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There is growing evidence that M-dwarf stars suffer radius inflation whencompared to theoretical models, suggesting that models are missing some keyphysics required to completely describe stars at effective temperatures$(T_{\rm SED})$ less than about 4000K. The advent of Gaia DR2 distances finallymakes available large datasets to determine the nature and extent of thiseffect. We employ an all-sky sample, comprising of $>$15\,000 stars, todetermine empirical relationships between luminosity, temperature and radius.This is accomplished using only geometric distances and multiwave-bandphotometry, by utilising a modified spectral energy distribution fittingmethod. The radii we measure show an inflation of $3 - 7\%$ compared to models,but no more than a $1 - 2\%$ intrinsic spread in the inflated sequence. We showthat we are currently able to determine M-dwarf radii to an accuracy of $2.4\%$using our method. However, we determine that this is limited by the precisionof metallicity measurements, which contribute $1.7\%$ to the measured radiusscatter. We also present evidence that stellar magnetism is currently unable toexplain radius inflation in M-dwarfs.

Exploring the M-dwarf Luminosity--Temperature--Radius Relationships using Gaia DR2