Let me try to do this question as much justice as xkcd's whatif would.
A little bit of research suggests that an average human breathes in about 10-20 liters of air per minute across all activities. Of course, you don't fart all the air you breathe in, so let's assume that we fart a percentage of that back out and rest comes out as exhalation. Let's assume that the ratio is 0.1% of all air breathed in. This gives us .01-.02 liters of fart per minute per person. Therefore, for the average person, they'll fart ~7900 liters per year.
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an interesting theory. but i wonder how you came to the conclusion that the farted air depends on the air breathed in. last time my biology teacher said something about lungs, it didn't look like they were connected to the fart hole. but i could be wrong
also, it seems like quite a lot to think each person farts 1-2 decilitre every 10 minutes. even when having eaten something that doesn't agree too well with my stomach, i don't think i'd be even close to that ammount. guess it would be closer to 1 litre per day, but in the end, this only makes your result differ in a factor of ~10.
the thing about refarting sounds also intriguing, didn't think of that. but what you didn't include there was that air can even be tripple refarted. and quadruple... i wonder how often air can be refarted, before it turns into dark matter. but overall, this shouldn't really make any difference as per your calculation, the total farted air is a very low percentage of the total air.
and yeah, i agree with the others, including animals other than humans would be interesting. but then again, i don't think they'd give a difference of more than a factor of 10. so in the end we're probably again at about the same spot where your calculation arrived.
so thanks for the calculation, was interesting to read.
my mind is now pressing for more questions though:
assuming 0.0001% of earths atmosphere are farts, how much farts does one breathe in during a lifetime? and according to that, how many kilos of actual shit is that? ... that is a very disturbing thought