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I'm trying to find out how I can convert calories into Watt hours on Strava rides. I know the formula that 1 kJ = 1000 Ws but calorie unit is different. When I looked up to the formula to convert calories to joules, I found this:

1 cal(th) = 4.184 J

However, when I calculate with this formula it doesn't give me any meaningful result.

Can you check out below ride and tell me how to find out average power in Watts?

https://www.strava.com/activities/6797539669

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    I wonder how these calcuations would compare to the empirical readings from a power meter for the same ride.
    – Criggie
    Commented Mar 10, 2022 at 10:20
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    Strava estimated power calculations are much lower comparing to power meter readings: youtu.be/7vG8Z906rPo
    – Ender
    Commented Mar 10, 2022 at 10:40
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    "Watts per hour" makes no sense, as watts are a unit of power, i.e. a rate of energy. You can convert between energy in calories and in watt-hours - is that what you meant? Commented Mar 10, 2022 at 16:45
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    The correct formula is 1J = 1Ws, where J, W, and s are the units Joule, Watt, and second, respectively. Please correct the formula in the first paragraph. Also note that Americans have the annoying habit of calling the kilo-calorie kcal, or big calorie Cal, simply calorie. Which, of course, is plain wrong. And which easily, and unnecessarily confuses such calculations by a factor of 1000: 1cal = 4.184J and 1kcal = 1Cal = 4.184kJ. Commented Mar 10, 2022 at 17:17
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    @TobySpeight Watts per hour might be a bit redundant in the cycling use case, but W/s would be the rate (slope) of ramp up or ramp down of power in a ERG mode workout on Zwift or similar. Definitely a thing, at least IMO. 'Acceleration of energy', if you will, although that's a bit confusing 😆 Commented Mar 10, 2022 at 23:36

4 Answers 4

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Turning my comment into an answer:

Watts in a bicycling context are usually measured (or estimated) as mechanical power at the wheel (or crank). Calories burned are the (estimated) total input energy. 2720kcal are 11.3MWs. Over 4h3m that’s an average of 765W total (heat+mechanical) power output. Assuming 22% muscle efficiency that would be 168W average mechanical output power.

Usually calories burned are estimated based on measured mechanical power. The big uncertainty is really the muscle (in)efficiency. I dimly recalled 30% but a quick Google search shows up 18 – 24%. It very much varies between individuals and also depends on intensity.

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  • I think the exact numbers should be: 2.720 kcal are 11.38MWs. (1 cal = 4,184 J) Over 4h3m that’s an average of 780,55W total (heat+mechanical) power output. Assuming 22% muscle efficiency that would be 171W average mechanical output power.
    – Ender
    Commented Mar 10, 2022 at 10:09
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    A minor nitpick: 22% muscle efficiency is an assumption, and moreover it's something like an average value. Individuals will vary somewhat in what their actual muscle efficiency is. Unfortunately, there's no practical way for you to actually measure yours (lab testing would be it). Some more info here, article is (I believe) open access ncbi.nlm.nih.gov/pmc/articles/PMC3761728
    – Weiwen Ng
    Commented Mar 10, 2022 at 15:06
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    @WeiwenNg: Yes, but a power meter (or Strava) is also making a simple assumption to produce the “calories burned” number. I think van Vleuten in OP’s example simply chose not to publish her power numbers. But maybe her “calories” are still based on real power meter values and can be converted back to actual power if one knew the conversion factor Garmin (or Strava) uses.
    – Michael
    Commented Mar 10, 2022 at 17:51
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    @Michael: Yes, it appears from my rides that I can hide power and the Calories don't change, so it appears they're based on real power data. Also, when I back-calculate what Gross metabolic efficiency must be to match what Strava shows, I get 0.215 (to within the rounding that Strava uses).
    – R. Chung
    Commented Mar 12, 2022 at 16:01
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Gross efficiency is a parameter the apps are assuming

Just to recap, the power meter measures the amount of work you did to the crank1. Your body burns energy, and wastes most of it as heat (all machines do this, it basically can't be helped due to physics). The work done field (reported in kJ) is the directly measured input to the cranks. The calories burnt field is estimated calories. Strava assumes how efficient your body is, presumably by at least browsing peer-reviewed literature. Its assumption might be different from another app, so if you see calorie discrepancies between apps, this is why. If you want to search, this parameter is called gross efficiency (GE).

