If an elephant farted in a gym, would everyone be able to smell it?
Not long ago, I was scrolling through twitter and came across a tweet from a friend of mine:
Just asked my niece "If an elephant farted in a gym, would everyone be able to smell it?", and I feel confident about my ability to set a mature adult example. 😆
— Dani Alexis, A Writer(TM) (@danialexis) April 1, 2021
This tweet made my day. It’s very cute, it’s got a great question. And the fact that it was tweeted on April Fools? Perfect.
But I take issue with the notion that thinking about elephant farts is somehow not mature. Farts are funny and elephants are interesting, no matter how old or “mature” you are. But even if I accept the premise that this is not setting a mature example, I had an epiphany on how to flip this into setting an incredibly mature example. It all hinges on the question:
If an elephant farted in a gym, would everyone be able to smell it?
This, my friend, is an empirical question. It can be answered. We can science this. And what better way to set a shining example for young people than to show them how awesome science can be?
Rather than provide a simple answer, we can walk through the science of it and learn some things! Like all great questions, the answer is a little complicated. So let’s start small.
If a human farted in a gym, would everyone be able to smell it?
We already know the answer to this but understanding the science and math behind smelling farts in a gym is a crucial first step on our journey! The easiest way to do that is by thinking about ourselves. After all, we experience human farts every day! To start, we need to define, precisely, what we mean when we say “would everyone be able to smell it”.
We want to make things easy on ourselves so we’ll assume this is a closed system - no ventilation or people coming and going through the doors. Because people play sports in gyms, we’ll assume the people in the gym are dispersed, in every corner doing something. The last point to be made here is that “being able to smell it” is an empirical. The concentration at which we can smell a gas is called its olfactory threshold. That yields the following definition:
Once a fart has dispersed through the entire gym, would the concentration of its odorous gases be above the human olfactory threshold?
With our question in hand, we can define the 4 variables we need to figure out: the size of the gym, the sensitivity of our noses, the size of the fart, and the potency of the fart.
1. How big is the gym?
As it happens, there is a very useful guide on gym sizes available from, of all places, the Department of Defense. They recommend a gym accommodates a 50 foot by 84 foot basketball court with 10 extra feet on either side length-wise and 6 feet on either side width-wise. That means our total dimensions are 104 feet by 62 feet. The height recommendation is 24 feet.
Doing science requires that we have sensible units, which translates to metric. And because we’re doing science for fun, we want to use nice round numbers. So let’s say our gym is 30 x 20 x 8 meters. This is a total volume of 4800 cubic meters, or 4.8 million liters.
2. How sensitive are we to fart smells?
Before we establish how sensitive we are to farts, we need to establish what, exactly, makes farts smell in the first place. The common misconception is that our farts smell because of methane, but that can’t be it. Methane is odorless! Lucky for us, there is a collection of scientists who spend non-trivial amounts of time and money studying farts - they’re called flatologists. And like any bona fide science, flatology work is published in academic journals.
There is one paper in particular, published by Suarez, Springfield, and Levitt in 1998, which answers our question. But before we dive into the findings, I feel it appropriate to pause and admire perhaps the greatest opening paragraph to a scientific paper of all time.
Rectal gas has been a topic of scientific and scatological interest since the beginning of recorded history. This fascination with flatus has little to do with its volume, 200–2500 ml per day, but rather its offensive odour. Nevertheless, virtually all scientific publications concerning flatus, which date back to 1816, have focused on the quantitatively important, but non-odoriferous components (oxygen, nitrogen, carbon dioxide, hydrogen, and methane). The odour results from trace components that have proved difficult to identify and quantify.
Attention grabbing opening statement? Check. Using the British spelling to subtly convey authority? Check. Throwing shade at colleagues who study the less interesting parts of your field? Check. Calling out every scientist practicing in your field over the last 200 years? Check. Subtle flex suggesting you’re better at gas chromatography better than your peers? Check. This is nothing short of a tour de force on how to open your argument.
Back to the task at hand. The paper identifies three primary gases that appear in farts at high enough concentrations to smell: hydrogen sulfide, methyl mercaptan, and dimethyl sulfide. Each of these gases contain sulfur, which has a trademark “rotten eggs” smell. Hydrogen sulfide is the most important of the three by far, so that’s the one we’ll focus on.
I don’t know why, but the flatology literature is lacking when it comes to determining our sensitivity to hydrogen sulfide. As far as I can tell, flatologists feel it is out of scope for their field. I disagree, but alas. Luckily, there are lots of other reasons to study our olfactory thresholds to various gases, and finding a paper on it isn’t too hard. Our olfactory threshold for hydrogen sulphide is 0.0047 parts per million.
