to
determine the primary star metallicity. We show that our method gives
consistent metallicities for the components of M+M wide binaries. We verify
that our new formula works for unresolved binaries by combining spectra of
single stars. Lastly, we show that our calibration gives consistent
metallicities with the Mann et al. (2013a) study for overlapping (M4-M5) stars,
establishing that the two calibrations can be used in combination to determine
metallicities across the entire M dwarf sequence.