A complicating factor is that every person's GE varies a bit. Moreover, your own GE varies a bit depending on power output - it tends to increase a bit with higher workload (open access article).

One study I found estimated that of its sample of experienced female cyclists, the average gross efficiency at lactate threshold was 23.2%, with a standard deviation of 3.5 percentage points at 60% of VO2max. That is, if the sample is representative, 95% of female cyclists should have gross efficiency within about 2 standard deviations of the mean - implying a range of 16.2% to 30.2%. That's quite a big range. Men may have a slightly lower gross efficiency and this sample of men had less variability. This study is small in absolute terms.3

There may be other studies on gross efficiency, which I didn't bother to search for. If you are searching on Pubmed, "gross efficiency" may be a standard keyword, which would make it easier to search. Note that not all studies may use the same standard keyword, however.

If you did VO2max testing in a lab, some labs should be able to estimate your GE at various intensities.


A worked example incorporating individual variation

On a 78.4 mile ride I did in 2022, Strava reported:

  • 1,916 kJ total work (i.e. measured at the drivetrain)
  • 1,963 calories burnt (i.e. estimated work done by my body)

One calorie is 4.184 J. So, you divide the work done by the GE assumption to get kJ produced by the body. You divide by 4.184 to get calories. Using arithmetic, it appears that Strava assumed a GE of 23.3% at the time.

To illustrate how calories burnt by an individual vary, we can use the standard deviation (SD) around the GE estimate. If the data are normally distributed (which the study authors said appeared to be approximately true - it's always an approximation), 68% of people are within 1 SD of the mean, and just over 95% are within 2 SDs.

Let's take that ride, and apply the GE estimate at an output of 150W for male cyclists. That's closer to my average power for the ride. The study reported average GE by sex at 150W, 180W, lactate threshold, and at 60% of VO2max. At 150W, the study estimated a GE for men of 19.9%, SD 1.8 percentage points. Interested parties can do the work on their rides with a different GE estimate if they want.

I believe the following interpretation is reasonable. To do 1,916 kJ of work at about 150W:

  • The average trained male cyclist probably burned about 2,301 calories.
  • About 2/3 of male cyclists should have burned 2,110 to 2,530 calories.
  • Almost all male cyclists should have burned 1,949 to 2,809 calories, barring unusual physiology.

You might want to assess the study population. The cited study is not professional athletes, but it is very fit - the men had an average VO2max just over 60, and the women had an average of nearly 49. The average age was in the mid 30s. I don't know how cycling GE is in less trained cyclists, but I assume it should increase with training up to some limit (e.g. can elite athletes increase it substantially? Maybe not?). And perhaps it changes with age. Interested parties might want to consider that in searching.

Basically, if you are on a strict diet, then do remember that even with a power meter, you should refine your intake depending on other measurements, like weighing yourself regularly. I am not currently aware of a practical method to estimate your own gross efficiency.

What if you absolutely must have an accurate calorie count? You could wear a portable VO2 analyzer - I know one sports scientist who compared the one I linked favorably to the usual metabolic cart. However, this means you need to exercise with a mask strapped over your face. The manufacturer reported battery life is about 8 hours, with the mask using single AAA alkaline batteries. On the ride above, which was 3+ hours in the heat, wearing the mask doesn't sound practical. Nevertheless, you should do you.


What determines GE?

As far as I know, one known factor is the proportion of slow-twitch (type I) muscle fibers. That is, if you're anaerobically dominant, your GE may be lower than average and you deserve or at least you can ingest more french fries, cookies, ice cream, etc. Aside from that, the physiological determinants of GE aren't well understood.

