The influence of meteorological conditions on wildfire behaviour and propagation has been recognised through the development of a variety of fire weather indices, which combine information on air temperature, atmospheric moisture and wind, amongst other factors. These indices have been employed in several different contexts ranging from fire behaviour prediction and understanding wildfire potential to identifying conditions conducive to blow-up fires. This paper considers four such indices in the absence of free moisture (i.e. zero rainfall, no dew, etc.) and demonstrates that to a very good approximation, and up to rescaling, all four fire weather indices are equivalent.