Functional Threshold Work Rate (kcal/kg/h): The maximum Calorie output an athlete can achieve in 1 hour per kilogram of body weight.

You've got inputs and outputs, some of which are measurable and some aren't. Tools like indirect calorimeters use input/output gas exchange to measure the human body's processes, while a direct calorimeter simply measures heat.

Cyclists use power output. It's easy to measure (these days) and efficiency doesn't seem to vary much with training, so this is a decent measure of input too. FTP is in W/kg. Since kJ of output is just power and time (a Joule is a Watt·Second), we combine two fun facts to know that kJ of output is roughly the same as kcal of input. First, 1 kJ = 4.184 kcal . Second, humans are about 25% efficient at taking the input calories to output work, and these two cancel! To this end, FTWR = (W/kg) * 3600/1000/4.184 first converting W into J by multiplying by an hour of seconds, converting the J to kJ, then convering those kJ into kcal by dividing by the conversion. Altogether, FTWR = FTP * .86 kcal/W/h .

Runners use pace. Most apps or fitness trackers (garmin, etc) will use the available data to estimate Calories burned (capital C means kcal). These take into account pace, gradient, and body weight (but not efficiency. Using these output Calorie estimates, it's not so straightfoward to convert into FTWR: efficiency varies by relative pace of the athlete (Barnes 2015). We're looking at a maximal effort here, so at 5 calories burned per liter of oxygen (Scott 2005) and using efficiencies in the range of 15-30% (Hoogkamer 2019) we'll just use 25% for easiest math and say: FTWR = Calories burned * .25 / kg . This isn't very satisfying, still. If you go from pace -> power (W/kg), you could do something like * 10 min/mile or 6.2 min/km: ~3.5 - 4.0 W/kg * 8 min/mile or 5.0 min/km: ~4.5 - 5.0 W/kg * 6 min/mile or 3.7 min/km: ~6.0 - 7.0 W/kg * ~4.5 min/mile or 2.8 min/km: ~7.5 - 8.5 W/kg to account for the nonlinearity, and use the cycling formula.

Weight training, albeit less commonly, uses velocity. Newton's law: F = m·a , so while VBT trackers have velocity, with knowledge of the weight they also have power and work. The values likely aren't comparable to running/cycling over an hour (an hour of deadlifts...).

All this leads me to think that we should measure this with the *input* rather than the output.
Or maybe don't worry about comparing between sports: cycling we can measure output, running we have to measure inputs.