In running, it's possible that running form may influence GE, although this isn't that well-understood either. As for cycling, this 2008 open-access article discussed the state of knowledge at the time.2 This article discussed the link between training pedaling technique and cycling performance - many of us were probably told to pedal in circles, but there is no biomechanical evidence that this is helpful. Empirically, interventions to improve pedaling technique aren't connected to performance improvements. If anything, there's some evidence that those interventions increase energy expenditure, i.e. they reduce GE.


Footnotes

  1. The ride linked in the comments doesn't have actual power meter data. It reports power estimated from Strava's algorithm that makes a lot of simplifying assumptions. The cyclist in question probably wanted her actual numbers not visible for tactical reasons.
  2. Edward Coyle is one of the authors. He published an article that showed what he thought were longitudinal changes in Lance Armstrong's gross efficiency as he developed as an elite athlete. That study showed Armstrong's GE increasing by about 8% (NB: not percentage points) over 7 years. The findings of that study were called into question and I believe it was later retracted. One calculation error was found from a partial dataset. Coyle wasn't willing to release the full dataset. I don't know how this affects how the sports science community evaluates Coyle's full body of work. His unwillingness to release the full dataset to scrutiny does increase my uncertainty about his reliability. However, his full body of work is larger than this one study.
  3. The range for women is pretty wide. The study in question only had 13 men and 13 women. It would be better if we had a bigger study. I don't know the typical studies of GE are this small. Researchers could use a technique called meta-analysis to combine multiple studies. This would increase our certainty about the mean GE. Each study is usually weighted by the inverse of its variance - that is, in general, larger studies will be weighted more than small ones. That weight depends in part on the standard deviation of the data. I'm not currently aware of a technique to produce a meta-analytic estimate of the pooled SD of multiple studies. NB: In meta-analysis, you get a standard error (SE). This reflects your uncertainty about the mean. In this study's case, with 26 total people, we aren't that certain about the average GE. If you meta-analyzed many studies, you might get a pooled estimated mean GE with a small SE. You can't take that SE and make the inference above. The SE tells you the range in which the mean is likely to be (i.e. 1.96 * SE gives you the upper and lower bounds of the 95% confidence interval).
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    Another possible cause of errors in estimated power is that Strava doesn't know if the rider is riding solo vs. in a bunch. That makes a huge difference which Strava can not compensate for. Commented Mar 10, 2022 at 23:22
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    It's not a race. Just a training ride.
    – Ender
    Commented Mar 11, 2022 at 8:02
  • @RoelSchroeven and when in a bunch, where in the bunch? Even for us normal people solo vs taking turns in a pair makes a big difference
    – Chris H
    Commented Mar 11, 2022 at 12:34
  • @FreeMan fair enough. There are a few sources of weather data for Strava, so none of us can be expected to keep up with all the changes
    – Chris H
    Commented Mar 11, 2022 at 13:24
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    One can "hide" power in Strava even if using a power meter, and it does not appear to affect the displayed value for Calories; I just checked that on a couple of different rides. So if AvV were collecting power data (likely) but chose to hide them, it appears Strava does not re-estimate the power and base Calories on that. I also checked my own raw data, and it appears Strava makes an assumption of gross metabolic efficiency near 0.215.
    – R. Chung
    Commented Mar 12, 2022 at 14:32
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Every rider will have a different efficiency which will change things slightly, but a commonly used formula that provides a 'good enough' estimate is:

Caloric intake needed (kcal) = Watts * Hours * 4

We can re-arrange this to estimate Watts from Calories (kcal):

Watts = Calories / (Hours * 4)

I would point out that for the ride you linked average power is not a particularly useful metric - there is a lot of climbing/descending. It is likely the climbing was done at a much higher power and the descending much lower.

Edit: Including the full maths for the commenters and downvoters.

