# How much energy in form of heat does a human body emit?

How much energy in form of heat does a human body emit at rest level?

That's easy. The energy requirement of an average man is 2,500 Calories per day, and one Calorie is 4184J. Therefore he emits about 10.5MJ/day or about 120W.

An average woman requires 2,000 Calories per day, so she emits about 97W.

• Does the human body emit as heat, all the energy it got from food? If yes, in typing this answer, you spent some energy - what is its energy source? – 299792458 Jun 5 '14 at 10:09
• @New_new_newbie: assuming your weight stays the same you are emitting all the energy from your food as heat. If you're getting fatter it means you're retaining some of the energy and converting it to chemical energy (i.e. fat). Conversely if you're getting thinner it means you're converting chemical energy in fat to heat, so you're emitting more heat than you get from your food. I got the energy to type this from my body reacting glucose with oxygen to produce water, carbon dioxide and energy. – John Rennie Jun 5 '14 at 10:14
• Wrong. Energy gets stored in human body as ATPs (en.wikipedia.org/wiki/Adenosine_triphosphate). The chemical energy stored as a P-O bond gets released. Of course, some part of that will be lost as heat, but if picking up a 400g stone to 1m height required 4J of work, that 4J does come from the food you have consumed. Otherwise energy conservation would stand violated, if your input = output as heat'' conjecture was true. So, again, what is the energy source of typing this post if all the energy you got from food got EMITTED out as heat? – 299792458 Jun 5 '14 at 10:32
• @New_new_newbie: yes, if I lift a weight some of the energy I get from food has been converted to potential energy of the weight. So I suppose it would be more precise to say the energy from food ends as heat + any potential energy gain. In real life we are unlikely to make any long term potential energy changes to our environment (I suppose builders do, though their buildings will fall down eventually so the energy ends up as heat eventually). – John Rennie Jun 5 '14 at 10:42
• @jameslarge Of course it's not exactly true, but you're missing the point - this is a great back-of-the-hand calculation that gives you something very close to the real value for the average Joe. Even if you did nothing all day but eat and put heavy objects up, almost all the energy you got in would be released as heat. Mammals are extremely inefficient heat engines - depending on the amount of work you do, the effective "food -> work done" efficiency is somewhere around 20% to as low as 1%. And the upper limit is the "cycle all day" kind, not "workout a bit once a day". – Luaan Jan 11 '16 at 14:11

I hesitate to contradict John, but: it's simplistic to assume caloric input equals caloric output, or that caloric output is purely heat, as opposed to moving from one place to another, lifting boxes, etc. A far better model IMHO is to set up the human body as a black-body source with $\epsilon = 0.98$ (emissivity), temperature = 310K, and some reasonable estimate as to total body area. Then you compare the absorption of heat from, say an ambient environment of 294K to see the net outflow of heat.

That does ignore conductive and convective heat flow :-) .

See, for example, the excellent calculator at hyperphysics

• Yes, I recall that the result using Stefan-Boltzmann's law is close to that of John Rennie. In space, the power output is close to $1 kW$, quite impressive! – auxsvr Jun 5 '14 at 12:26
• I expect that black body radiation losses are small compared to other heat losses of the human body in most ordinary circumstances. I haven't done the numbers, but I betcha the heat loss from inhaling gas at ambient temperature and exhaling it at body temperature is much greater than black body radiation when sitting behind a desk in a typical office. Add to that evaporative cooling since exhaled breath usually contains more moisture. – Olin Lathrop Jun 5 '14 at 12:47
• Unless you're building a ziggurat or otherwise storing lots of gravitational potential, don't you think all of that mechanical energy also ends up as heat? – rob Jun 5 '14 at 12:55
• @Carl Well, if I commit a terabyte of information to memory (seems unreasonably large), the minimum entropy change is $S=k\ln2^{40}\approx 1200\,\mathrm{K/eV}$. At my body temperature the minimum energy release is only about 1/4 eV. Even if the ratio of physical to information entropy is a billion to one I still have much less than a joule of heat associated with learning. I don't think it's a big correction. – rob Jun 5 '14 at 13:51
• This answer means that, during a hot summer week in my really hot appartment, I emit no heat, and I will directly convert all my food calories into work at 100% efficiency. During summer, I regularly break the 2nd law of thermodynamics. – Sanchises Sep 15 '15 at 18:55

As a rough planning figure for building design etc, 1 human = 100 watt.

John Rennie's answer is correct +/- 1% or so.

Sure, you can lift something up, doing work instead of emitting heat. But you equally often lift something down, converting its potential energy to heat that your body emits. Besides, most of the loads you lift are small compared to the energy "cost" of running the chemical factory that is your body.

Or say you climb up the stairs in a 20-story building. Assuming 1 floor = 10', that's 200 ft-lb. of work, or around 270J. Let's say that takes you 2 minutes, during which your body emits 120*100 = 12,000J of heat. So the work you did amounts to only about 2% of the total energy you consumed during that stair climb. And a modern human doesn't do physical work for very much of the day, so the conversion to work amounts to less than 1% error.

Besides, you (usually) climb down about as much as you climb up -- again converting your potential energy to heat -- so that pretty much cancels out.

Just assume that it takes around 100W to run your body at idle, more if you have to do "work" (running, etc.)

• Umm... you forgot to include the weight of the person in your 200 ft stair climb calculation! A typical person can provide over 100W of sustained mechanical power, elite athletes can do closer to 500W. Sprint exertion is perhaps double. Tempted to edit this answer... – Michael Jan 11 '17 at 20:13
• @Michael and bgold: we're not very efficient in converting chemically stored energy into mechanical work. IIRC, around 20 % for running, up to 25 % for biking. So when our output is 100 W mechanical, we have at the same time an additional output of 300 - 400 W in form of heat. When lifting something down, we're not only emitting heat due to the loss in potential energy of the weight but also additional head from our muscles (lifting things down makes hungry as well!) – cbeleites Jun 11 '18 at 17:28

## protected by Qmechanic♦Nov 11 '15 at 15:24

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