I have got about 18 months worth of power data, the power meter calculates energy transferred to the crank in kJ (since it knows torque and rate of rotation this can be computed), if you look up the relationship between kJ and kCal and also the accepted range of human efficiencies (25% give or take a few %), you will find that these 2 conversion factors very nearly cancel out (with some individual variance accepted).
Even though they do not exactly cancel out, assuming they do still tends to lead to a better estimate than most other methods outside of a lab, i.e. I have a pretty good idea of how many calories I am burning per mile, or per hour etc.
If I calculate total energy expended over total miles, I get the value 44.22 kJ/mile, assuming the 1:1 ratio, we come to an estimate of ~44 kCal per mile. Total energy expendature over total time riding, I get the value 770.15 kJ/hour, so an estimate of 770 kCal/hour. Of course this then suggests an average speed (all time) of 17.5 mph.
Take the 1st one, 44 kCal per mile, is close to the rule of thumb Vickster commented on. Not sure where she read that? But I have posted the above before, albeit with less data.