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 \sim 2000 ) K - band ( \simeq 2.2 \mu m ) 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 \sim 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 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 .