While moving to our new home, many of my hard-won good health habits fell by the wayside, including getting on the trainer several times a week. Yesterday I got back on at last. Hooray! I’ll be doing it again today, you can be sure.

I’ve mused in the past about the physiological effects of burning 500 calories at a stretch, but I’ve been wondering just how accurate the readout is on the exercise machine. Do I really burn more than 500 calories each time, or is the number inflated to make me feel good? Well, let’s do a little math and see what comes out, shall we?

A calorie is a measure of energy. The first thing to do is convert that to a unit that’s easier to work with, the joule. Several conversion factors from calorie to joule exist (the calorie changes depending on conditions), but they all fall in the ballpark of 4.2 joules per calorie, or 4200 joules per dietary calorie. Multiply by roughly 500 and you get in the neighborhood of 2,000,000 joules. (We’re rounding things off aggressively here, because we are dealing with estimates anyway.)

Is that a reasonable number? It’s harder than ever to tell, but now we can figure out how many watts I’m generating. A watt is a joule per second. It takes me half an hour to burn the alleged 500 cal, so if we take our 2 megajoules and divide by the number of seconds, we get 2000000/(30*60) ≈ 1100 watts. Now there’s a number we can check.

I found this interesting article which has a lot of facts but no references. It seems to borrow (without attribution) from this wikipedia article which in turn cites “lab experiments”. Wherever the original source, we get that an in-shape person can sustain 3 watts/kg of body mass for more than an hour. So if we take what I would weigh if I was in shape and multiply by 3, that would be a reasonable output.

And that’s… 220 watts at the heaviest definition of “in shape” for me. Not even close to what the machine says.

OK, I could never sustain that rate for a full hour, so let’s fudge the number upwards a little and call it 250 watts.

That’s still less than a fourth of what the machine says I’m burning. Could it really be so far off?

Well, there’s another factor in the muddle. The articles above talk about the energy I’m producing, not the calories I’m burning. this article gives a once-more-unattributed (“has been measured”) number of 18-25% for the efficiency of human muscle. So, every joule a cyclist produces requires burning at least four joules of stored food energy.

By that estimate, if I’m producing 250 watts of power, I have to be metabolizing at a rate of about… 1100 watts!

Which is to say, 500 dietary calories in half an hour is probably a reasonable estimate, as long as we don’t forget the “estimate” part.

BONUS! Here’s another interesting article, in which the author actually cites his sources. Hooray!