We apply a new method to determine the local disc matter and dark halo matter density to kinematic and position data for ˜2000 K dwarf stars taken from the literature. Our method assumes only that the disc is locally in dynamical equilibrium, and that the 'tilt' term in the Jeans equations is small up to ˜1 kpc above the plane. We present a new calculation of the photometric distances to the K dwarf stars, and use a Monte Carlo Markov chain to marginalize over uncertainties in both the baryonic mass distribution, and the velocity and distance errors for each individual star. We perform a series of tests to demonstrate that our results are insensitive to plausible systematic errors in our distance calibration, and we show that our method recovers the correct answer from a dynamically evolved N-body simulation of the Milky Way. We find a local dark matter density of ρ dm =0.025-0.013+0.014 Msun pc-3 (0.95-0.49+0.53 GeV cm-3) at 90 per cent confidence assuming no correction for the non-flatness of the local rotation curve, and ρ dm =0.022-0.013+0.015 Msun pc-3 (0.85-0.50+0.57 GeV cm-3) if the correction is included. Our 90 per cent lower bound on ρdm is larger than the canonical value typically assumed in the literature, and is at mild tension with extrapolations from the rotation curve that assume a spherical halo. Our result can be explained by a larger normalization for the local Milky Way rotation curve, an oblate dark matter halo, a local disc of dark matter or some combination of these.