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(Inspired by many other questions that I'm not going to try to list...)

According to most sources I've seen, a "typical adult human" burns around 10-15 kcal/min while doing "strenuous" exercise. (Some sources may go as high as 25 kcal/min. Also, the number can increase depending on mass, so let's say we're talking about someone who masses ~100 kg or less.) However, it seems to me that even a "full body workout", isn't really. (If nothing else, you're usually not using opposing muscles simultaneously.)

If I had some way of causing every cell in the body to spontaneously metabolize as quickly as possible, how much Power could this produce? (Mind that I'm talking about Power in the physics sense, not electricity. Also mind that I'm not asking about burning cells or matter-energy conversion, I'm asking about producing power via normal metabolic processes, i.e. without destroying the body in the process.)

For the purpose of this question, don't worry about waste products or waste heat. I'll ask about those separately. For now, just assume that they are all magically whisked away.

(Note: Yes, this is very similar to this question. Please don't close this as a duplicate, as a) it isn't quite the same, and b) that question doesn't answer this one.)

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    $\begingroup$ The other question asks, verbatim: How much caloric energy can an average human put out?. You are asking how much power (energy over time) a human can produce, which is indeed present in answers to the other question. In light of this, how is this one not a duplicate? $\endgroup$
    – The Square-Cube Law
    Jul 20, 2020 at 14:44
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    $\begingroup$ It may be, but the other question doesn't have an answer to that, specifically; only citations of existing sources based on exercise. I'm asking what difference does it make if I'm not limited to exercise. Unless someone goes back and provides a useful answer to the other question, closing this as a duplicate would be completely unhelpful. $\endgroup$
    – Matthew
    Jul 20, 2020 at 14:46
  • $\begingroup$ Got it, and I'll take a shot at answering here. $\endgroup$
    – The Square-Cube Law
    Jul 20, 2020 at 14:49
  • $\begingroup$ What could differentiate that question from this one is: "... some way of causing every cell in the body to spontaneously metabolize as quickly as possible." The answers in the linked question address roughly what is physically possible for an average human, while forcing every cell to metabolize at the greatest rate possible is probably not physically possible. $\endgroup$
    – BMF
    Jul 20, 2020 at 14:50
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    $\begingroup$ I wonder if there is a study of caloric output of people close to OD on ecstasy. That might be close to the maximum output of a human body (death from ecstasy is generally due to exhaustion and hyperthermia as far as I'm aware) $\endgroup$
    – Curiosity
    Dec 14, 2021 at 19:35

5 Answers 5

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A zeroth order approximation from first principles

Let's try to arrive at a Fermi approximation of the maximum sustained primary energy production of the human body.

("Sustained" is important. The human body can output 2 kW or more of mechanical power, corresponding of about 7 kW primary energy production, for a brief period of time, using ATP and oxygen already stored in the muscles. Sprint runners use this mode of operation.)

Disregarding all the details which make the joy of biochemistry, the human body produces energy by burning glucose. The gross reaction is

$$\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + 6\mathrm{O}_2 \rightarrow 6\mathrm{CO_2} + 6\mathrm{H_2O} + 2{,}880\ \text{kJ/mol}_{\text{glucose}}$$

The human heart pumps no more than about 2 $\times$ 100 mL of blood per beat, and the maximum heart rate is about 200 beats/minute, giving about 20 liters of blood per minute in the systemic circulation. One liter of fully oxygenated blood contains a little less than 0.3 grams of oxygen. All in all, you have no more than 6 grams of oxygen per minute to burn your glucose.

6 grams of oxygen is about 0.2 moles. Since you need 6 moles of oxygen to burn one mole of glucose, you cannot burn more than 0.03125 moles of glucose per minute; times 2,880 kJ/mol, we get a top theoretical energy prodution rate of

$$90\ \text{kJ/minute} = 21.5\ \text{kcal/minute}$$

That's about 1.5 kW, for those who care.

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    $\begingroup$ Excellent answer. Would deserve a +2. $\endgroup$
    – cmaster - reinstate monica
    Jul 20, 2020 at 23:22
  • $\begingroup$ That meshes with my answer, since short burst exercise would involve some anaerobic output as well (no oxygen but also very inefficient). With sustained exercise oxygen exchange becomes the limiting factor. The average untrained healthy male can uptake oxygen at a max of about ~35–40 mL/(kg·min) top athlete max out at around 6.1±0.6 L/min sustained. $\endgroup$
    – John
    Jul 21, 2020 at 13:51
  • $\begingroup$ A similar approach is to use VO2 max. During a controled test, Rob Wadeell has been "burning" 4g of oxygen per minute (see en.wikipedia.org/wiki/VO2_max#Athletes ). That's unsuprisingly a lower value as you cannot have the maximum blood oxygenation at the same time than the maximum heart rate and oxygen burning $\endgroup$
    – Madlozoz
    Jul 21, 2020 at 15:18
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I can make a very rough calculation assuming that the maximum heat loss for a body in water corresponds to a power of about 24 kW, and "immersing a person in iced water" is not enough to lower his temperature in case of severe TFMPH poisoning.

