The answer is that there is no way to calculate it based on HR. The estimations that you can find will vary wildly, as each is based on a whole series of assumptions that are designed to give an average for the population - not useful at all for calculating what a particular person burns with any kind of precision or accuracy.

The only way to accurately assess calories is through the use of a power meter, as it objectively and precisely quantifies output (ie energy spent). Even then, however, there is a bit of a fudge factor, because even though 1 kJ is more or less equal to 1 kCal (or .9kCal), the precise efficiency at which a person converts calories into energy output varies. The range of variation across the population is reasonably small, and for an individual it can vary over the course of a season, so it is not that worth losing sleep over, but even in this case there is some loss of precision. Still, a power meter actually gives a meaningful quantification of calories burned, which HR cannot do.