rm -rf

Indoors, on a "smart trainer", the watts come from variable pedaling resistance built into the bike.
Outside, watts usage include 1. wind resistance, 2. elevation gain, 3. drivetrain losses.

Watts from:
Wind resistance goes up by the cube of the speed. For example, using an online bike speed calculator, with the same rider, 100w is 15 mph, 210 watts is just 20 mph. More than double the watts to add 33% more speed! (Even 1 or 2 mph increase is a significant amount of increased work.)
Elevation gain is quite proportional to the climbing speed for a rider -- 20% faster climbing is 20% more watts (ignoring the low speed's wind resistance changes, and power train changes). And climbing watts is proportional to the rider+bike weights at the same speeds
Drivetrain losses are fairly linear.

In summary, food calories consumed by exercise can be fairly accurately estimated from recorded watts and the exercise elapsed time. Calories have been estimated from heart rates and/or road speeds, but those numbers vary depending on conditions, so the accuracy is much lower.

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Calories calculated: (The "nerdy curiosity" section, my favorite.)
It's actually kilocalories, but we just say calories most of the time when talking about food energy. It can be fairly accurately estimated from the ride's watts x ride time.

Humans aren't very efficient. Approximately 20% to 24% of the food energy goes to actual work. The rest of the calories burned becomes heat! No wonder we need cooling!

The formulas:
kilojoules = kilowatts * time in seconds
kcals of useful work pedaling = kilojoules *0.24 (a units conversion multiplier)
kcals including heat losses = work kcals / 0.24 approx (the 20% to 24% human efficiency number) We want to know how much food energy was consumed by the exercise, including the heat lost.

Note that the "human efficiency factor of 20-24% kind of cancels out the typical 0.24 kcals multiplier.


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An example: I did a ride, recorded on Strava. It reports:
Time 1:09:23
Avg power 99 w
kjoules 413
calories 509

Checking the math:
joules: 99w* (69minutes*60seconds per minute) = 409,860. Divide by 1000, kjoules=409.8 Strava rounded off the displayed average watts to a whole number, that's why it's slightly different.
Using 22% useful work: calories burned = kjoules *0.24 / 0.22 = 450 food calories.
That's 13% lower than Strava's estimate. It looks like they use 19.5% as the human efficiency number. Huh, interesting. Or are they adding in some kind of baseline "sitting on the couch" calorie usage? It's not clear.

Anyway, whether it's 509 calories or 460 calories or 530 calories, that gives a good idea of how few calories are burned in real life pedaling. Humans on bikes are very efficient!

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But, the same ride uploaded to ridewithgps.com shows higher numbers:
kjoules = 434
calories=664. Seems high. I wonder how rwgps calculated this.