Therefore, the human body can produce at least 24 kW of heat.

TFMPH, as well as other proton translocators, causes exactly what you describe: "causing every cell in the body to spontaneously metabolize as quickly as possible" (it is used for this purpose in some highly illegal "weight loss" concoctions).

However, be advised that this results in death in a matter of minutes, because the organism literally cooks itself alive. You asked instead "without destroying the body in the process".

Also, this is not the same as producing useable energy (rather the opposite: all energy goes away as heat). The latter would require muscular activity, so you might maybe found some estimates in medical papers on malignant hyperthermia.

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  • $\begingroup$ note the human body is also really inefficient at producing heat, compared to say generating mechanical force, so heat may not be the best measure. $\endgroup$
    – John
    Jul 20, 2020 at 16:07
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    $\begingroup$ @John, are you sure? Heat is the end result of entropy; what exactly happens to the energy that doesn't end up as heat? $\endgroup$
    – Matthew
    Jul 20, 2020 at 16:14
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    $\begingroup$ I think this is the most useful answer so far! This sounds plausible, I will definitely have to do more research here. Also, note that I said to not worry about the heat 😉; for my ultimate purposes (metabolism-powered magic), I can't totally hand-wave it away, but my working theory is that, depending on the application, I can convert ~80% of that into something "useful", or even simply dump most of it (as heat) somewhere else. This is the point at which my other question becomes important 🙂. $\endgroup$
    – Matthew
    Jul 20, 2020 at 16:25
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    $\begingroup$ @John: The human body is very much more "efficient" at producing heat than mechanical output; for each joule of mechanical output it produces at least 2 joules of heat. $\endgroup$
    – AlexP
    Jul 20, 2020 at 16:26
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    $\begingroup$ @John: I'm not sure that you understand how this energy thing works. "Creating potential energy that is never used" is not physically possible; and there is no difference between waste heat and "purposefully generated" heat. Heat is heat. $\endgroup$
    – AlexP
    Jul 20, 2020 at 18:53
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According to this link, cyclist Chris Hoy could blast 2500W of mechanical power during a short time.

Assuming a 30% muscular efficiency, that's 8333W metabolized.

Obviously, Hafþór Björnsson can do much better

This does not exactly answer your question, but that's a lower bound

Note: As your question implies some level of magic in the metabolism, I focused on the idea of the maximum Energy a human can make without destroying the body in the process. Of course, such an effort can not be sustained for many reasons.
You explicitaly told us not to care about overheating and waste management, but oxygen (as detailled by AlexP) and glucose flux are the next limitation in realistic biology

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  • $\begingroup$ That would work out to 120 kcal/min, which is six times higher than the highest figure I've seen anywhere. I seem to recall some sources (I'll try to find the article again) citing ~1kW but also ~15-20 kcal/min, which is why I'm still scratching my head. Do you know any sources that can confirm that presumed 120 kcal/min? $\endgroup$
    – Matthew
    Jul 20, 2020 at 16:03
  • $\begingroup$ @Matthew Most of the time, cyclist boast about their sustained output (typically 400W). Chris Hoy number is about sprinting. And performed by a man whose only purpose in life is sprinting on a bike. Also, those Numbers (I mean 2500W) are mechanical output. When people talk about calories, they usually mean metabolism. Typically sustained metabolism $\endgroup$
    – Madlozoz
    Jul 20, 2020 at 16:10
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    $\begingroup$ @Matthew: By and large, short spurs of mechanical output power use the ATP and oxygen already available in the muscles, which get depleted pretty quickly, usually in less than a minute. It's a very limited metabolism -- basically just burning ATP to release energy. On the other hand, those 400 W of sustained mechanical output do correspond to a complete metabolic rate of about 20 kcal/minute. (Assuming a muscle efficiency of about 30%.) Note that the difference (about 900 W) is waste heat which the body needs to dissipate, which is not so easy at all without a very strong air current... $\endgroup$
    – AlexP
    Jul 20, 2020 at 16:22
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    $\begingroup$ @John: Ah, that article makes it clear that it measures only the efficiency from ATP to mechanical output. That's OK. $\endgroup$
    – AlexP
    Jul 20, 2020 at 20:23
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    $\begingroup$ @AlexP Also note that human metabolism is not a heat engine. Nowhere in the process does it even try to convert heat into mechanical work. It directly turns the chemical energy into mechanical work + waste heat, keeping working temperatures down to around frosty 40°C, even in the case of a top athlete. A Carnot engine with a heat source at 40°C (athletes muscles) and a sink at 0°C (riding in winter) would have an efficiency around 13%. The athlete can do better than that, even in summer. $\endgroup$
    – cmaster - reinstate monica
    Jul 20, 2020 at 23:20
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For the purpose of this question, don't worry about waste products or waste heat. I'll ask about those separately.

