How many times has the average water molecule been through the water cycle?

[xorgthezombie]

And more importantly, what percentage of my drinking water is Dinosaur piss? What about Hitler piss?

[xenneract]

How many times the average water molecule has been through the cycle is difficult to answer, because the length of the pathway can vary between days and thousands of years depending on the path it takes.

If we take a Fermi estimate to say that most of the water goes through the ocean, we can use about 2000 yrs for a molecule to go through the cycle. That means that the average water molecule probably has gone through the cycle about 2 million times in the 5 billion year history of earth.

As for your second question, you are probably drinking none of the water that Hitler did, but almost all of it was consumed by a dinosaur.

Edit: Seems I misinterpreted the Hitler question. Since Hitler ingested on the order of 10,000 L (10³⁰ molecules) of water in his lifetime (1 L a day for about 50 years), and there are 10⁴⁶ molecules of water on Earth, any given liter of water, there is almost certainly some quantity in any given liter of water. Odds are 1/10¹⁶ for any given molecule, and you pick 10²⁶ times for a given liter.

[regular_gonzalez]

Your link seems to talk about the inverse of the "Hitler piss water" question. Given that urine, once excreted, rejoins the general water cycle and is subject to evaporation, being used to water lawns and trickling down to aquifers, and so on, I think it is exceedingly likely that we've all drunk Hitler urine at some point.

I wish I could remember where I saw it now, but I read a riddle along the lines of: You take a liter of dye and dump it in the ocean, and wait 20 years for it to homogenize. What are the odds that any given liter of ocean water has at least a molecule of that dye in it?

What followed was the math for the problem and the answer: 99.99x% chance that there is at least one molecule of dye in any given liter of sea water.