3. How big is the fart?
This question is surprisingly easy to answer. Flatologists Tomlin, Lowis, and Read published this study in 1991 and found that the median fart volume was about 90 milliliters. Note that, because they’re doing science, they used metric units. To make the math easy, we’ll define our average fart to be 100 milliliters, or 0.1 liters.
Do you want a fun fact? The typical fart is 0.000002% the volume of a typical gym.
4. How potent is the fart?
Remember that paper with the best opening paragraph ever? Initially, we were interested in it because it told us what made farts stink. But just as the authors went above and beyond in the writing of their introduction, they went above and beyond in doing science. They also told us how much farts stink, by calculating the hydrogen sulfide concentration in the average fart. The average concentration is 1.06 micromoles per liter.
Do you want a fun fact? In the average human fart, there are more than 63 quadrillion (specifically, 6.38 * 10^16) molecules of hydrogen sulfide.
Human Math
Our olfactory threshold data is in units of parts per million, or ppm. This is defined in terms of weight, so if Substance A (say, hydrogen sulfide) is at a concentration of 1 ppm in Substance B (say, a fart), Substance A makes up 1 millionth of the weight Substance B. The easiest way to think about this is in units of milligrams per kilogram (metric!), where 1 milligram per kilogram translates to 1 ppm.
To determine the hydrogen sulfide concentration in the gym after the fart, we will calculate the kilograms of air in the gym and the milligrams of hydrogen sulfide released by the fart1. We divide the latter by the former to arrive at ppm.
The kilograms of air can be calculated like so:
\[ 4.8 \cdot 10^{6}L * \frac{1 mole}{24 L} * \frac{0.029 kg}{1 mole} = 5800 kg \] Let’s walk through this one step at a time, from left to right.
We start with the volume of the gym, 4.8 million liters.
In order to calculate the air’s weight, we need to know how many molecules there are. The unit for the number of molecules is called a mole. Using the ideal gas law, a mole of room temperature gas takes up 24 liters of space.
Next, we convert from moles to kilograms, using air’s molecular weight.
So, we have 5800 kilograms of air. Next, we need to calculate the number of milligrams of hydrogen sulfide:
\[ \frac{1.06\mu m}{1 L} * 0.1 L * \frac{1 mole}{10^6\mu m} * \frac{34100 mg}{1mole} = 0.0036 mg \]
Once again, we can work from left to right:
We start with the concentration of hydrogen sulfide.
Then we multiply by the size of the fart, converting from concentration to total output.
We convert from micro-moles to moles to make things easier.
Finally, we use the molecular weight of hydrogen sulfide to convert from moles to milligrams.
We have 0.0036 milligrams of sulfide mixed in 5800 kilograms of air, which comes out to 0.000000623 (6.23 * 10-7) ppm. This is well below our olfactory threshold of 0.0047 ppm, so we conclude that: if a human farted in a gym, not everyone would be able to smell it. It’s true that we already knew that from our lived experience, but this was a good way to learn the math behind it. Plus, we know what we need to know in order to move onto our main goal: elephant farts.
One parting note for this section - human farts miss the mark by 4 orders of magnitude. This means an elephant fart must deliver 10,000 times as much hydrogen sulphide as a human for everyone to be able to smell it.
So what about elephant farts?
First, we should establish that elephants do fart. In fact, there’s lots of evidence that their farts are both large and foul. Take, for example, this quote from a 1936 book on the physiology of the elephant:
No indication of eructation or belching has been noted with the elephant, although this would be difficult to determine exactly. On the other hand, relatively enormous volumes of gas are given off through the anus, especially when the elephant is lying down.
Likewise, this Quora post contains an insightful answer for how bad elephant farts smell:
I was in Thailand at a elephant retirement village a I was passing a elephant when it farted and let tell you it was like a hurricane and it stunk like nothing i could describe. It made me vomit on the spot.
Recall the four factors that determined whether or not we can smell a fart in a gym: the size of the gym, the sensitivity of our noses, the size of the fart, and the potency of the fart. Our gym size and olfactory thresholds don’t change, so that leaves 2 questions about elephant farts: how big are they, and how strong are they?
Unfortunately, the literature on elephants farts not isn’t very deep beyond establishing that they do fart. Try as I might, I was unable to find hard data on elephant farts - either size or concentration. This leaves us no choice but to take a detour and get back to the basics of elephant (and fart) biology.
Elephant Digestion
Elephants are herbivores, which means they only eat plants. Like all herbivores, elephants have a problem: getting energy out of plants alone is difficult. Like all mammals, they don’t have the necessary enzymes to break down cellulose, the main building block of plant matter. Their solution was to turn to the microbial world and digest plants via fermentation. For our purposes, we can boil millennia of complex symbiotic evolution down to one conversation:
Elephant: Hey, I can’t digest this food.