I have no data on how fast human temperature can go up and down, only the anecdotal evidence that fast temperature changes due to fever (going either up due to sickness or down due to antipyretic) usually take no less than an hour to happen.

I do have a link to a question in chemistry.se stating that the specific heat for the human body is 3.5kJ/kgK. So for a 100kg person to go from 36C to 40C in 1h, that is an energy expenditure of 1,400kJ. Over 3,600 seconds, that is ~389 watts.

That is enough to power maybe a couple 60" TV's, or seven laptops. Not enough to power a coffee maker machine, though, so I wouldn't even bother. If I'm using magic to get energy from people I'd rather mix pyromancy with necromancy - completely burning a person yelds 1kWh/kg, which is 3,600,000 joules/Kg. If a 100kg person takes an hour to completely roast, that's 360,000,000 joules in one hour, so 100kW - three orders of magnitude more power!

To be clear: this is energy coming from all cells, just wasting energy generating heat. Muscles contracting can reach higher watt counts. See Madlozoz's answer.

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  • $\begingroup$ Interesting, but 15 kcal/min is already about 1,000 watts (note Madlozoz's comment!) ; we can probably get to at least 1,600 or so. You might be on the right track, though; I'm going to try to see if anyone has numbers for e.g. people in extreme cold. I hadn't thought of that when I asked the question. BTW, one of the reasons I'm sticking with metabolism as a power source is because I don't want overpowered magic 😉. $\endgroup$
    – Matthew
    Jul 20, 2020 at 15:36
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    $\begingroup$ That's a first lower bond, but I metabolize MUCH more that 389 W while cycling. $\endgroup$
    – Madlozoz
    Jul 20, 2020 at 15:36
  • $\begingroup$ My prior comment notwithstanding, I think this is still interesting, because I don't think temperature increase due to fever is necessarily using muscles, which makes me suspect we can, at the very least, add those additional ~400W to the 1kW we get from exercise. If I had to guess, I'd guess the "right" answer is somewhere around 2-3kW, but it would be nice to have something backing that up. $\endgroup$
    – Matthew
    Jul 20, 2020 at 15:40
  • $\begingroup$ @Matthew according to Wikipedia human heat is generated not only in muscles but also in the brain and viscerae. It is a result of metabolism simply happening. One of my biology teachers in high school told me sodium pumps keep causing cells to use up energy constantly in mammals, being the mechanism through which we become homeothermic. $\endgroup$
    – The Square-Cube Law
    Jul 20, 2020 at 15:54
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    $\begingroup$ The main problem with this answer is, that the body is nowhere near its limits when it increases its body temperature in response to an infect. Otherwise, you wouldn't need to wait for the temperature to rise, you'd recognize the starting fever from the increase in breathing and heart rate. They would need to rise to levels that a cyclist has during a race. But they do not. Feverish persons do not breathe recognizably faster than a person at rest, so they must be very far from top metabolism. $\endgroup$
    – cmaster - reinstate monica
    Jul 20, 2020 at 23:33
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According to Stanford around 2000 watts in short bursts or 300-400 watts sustained.

This from studies interested in using metabolic energy to power implants, they wanted a baseline of how much energy was theoretically possible. Without knowing what time interval you want this is about the best you are going to get, how much energy the body can put out over minutes is drastically different than over seconds because they involve drastically different metabolic pathways and limiting factors.

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  • $\begingroup$ I also came on this Stanford page. But I realized they put on the same level the energy consumption (when they say "100W") and the mechanical output (when they say "300-400W"). In my opinion, this is just an electric engineer toying with the idea. He knows as much about human body than Alberto Contador about reverse electrowetting $\endgroup$
    – Madlozoz
    Jul 21, 2020 at 14:41
  • $\begingroup$ @Madlozoz I am confuses as to what you think the problem is, 100W was not consumption it was the resting output (which would be close to consumption) 3-400W is the sustained output during exercise. I have seen several BMR estimates that are near 100W , (80W for bed ridden patients) and sustained exercise estimate that are within their estimates if not a little higher. $\endgroup$
    – John
    Jul 21, 2020 at 16:53

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