Farting around

Published 2026-04-15 by Michel Anders

The other day I was at some gathering when I heard a serious toot from across the room. Even though I estimated the epic ass trombone to have been played at least four meters away, I started wondering whether dangerous amounts would reach me at that distance. Yes, it was a fairly boring gathering 😁

Assumption

Hydrogen Sulfide ($H_2S$) is the main smelly component.

This might not be completely true, there are certainly other smelly sulfur components present, but hydrogen sulfide is not only a very toxic gas but it also has a very low safety limit, so this might be the component we should be concerned about the most.

Luckily the detection limit for $H_2S$ is way below the threshold safety limit of 1ppm (part per million). It is amazingly low even, at 1ppb (part per billion, or 0.47 ppb to be exact) it is detectable at 4 to 5 times lower concentrations even than the sulfur compound added to natural gas (in most countries ethanethiol $C_2H_5SH$) so that we can smell a gas leak (as natural gas is odourless otherwise)

So the real questions are:

will the concentration stay below 1ppm at 4 meter distance?
can we even detect it at that distance?

Farts can have varying volumes, but we assume that a "good fart"™, one that can be heard quite well, is 1 liter.

A fart contains 50 ppm sulfuric compounds (which would be considered a serious toxic concentration of it were just hydrogen sulfide), so a fart would need to be diluted 50 times to get below the 1ppm safety limit. 50 liters is not a big volume, so even at half a meter away you would probably be quite safe, even from your own farts (but you may want to hold your breath when in an elevator).

This doesn´t mean it wouldn´t be a nuisance: with a detection limit of about 0.5 ppb the concentration would need to be diluted $ 50 ppm / 0.5 ppb = 10⁵ $

Diluting a 1 liter volume by 10⁵ would equate to 100 m³, or roughly a cube of 4.5m to a side. That is enough to stink up a fair sized room!

Now not all smelly compounds are hydrogen sulfide, and most of the ones present have detection limits that are 5 to 10 times higher, but that still equates to quite a big volume, making it likely that it would be detectable at 4 meters.

However, whether we would be able to detect it would not be dependent on dilution alone: Diffusion is a fairly slow process (typically measured in centimeters per second for gases in air at room temperature and standard pressure), and in that time air movement through room ventilation, convection, or movement by people could well have a bigger impact than the dilution. So you might not be able to smell it at all (if you are lucky), or smell it way quicker if air movement was in your general direction.