Bacteria: We can help you with that. Do you have something to offer in exchange?
Elephant: How about a place to live that’s warm and insulated from the elements?
Bacteria: That sounds great! One more problem: we’re gonna end up producing poisonous gas that could kill both of us unless you do something about it.
Elephant: Don’t worry, I know exactly what to do about it.
By now we all know what elephants do about it, but we’ll return to that in a bit. For now, we have more biology to learn.
All mammals that digest plants by fermentation take advantage of the same chemical and biological processes. The bacteria that eat the cellulose release lots of gas, including hydrogen sulfide. These fermenting mammals are grouped into 2 categories based on where the fermentation takes place.
- Foregut fermenters, most of which are also called ruminants, ferment at the beginning of the digestive process. This includes cows, deer, antelopes, goats, and the like. Most foregut fermenters have a special organ called the rumen that serves as the fermentation chamber. They remove digestive gases mostly by belching2.
- Hindgut fermenters, on the other hand, ferment at the end of the digestive process. Ungulates like horses and rhinos as well as most rodents are hindgut fermenters. Unlike their foregut friends, these fermenters don’t have a special chamber for fermentation. They use their colon (aka large intestine), and accordingly, remove digestive gases mostly by farting.
Elephants are hindgut fermenters.
How big is an elephant fart?
Because elephants ferment in the colon, their farts serve the same purpose as human farts. When enough gas builds up in the colon, our bodies relieve pressure through the most convenient exit. There’s no hard data on the size of an elephant fart, but we can estimate it using three facts and one assumption.
Fact 1: As previously established, the average human fart is 100 milliliters, or 0.1 liters.
Fact 2: [The average human colon is 5 feet long and about 3 inches wide](https://www.webmd.com/digestive-disorders/picture-of-the-intestines#:~:text=The%20large%20intestine%20(colon%20or,in%20diameter). This translates to a volume of 0.25 cubic feet, but we’re doing science so we need metric units. In metric, the human colon holds about 7 liters.
Fact 3: According to an autopsy, a typical elephant’s colon is around 480 liters.
Assumption: Elephants and humans feel the need to relieve pressure when the colon is at about the same fullness - that is, the fart size is directly proportional to the colon size.
Putting these together is fairly straightforward. The average human fart is 0.1 liters out of a 7 liter colon, which means the fart is about 1.5% the volume of the colon. 1.5% of 480 gives us 7.2, so the average elephant fart is probably around 7.2 liters.
How strong is an elephant fart?
Despite the different location of fermentation, the distinction between foregut and hindgut fermenters doesn’t matter when it comes to which gases are formed and how much. The biological and chemical processes are largely the same. Therefore, we can use the chemical composition of cow belches as an approximation for the chemical composition of elephant farts3. And lucky for us, the gas profiles in a cow’s rumen, and therefore its belch, is very well studied!
The strength of the fart comes down to the concentration of hydrogen sulfide in the fermentation chamber. The most cited paper on hydrogen sulfide concentration in the cow’s rumen is by Kleiber et al. back in 1943. In it, the average hydrogen sulfide concentration of all cows they measured is 0.11%. Because we use the rumen as a proxy for elephant farts, that translates to 1100 milligrams of hydrogen sulfide per kilogram of fart.
When we calculate the total amount released by a fart, we need the fart’s molecular weight. So let’s note the makeup of the entire fart: 0.11% hydrogen sulfide, 66.5% carbon dioxide, 25.2% methane, 0.59% oxygen, and 7.6% nitrogen. The molecular weight is 35.65 grams.
Do you want a fun fact? The average elephant fart weighs about 21% more than air.
Elephant Math
Once again, our goal is to compare the milligrams of hydrogen sulfide released by the elephant to the kilograms of air in the gym. We already established that the weight of the air in the gym is 5800 kilograms, so we just need to calculate the weight of the elephant’s hydrogen sulfide emissions:
\[ \frac{1100 mg}{kg} * 7.2 L * \frac{1 mole}{24 L} * \frac{0.03565 kg}{mole} = 11.75 mg \] Let’s work from left to right:
We start with the concentration of the elephant fart, which is 1100 milligrams per kilogram.
Next, we include the size of the elephant fart (7.2 liters) to convert concentration to total output.
To calculate the number of molecules the elephant released (remember, the unit for this is called a mole), we use the same conversion as before, where 1 mole’s worth of room temperature gas take up 24 liters4.
