Published data for large-amplitude asymptotic giant branch variables in the Large Magellanic Cloud (LMC) are re-analysed to establish the constants for an infrared (K) period-luminosity relation of the form MK={rho}[logP-2.38]+{delta}. A slope of {rho}=-3.51+/-0.20 and a zero-point of {delta}=-7.15+/-0.06 are found for oxygen-rich Miras (if a distance modulus of 18.39+/-0.05 is used for the LMC). Assuming this slope is applicable to Galactic Miras we discuss the zero-point for these stars using the revised Hipparcos parallaxes together with published very long baseline interferometry (VLBI) parallaxes for OH masers and Miras in globular clusters. These result in a mean zero-point of {delta}=-7.25+/-0.07 for O-rich Galactic Miras. The zero-point for Miras in the Galactic bulge is not significantly different from this value.