100 Watts = 100 J/s

100 J/s * 3600 (seconds per hour) = 360000 J/hr

360000 / 4.186 = 86001calories = 86kcal (Calories) per hour

Note the difference between calorie with a small c and the dietary unit with a big C

Cyclists have an efficiency of between 18-25% depending on the individual - the number in the middle of that range is 21.5%

Kcal required to generate 100W at the pedals for 1 hour = 86 / 0.215 = 400kcal

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  • No, no, no. Something's missing in your "good enough" estimate. An efficiency should be added, because one kcal is approximately 1.163Wh and surely not 4Wh. I know we're on bicycles.stackexchange, but still : the question already contains completely wrong units, the answers shouldn't also include wrong physics equations. Commented Mar 10, 2022 at 18:27
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    Yes, my comment was directed at you, I would have included "at"Eric otherwise. And thanks for the clarification. And sorry for not doing the math myself, as it's not exactly complicated... Commented Mar 11, 2022 at 9:12
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    That looks like a decent match to Strava, to me (reading a few hours after the edit adding the maths). Strava claims I averaged 133W for just under 10 riding hours, and burnt 4291 kcal. Working backwards Strava's assumption comes out to about 26%. I'm pretty certain I've found them to be 25.0% before
    – Chris H
    Commented Mar 11, 2022 at 12:47
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    @EricDuminil the rule of thumb ("good enough estimate") effectively takes advantage of a lot of factors being close to 4 (x10^3): the number of J in one kcal, the number of seconds in an hour, and the inverse of human efficiency. Multiply 2 of those together, divide by the 3rd and you've got 4 (to within an error far smaller than the error in Strava's estimation of power). While you might prefer a different presentation, the approximate formula just rolls up all the constants into one
    – Chris H
    Commented Mar 11, 2022 at 12:51
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    If you're interested, I asked a question on physics stackexchange (physics.stackexchange.com/q/699915/148854) on how to write the above rule of thumb. physics.stackexchange.com/a/699927/148854 has good tips. Commented Mar 21, 2022 at 13:36
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I think there's a basic misunderstanding in the question that none of the answer highlights. The existing answers seem to highlight only that there are two energy measures, energy input and energy output, but seem to miss that who asked this question obviously doesn't know what's the difference between energy and power.

Calories and joules are a measure of energy. Energy is something that for example food contains. More food, more energy.

Watts are a measure of power, the rate of energy transfer. One watt is one joule per second.

Also you should note that calorie can refer to either real calorie or kilocalorie. To get kilocalories from calories, divide by 1000; to get calories from kilocalories, multiply by 1000. If someone says kilocalories you can trust it. If someone says calories it may either refer to real calories or kilocalories. You will need to try both and see which unit gives reasonable values.

So if in a ride of 15 minutes you burn 120 kilocalories, that's 4.184 * 120 * 1000 = 502080 joules. 15 minutes is 900 seconds. So the rate of using additional food energy is 502080/900 = 557.87 watts (or joules per second). Of course in this ride the cyclist is also using energy needed for basic metabolism, the 557.87 watts is the rate at which additional food energy, over that of basic metabolism, is used.

You may leave it there if you are interested in energy input. However, if you want energy output, you need to know how efficiently a human converts food energy into mechanical energy. I assume 25% is a reasonable conversion efficiency so that would give 0.25 * 557.87 W = 139.47 W. From that, we can observe that the values I invented weren't for a racing cyclist but rather a casual Sunday rider, as a racing cyclist would produce more power.

Note that both 557.87 W and 139.47 W are correct. The 557.87 W is the rate at which the cyclist converts extra food energy into both mechanical energy and heat. 139.47 W is that mechanical energy. The heat would be then 557.87 W - 139.47 W = 418.40 W. The produced heat is why cyclists sweat.

So to calculate watts from calories, you also need the duration of the ride, just calories isn't enough. If you don't know that, you can't say at how many watts the cyclist is producing power. It may be the ride is a short-duration intense ride and power production rate is extreme, something only racing cyclists can achieve. It may also be the ride is a long-duration casual ride and power production rate is practically nothing, easily achievable by a Sunday cyclist. Both of those two rides can have the same amount of calories burnt.

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