- Finally, we need to multiply by the molecular weight of the elephant fart to isolate the milligrams of hydrogen sulfide.
Overall, this comes out to 11.75 milligrams of hydrogen sulfide, which dwarfs the puny 0.0036 milligrams our human released. Once we account for the amount of air in the gym, the concentration comes out to 0.002 ppm. Unfortunately (or fortunately, depending on your point of view), this is less than half the human olfactory threshold of 0.0047 ppm.
We are forced to conclude, then, that if an elephant farted in a gym, it’s unlikely everybody would be able smell it.
Darn. But after all this work, we’re not gonna stop there. That would be silly. At overthinkDCIscores.com, we commit to the rep.
Under what conditions would everyone smell the fart?
Our conclusion comes with a lot of uncertainty because we don’t know that much about elephant farts. I think there’s a strong argument to be made that we are underestimating both the size of an elephant fart and its potency.
We start with the size of the elephant fart. To calculate the average of 7.2 liters, we had to assume that fart size scales linearly with colon size. But this may not be the case. Humans aren’t hindgut fermenters5 so the elephant’s colon is a lot more active than ours. It could very well be the case that because the bacterial activity is a lot stronger, an elephant’s colon may fill with gas quicker than ours. If that’s true, then the average elephant fart could be more like 10-15 liters, rather than 7.2.
If you’re a footnote reader, you know that our use of the cow’s rumen as a proxy for the elephant’s colon is a little too good to be true. The result of this convenient lie is that the estimated potency of the fart is, if I had to guess, too low. To understand why, we need to do a bit more biology.
Both cows and elephants ferment cellulose primarily using anaerobic fermentation. However, a cow’s rumen has access to more oxygen because it’s near the mouth and throat - air gets in when cows chew, swallow, or moo. This steady dose of regular air as the cow chews and swallows allows for aerobic reactions, and aerobic digestion is far more efficient.
This paper suggests that there probably are some differences between the cow’s rumen and elephant’s colon. Both ferment cellulose using primarily anaerobic fermentation, but a cow’s rumen has access to oxygen because it’s near the mouth and esophagus.
The elephant’s colon doesn’t get any air, so it’s fairly inefficient. To make the energy balance work requires more dissimilatory sulfate reduction, which creates energy by creating hydrogen sulfide. This study supports the notion that there would be more hydrogen sulfide in the colon than the rumen. Naturally, this creates more potent farts. The Kleiber et al. study saw hydrogen suflide concentration in a cow’s rumen close to 0.2% when a cow was bloated, so it’s not crazy to think an elephant’s fart would be two to three times stronger than our original estimate.
Finally, we could also consider a smaller gym in our hypothetical. An elementary school gym is typically 74 feet by 42 feet, as opposed to the 104x64 feet used in high schools. Keeping the same ceiling height, this results in a gym that only holds half as much air as a high school gym. The smaller the gym, the better it is for the elephant.
If we increase the size of the fart to 10 liters and double the hydrogen sulfide concentration, the resulting concentration once the fart has dispersed throughout the gym is 0.005 ppm. This is above our olfactory threshold of 0.0047 ppm, so everyone would be able to smell it! Likewise, keeping our original elephant fart properties but moving to an elementary school gym gets the elephant fart very close to our olfactory threshold.
Overall, our average elephant fart in our average gym doesn’t cross the olfactory threshold. But it’s pretty reasonable to argue that it could and, especially if we use a smaller gym, probably would.
The Final Verdict
To wrap up, let’s view this question Mythbusters-style. Our original question, expressed in the form of a myth, is the following:
One time, an elephant farted in a gym and everybody was able to smell it.
Knowing what we know right now, we can’t outright confirm the myth. But it is definitively plausible. I wouldn’t be surprised by this scenario in the slightest.
Ultimately, we need to perform more experiments to have a better idea. Get on it, elephant flatologists!
Footnotes
Yes yes, I know. Technically we should account for the weight of the fart as well. But the weight of a single fart is so small compared the size of the gym, it doesn’t actually matter. Besides, we’re doing this for fun.↩︎
There is a common misconception that cow farts release a lot of methane, making them partly responsible for climate change. It is true that cows release a lot of methane that is bad for climate change (methane is 30 times more potent than CO2), but they do so by burping. In reality, cows fart very little!↩︎
If this sounds too convenient to be completely true, well … it is. We’ll come back to this.↩︎
Yes yes, I know. Technically, this isn’t really accurate, because an elephants fart is warmer than room temperature. But the effect this would have on our calculations is small enough that it doesn’t matter.↩︎
There is some fermentation that happens in the human colon - this is part of why our farts smell. But it’s mostly incidental.↩︎