Have you ever wondered how many people are taking a dump right now??
I will attempt to recreate a bar conversation and its associated notes from a few weeks ago. This is a Fermi problem, in which the factors need not be very precise, as its purpose is only to guess the order of magnitude of the answer.
There are just over 7 billion people living right now.
Children and malnourished people considered, suppose the average person poops once per day.
Originally we were curious how many people are pooping on an average moment of the day. Pooping can be considered as all the time one spends squatting or sitting on the toilet (say, 5 minutes). Again considering the great number of people who likely do not take the need to defecate as a chance to relax, this should be reduced to, say, 2 minutes) or the shorter period one spends actually excreting waste (say, 30 seconds).
It is worth noting that, as part of the circadian cycle, people are most likely to defecate in the morning; half of the world’s population lives in just a few time zones (those including Southeast Asia), so. However, due to the variability of pooping times, possibility of zero poops or more than one poop per day, and complexity involved, we will not consider population distribution nor time of day in these calculations. They will deal with the average moment of the day.
Supposing each of these 7,000,000,000 people spends 30 of the day’s 86,400 seconds (1/2,880 of the time) pooping, there are 972,200 people pooping at a given moment. The upper bound of 60 seconds of course yields double that amount. There are on the order of one million people actually pushing crap out of their assholes at any time.
How many people are sitting on or squatting over the toilet, waiting for a bowel movement, wiping their butts, or otherwise engaged in activity they would probably also just describe as “taking a shit”? The shorter estimate of 2 minutes (one 720th of a day) yields 9.722 million shitters at any time. The greater, 5 minutes, is a full 288th of a day, over a third of a percent; think of one in two hundred eighty-eight people shitting as you read this! This factor yields a thunderous 24.305 million shitters currently open for business. There are on the order of ten million people “taking a shit” at a given moment.
But wait — there’s more! Oh, is there ever more.
“How much is being produced?” we asked ourselves. We guessed, again pausing to explore the importance of global malnourishment, that the average turd weighs about a third of a pound (151g).
I’m cheating now, as this is very hard to estimate, and I’ve found various unreliable sources for the weight of a regular poop. Wikipedia points out that “the formal medical definition of diarrhea involves defecation of more than 200 grams per day (though formal weighing of stools to determine a diagnosis is never actually carried out)”. Since we’re already assuming one poop per day, this grants us a reasonable estimate. Encyclopaedia Britannica tells us “about 100 to 250[g] … are excreted by a human adult daily. There are many forum posts and Yahoo answers reporting losses of several pounds in a bowel movement. Two such posts include quotes whose language resembles that of a scientific journal, and is so much more intelligent than the rest of the post that it could hardly have been made up by the commenter. One cites 100-300g/day as normal for healthy Westerners; the other, mean 123.6g (n=115 SD=40.2) per bowel movement, language suggesting a study in the UK. So I guess something more than one bowel movement a day (200/123 = 1.6) is average, but we must reduce these values anyway, as they deal with (presumably adult) poopers in developed countries.
Turns out our first guess was fantastic! Let’s call the human average daily shit production mass 150g; less than the Westerners’ 200g, but not less than the average Westerner’s single bowel movement of 124g, and snugly in the lower end of Britannica’s given daily range.
150g/day times 7 billion people is a lot: 1,050,000,000,000. Just over a trillion grams, and unit conversion isn’t going to make this amount of poop much easier to imagine. That’s 1.05 billion kilograms, and 1.05 million metric tons.
What would this look like? Turds are mostly water (about 3/4), and have variable density, although they tend to be just slightly denser than water. Conveniently, the metric system doesn’t absolutely suck, and we already know one metric ton of water takes up one cubic meter. (Knowing poop is a littler denser, let’s take this chance to reduce the volume and call it a “clean” million.) These million tons of human feces would take up a million cubic meters, which could be formed by a cube 100m on each edge, or about 328 feet.
That is simply enormous.
The Internet helpfully tells me the Great Pyramid of Giza has a volume in stone of about 2.6 million cubic meters; if we all started defecating into molds for huge blocks first thing Monday morning, we’d have enough to build a replica Great Shitamid by Wednesday afternoon. We could replace the concrete in the Panama Canal in a day and a half. We could fill an Olympic size swimming pool with crap in three minutes and thirty-six seconds.
The amount of poop humanity makes in a day is staggering, and we’re just going to have to go further with unit conversion to make it more imaginable. 1,000,000 tons a day is still 694 tons a minute, and 11,574kg a second. That’s a few adult African elephants, or several automobiles.
We tried to imagine all the world’s poop flowing into the bar. I can’t remember quite what figures we had come up with at this point, but we knew the interior of the building would be filled with crap in no time, especially if it had no way to start flying outside. At a generous estimate of 40m long with 3m-high ceilings and an average of 15m across, its measly volume of 1800 cubic meters would last under 3 minutes. There would be little chance to escape, depending on your proximity to where the shitstorm originated. Surely some would not make it out alive.
How would the feces get in? Through a pipe, we agreed. We didn’t know how big to make the pipe. How about a 10cm diameter? That’s bigger than most plumbing you see, but this is a lot of poop, and due to laws of fluid mechanics, a pipe too narrow would produce not a modest hoselike flow but a high pressure jet, slicing through walls and trees and people with a death ray of shit. A 10cm pipe — a little wider than a coffee mug, but a little smaller than the circle you can make with the thumbs and fingers of both hands — has an area of 78.5cm^2. Perhaps you can see where this is going. I also remember we chose 10cm because we were getting drunk and didn’t want to have to multiply pi by a harder number.
Recall that 11.6 tons of shit are produced per second, or 11.6m^3/s. Before we divide by the pipe’s area, let’s do some unit elimination: (m^3/s)/(cm^2) = 10km/s. (11.6/78.5)(10km/s) = 1.47km/s. Multiply by 60 to get 88.6km/min, and again to get 5,317km/h, or 8,241mph. Jesus H. Christ in a chicken basket; poop will be coming out of this pipe at low-Earth orbital velocity. This is the fucking death cannon of turds I was talking about earlier. We must have gotten something wrong at the bar (I recall about twenty miles per hour). I’m leaving the above because it is worth picturing.
Let’s say the pipe is 50cm across. It has an area of about 0.2 square meters and will blast shit into the room at 59 meters per second, which is 212km/h, or 132mph, about as fast as you can make a regular car go. The stream of feces would blow forcefully across the room through a pipe big enough for a person to squeeze into. For a distance, it would still be more than enough to damage walls, break windows, blast away furniture, or cripple any bar patrons in the way, if not completely destroying them, as it would carry the initial force of being tackled by dozens of football players or being hit by a small school bus.
That is how much the world is pooping, all the time. If everyone in the world had their assholes somehow connected to a hose system with valves that kept their rectums from experiencing the intense pressure, and these hoses all connected to one big pipe, eventually flowing with absolutely everybody’s shit and half a meter in diameter, the feces would still be flying out the end of this giant pipe at well over 100 miles per hour, and it would never stop.