About 70-80% of stars in our solar and galactic neighborhood are M dwarfs. They span a range of low masses (0.08 -0.6 solar mass) and low temperatures (between 2500 K -4000 K), facilitating molecule formation throughout their atmospheres. Standard stellar atmosphere models primarily designed for FGK stars have challenges in accurately characterizing broadband molecular features in spectra of cool stars. Here, we introduce SPHINX-a new low-resolution (R∼250) 1-D self-consistent radiativeconvective thermochemical equilibrium chemistry grid of model atmospheres and spectra for characterizing M dwarfs. We incorporate the most up-to-date pre-computed absorption cross-section data with appropriate pressure-broadening treatment for key molecules dominant in late-K, early/main-sequence-M star atmospheres in our grid. We then validate our grid models by acquiring fundamental properties (T ef f , logg, metallicity, radius and C/O ratio) for a sample of 20 stars-10 benchmark M+G binary stars with known host star metallicities and 10 M dwarfs with interferometrically measured angular diameters. Incorporating a Gaussian-process inference tool Starf ish, we also account for correlated and systematic noise sources in our grid-model fitting routine for low-resolution (R∼120) (spectral stitching of SpeX, SN IF S, and HST ST IS) observations and derive robust estimates of fundamental M dwarf atmospheric parameters. We also assess the influence of stellar photospheric heterogeneity on the acquired metallicity for a couple targets and find that could explain some deviations from observations. Moreover, we also probe whether the model-assumed mixing-length parameter for convection influences inferred radii, stellar effective temperature, and [M/H] to explain possible discrepancies compared to interferometry data and again find that this may bridge the gap between observations and model-derived stellar parameter deviations for cooler M dwarfs. Mainly, we show the unique strength in leveraging broadband molecular absorption features occurring in low-resolution M dwarf spectra and demonstrate the ability to improve constraints on fundamental stellar properties of exoplanet hosts and late brown dwarf companions.