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I would like to make a magic system that follows the laws of conservation of energy, making it so that you can use magic to do something that you can do physically, like lift things, as well as do things that you normally couldn't, like boil water or start fire. What I want to know is:

  1. How much caloric energy can an average human put out?
  2. What determines this number?
  3. What other source(s) of energy could be used in a magical reaction?
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    $\begingroup$ I'm two and a half years late on this, but for anyone else reading: When applying these figures please note that when talking about food and daily activity, the term 'Calorie' typically refers to kilocalories. A snack marked '200 calories' in fact contains 200,000 calories of chemical energy, or 836,800 Joules. $\endgroup$ – Catgut Mar 13 '18 at 18:29
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    $\begingroup$ @catgut it's a somewhat little known fact, so it's still pretty helpful to know. Thanks for clarifying! $\endgroup$ – Desolationgame Mar 13 '18 at 18:46
  • $\begingroup$ @Catgut Capital 'C' Calories are kilocalories. The product won't say "200 calories" it will say "200 Calories" when talking about big calories or food calories. The difference in the capitalization. It's still confusing, but slightly less so. $\endgroup$ – Samuel Mar 13 '18 at 19:12
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    $\begingroup$ @Samuel That's correct, but even more confusingly, food calories are often simply called lower-case-c calories (as in several answers below) and the subtle distinction is lost. I just wanted to highlight that someone might easily think a 2,000-calorie-per-day diet translates to a mere 8.368kJ, but that's not the case. $\endgroup$ – Catgut Mar 13 '18 at 20:25
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Just look up what you can burn with sports; that should be about how much energy the body can provide. For example, looking at this link I get that by running you can burn up to 22 calories per minute (however that table may not be complete). Therefore the body should be able to provide those 22 calories per minute. However since the calories burnt depend on body weight, the calories that can be provided may depend on it, too. It might also depend on your training status; information sites targeted at professional athletes might also be a good source of information.

Note that at the end of the linked site there's a calculator where you can calculate the energy you burn for different types of sports depending on your weight. This should give you a good feeling about the available energy.

You'll also have to define how efficient the energy transfer from the body to magic is (that is, how much of the energy you draw from your body actually ends up in the magic). For example, the muscles are not too efficient for converting energy into work (according to Wikipedia between 18% and 26%); a lot of the energy you put into them ends up as heat, which is why you sweat when you do sports. So if you assume a similar efficiency for magic, the 22 calories figure above will only amount to between 5 and 6 calories available for magic.

If using body energy for magic also causes waste heat, then it might well be that the ability to get that waste heat out of your body is the limiting factor. That might even mean that a magician can do more magic in cold climate.

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A person typically burns 2000-2500 calories in a day, hence why most doctors recommend eating 2000 calories a day to sustain current weight.

What determines this number is a mix of daily activity and the metabolism/metabolic rate of that person. So in theory a person with a high metabolism would require more nourishment than average when using magic because that would increase their calorie burn.

In your world, where magic requires caloric output as opposed to mana or chakra or qi like in other worlds, the body would self cannibalize if they didn't have enough fat to produce energy and the body would start eating away at muscle mass to sustain magic without adequate fat reserves.

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The other answers are about the chemical energy used by the body. The only restriction was conservation of energy, why limit yourself to chemical energy? This is magic!

Your typical 65 kg human contains about 6e18 J or about the amount of energy the Earth receives from the Sun in 30 seconds or about a 1500 megaton explosion. How much magical power you desire is up to how much of yourself you're willing to convert into energy.

A limit on magic user's power output, aside from disintegrating themselves, could be the waste heat generated. They could literally cook themselves from the inside out. High power levels could also produce harmful radiation which would damage their health. Safe magic would be learning to use unimportant parts of the body (ie. fat) and to channel the resulting energy safely.

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  • $\begingroup$ OP could constrain his magic system to only letting practitioner's consume certain tissues. Let's say we limit it to hair. Googling around, it looks like 4' of hair weighs about 200g (and if this was how magic worked, it would be reasonable to assume practitioner's would be incentivized to grow their hair long). Then using all of one's "stored energy" would be closer to a 4.5MT explosion. Which is still a lot, but now we're getting closer to DBZ energy levels I think. $\endgroup$ – David Marx Mar 13 '18 at 18:59
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I like @Schwern's approach, but I think it makes magic users too powerful if they can convert any quantity of matter directly into energy. Instead, let's stick with you're original question about caloric energy.

A quick google search suggests there are about 679 calories in 251g of steak (or about 2700 calories per kg). Assuming the caloric density of human body tissue is about the same per-pound as a steak, then @Schwern's 65kg person contains about 176K calories of energy. 1 kCal = 4200 J: if a person sacrificed themselves for a spell, they'd have about 740 kJ of energy to work with. A good microwave oven operates at about 1000 W, or 1 kJ/s, so 740 kJ would be enough to power a microwave for about 12 minutes. Assuming your magic practitioner's don't plan to consume themselves completely, the magical exchange rate is about .011 J/g. Sacrificing a pinky (~100g) could power a 65 W lightbulb for about 1.5 min.

Where @Schwern's system is overpowered, my variant is probably too weak. Hopefully this analysis will help you come up with some kind of happy medium.

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