Farts per million

“If you think you are too small to make a difference, try sleeping with a mosquito.”

Dalai Lama XIV

I always liked this quote, but felt it didn’t have enough data behind it. It’s fine to say that small things really can make a difference, but how small are these things really?

To find out we are going to need some way of measuring the things in question. We have ways of measuring weight, in grams, kilograms and tonnes (which is also called a megagram, but no-one calls it that). To be totally correct we would be measuring weight but calling it mass and using the units for mass, not weight. But we’re, like, not going there. At least today. Forget I said anything about mass.

Let us instead consider how much space something takes up: volume. For this we can use litres, cubic metres, acre-feet, and a variety of other things. We won’t be using acre-feet today.

To start off on this explanation of little things that impcat bigger things I want to explore the event that at least some people have experienced or been a direct participant in, willing or otherwise, that of the gas-passing individual in a more or less airtight space. Put simply we’re talking about a fart in an elevator.

To start off we first need to know how big our elevator is. I wasn’t having a whole lot of success finding out the most popular elevator in the world, so I decided to measure the one at work. As a side note, measuring the inside of an elevator with a tape measure isn’t considered normal behaviour in the office environment – especially when you are the new guy – but at the time it felt like a reasonable thing to do.

The elevator in my building is a lovely little Finnish number, of the Kone marque. This elevator measures 2.4 metres high, a trim 1.4 metres front to back and a hefty, baby-got-back 2 metres wide. I don’t know much about elevators but I know what I like. This elevator’s total volume  is 6.7 cubic metres.

It seems if there is ever a question you may have, someone has asked it before and possibly done a lot of work in the process. So it goes with flatulence. According to a study conducted at Royal Hallamshire Hospital in Sheffield where 10 volunteers ate their normal diet plus 200g of baked beans a day, the volume of gas produced by a healthy human through flatulence was between 476ml to 1491ml per day (at atmospheric pressure). The most likely amount of gas produced was 705ml of gas and no difference was recorded between male and female volunteers. Also, most participants didn’t fart any methane (only three of the ten did). There you go.

Whilst knowing how much gas a day someone may make may be nice for posterity (ugh), what we really want to know is how big a flatulence event is.  Furthermore to find out the concentration of noxious gases in our hypothetical elevator we need to know what is in that gas.

The British study doesn’t disappoint: the volume of a single fart – politely called an ’emission’ – ranges from an asthmatic 33mL on the low end to a full rip-snorting 125mL at the high end, with a median (that’s the middle, not average) volume of 90mL. 90mL is about a third of a cup.

Another study that looked specifically at the composition of flatus (yes, that’s the name they use) noted that most of the gases in a fart have no odour. In fact 99% of the gas composition is odour-free. That means that the aforementioned 125mL widow-maker has less than 13mL of odour-causing gas in it. The smelly gases? Well the prime culprit is hydrogen sulphide (rotten egg gas), followed by big-hitters methanethiol and dimethyl sulphide with others in smaller amounts.

Back to the elevator. With its volume of 6.7 m³, 13mL makes up just under 1.9 parts per million of the total gas in that elevator. In reality people will take up a bit of the space as well,  say 0.1m³ per person. By probability the more people there are, the greater chance of an emission occurring and also the greater the fraction of the free air in the elevator the fart occupies. I smell trouble brewing.

Anyway, of all the gases in that box pretty much the only ones that matter are the ones in 13mL of volatile substances that your body produces, and that’s a worst case scenario. Our noses are actually far more sensitive to odours than that, even a faint whiff of fart is enough to elicit funny face contortions from the unlucky passerby.

There has been a good deal more research into the sensitivity of human smell than I am prepared to go into. Apparently, humans have quite a good sense of smell even when compared to other animals, including dogs. Knowing what dogs like to smell I personally wouldn’t exactly be putting my hand up to have a go at comparison for science. Studies other than what I have just described look across a range of different things we can smell, some which we can detect even when their concentration is less than one parts in a billion, like the odourant added to BBQ gas. One part per billion is like a tablespoon of water compared to 5 Olympic swimming pools.

Now just for fun, lets look a little at the quote we started out with regarding mosquitoes. Many common mosquitoes in Australia range from 4 to 6mm in length. If we split the difference and make some generalisations we might say that a mosquito flying about and flapping its wings would fill up a sphere with a 5mm diameter. This means our mosquito fills up a volume of 65.5mm³ (cubic millimeters). For context – assuming I can find context for this – there are 1000 cubic millimetres in a millilitre, which is one thousandth of a litre. It’s very small and confusing.

I couldn’t find statistics for bedroom size in Australia, but a bit of a look on renovation forums suggests that somewhere between 3 x 4 metres and 4 x 4 metres is pretty standard for a bedroom, so again we will split the difference and say that 3.5 x 3.5 metres is a pretty standard floor area for a bedroom. The Building Code of Australia has a minimum ceiling height of 2.4 metres, so lets take that too. That gives a room volume of 29.4 cubic metres.

If one were to apply (some may say misuse) the concept above looking at the volume taken up in a room, but instead of a fart consider a mosquito, we find that in terms of the volume occupied, a mosquito makes up 2.23 parts per billion of the room. Therefore, in summary and using a completely flawed comparison, mosquitoes are roughly 1000 times more annoying than the smelly parts of a fart on a volume/volume basis.

5 thoughts on “Farts per million”

  1. I want it rewritten using acre-feet, and the adjective trumpeting. The notion of a widow-maker is novel and apt. It got
    Me thinking, if the gas occupies was on the scale of the mosquito, would it be dangerous?

    1. Noah I’m not quite sure what you mean, because the gas is 1000 greater in volume than the mosquito. However if what you are asking is about a novel insect killer: i.e. would a mosquito in a box with the gas from a fart be in danger then, yes, probably. Hydrogen sulphide is toxic to humans at least above 10ppm, although there is a lot of tolerance at this level. Above may 50ppm cause eye damage, 500ppm may cause neurotoxicity and 1000ppm will lead to almost instant collapse. If a fart contains 0.5% H2S, and a mosquito is in sealed, full-fart environment, that would represent 5000ppm. You would pretty much burn up.

    1. Hi Dave, If you have a wordpress.com account you can subscribe to this newsletter by visiting this site once logged in and clicking “Follow”.

Leave a Reply to desertdates Cancel reply

Your email address will not be published. Required fields are marked *