# Gerry's World

A glimpse into my life

# Human flatulence is surprisingly bad for the environment

December 26, 2022

## Background

During some holiday sibling banter, the question arose of what biological “emission” (flatulence, eructation, breathing) is worst for the environment. This is a non-trivial question because, although e.g. we emit far less volume of flatus than exhaled CO$$_2$$, the methane is far more potent than CO$$_2$$ in terms of CO$$_2$$ equivalent emissions.

## Calculations

• For CO$$_2$$ equivalent conversions, we use the EPA’s Greenhouse Gas Equivalencies Calculator [1].

• Flatulence (Table 1) is calculated using mean compositional percentages (by volume) [2] and mean production rates [3]. Then, conversions are applied to arrive at CO$$_2$$ equivalent emissions.

• Breathing (Table 2) is calculated using mean production rates of CO$$_2$$ and CH$$_4$$ directly [4] and conversions to arrive at CO$$_2$$ equivalent emissions.

• Eructation data was unavailable :(

Results summarized in Table 3.

Code: Gas Constants
from IPython.display import Markdown
import pandas as pd

# Gas Constants
CO2_equivalent = {
'H2': 0,
'CO2': 1,
'CH4': 25,
'O2': 0,
'N2': 0,
} # https://www.epa.gov/energy/greenhouse-gas-equivalencies-calculator
L_PER_MOLE = 22.4  # common knowledge
DENSITY_G_PER_L = {
'H2':  2.016 / L_PER_MOLE,
'CO2': 44.01 / L_PER_MOLE,
'CH4': 16.04 / L_PER_MOLE,
'O2':  16.00 / L_PER_MOLE,
'N2':  14.01 / L_PER_MOLE,
}  # periodic table
Code: Flatus (Fart) Data
farts_pct = {'H2': 14.8,
'CO2': 34.7,
'CH4': 25.0, # see note in discussion
'O2': 3.3,
'N2': 22.2,
} # doi.org/10.1152/ajpgi.1997.272.5.G1028
gases = list(farts_pct.keys())
farts_volume_L_per_day = 3 # See discussion
farts_mass_g_per_day = {gas: DENSITY_G_PER_L[gas] * farts_volume_L_per_day * farts_pct[gas] for gas in gases}
farts_CO2e_g_per_day = {gas: farts_mass_g_per_day[gas] * CO2_equivalent[gas] for gas in gases}
farts = pd.DataFrame(
data=[farts_pct, farts_mass_g_per_day, farts_CO2e_g_per_day],
index=['% of total volume', 'mass (g/day)', 'CO2-equivalent (g/day)']
).T
farts.loc["Total"] = farts.sum()

Markdown(farts.to_markdown(floatfmt=".1f"))
Table 1: Fart Composition and CO2-equivalent Emissions
% of total volume mass (g/day) CO2-equivalent (g/day)
H2 14.8 4.0 0.0
CO2 34.7 204.5 204.5
CH4 25.0 53.7 1342.6
O2 3.3 7.1 0.0
N2 22.2 41.7 0.0
Total 100.0 311.0 1547.2
Code: Breathing Data
# Farts
breath_pct = {'CO2': '', 'CH4': ''} # Not used, but keeping for consistency
breath_g_per_day = {
'CO2': 28 * 24,
'CH4': 2.5e-3 * 24} # doi.org/10.1016/j.scitotenv.2022.155241
gases = list(breath_g_per_day.keys())
breath_CO2e_g_per_day = {gas: breath_g_per_day[gas] * CO2_equivalent[gas] for gas in gases}
breath = pd.DataFrame(
data=[breath_pct, breath_g_per_day, breath_CO2e_g_per_day],
index=['% of total volume', 'mass (g/day)', 'CO2-equivalent (g/day)']
).T
breath.loc["Total"] = breath.sum()

Markdown(breath.to_markdown(floatfmt='.1f'))
Table 2: Fart Composition and CO2-equivalent Emissions
% of total volume mass (g/day) CO2-equivalent (g/day)
CO2 672.0 672.0
CH4 0.1 1.5
Total 672.1 673.5

### Results Summary

Code
df = pd.concat((farts, breath), axis=0, keys=['Flatulence', 'Breathing'])
# df.plot.pie(y='CO2-equivalent (g/day)', figsize=(6, 6), autopct='%1.1f%%', title='CO2-equivalent Emissions')
df2 = df[df.index.get_level_values(1) == 'Total'].iloc[:, [2]]
df2['% of total'] = df2['CO2-equivalent (g/day)'] / df2['CO2-equivalent (g/day)'].sum() * 100
df2.loc["Total"] = df2.sum()
Markdown(df2.to_markdown(floatfmt='.1f'))
Table 3: Summary of CO2-equivalent Emissions
CO2-equivalent (g/day) % of total
(‘Flatulence’, ‘Total’) 1547.2 69.7
(‘Breathing’, ‘Total’) 673.5 30.3
Total 2220.7 100.0

To put this in perspective, the average American produces 17.38 metric tons of CO$$_2$$ equivalent per year [5, p. 2019], so farting and breathing combined is about 4.7% of that! Farting alone is about 3.2% of an American’s yearly CO$$_2$$ emissions! Worldwide carbon emissions per capita are lower at around 6.35 tons/year, making human farting and breathing about 12.8% of global CO$$_2$$ equivalent emissions! (See discussion for the caveat, though, that we assume a methane producing person, of which only about 1 in 3 people are, reducing it to about 3.9%). (Also, there’s the caveat that, since our food is grown/raised, our bodies are kind of “carbon neutral” in a sense, but this shouldn’t absolve us of our guilt because e.g. farmland fixes less carbon than fallowed land).

## Discussion

As one may expect, humans are highly diverse so these numbers often have very large standard deviations.

Notably, CH$$_4$$ concentration in both flatulence and breath is highly bimodal, with most people producing virtually no methane but some small percentage (about a third [6]) of people producing significantly more [6]. For sake of fun, I assume that the hypothetical person in question is in the latter category: a “methane producer” as it is referred to in the literature. For flatulence, I use a “reasonable” value of 25% methane (instead of the 5.6% mean) [2], then, to hack-ily make the percentages add up to 100 again, I reduced the H$$_2$$ percentage from 34.3 to 14.8%, since that was most negatively correlated with CH$$_4$$. For breath, from [4, Fig. 1], I estimate 2.5 mg/hour.

For the total daily production of flatulence, this is also highly variable, but is reportedly between 16-64 mL/hour [3]. Even this is probably an estimate based on citations from the meta-analysis [6], which states studies reporting 2.2, 3.5, and even 10 L/day (10 L/day = 416 mL / hour!). I’ll just call it 3 L/day.

Despite methane exhalation being highly variable (see above), CO$$_2$$ production from breathing appears have relatively little variation [4]. From [4, Fig. 1], I estimate 28 g/hour. Other sources claim CO$$_2$$ production can also be very well estimated from biomass across a wide range of ectotherm species.

## Conclusions

Even though a lot of these numbers are highly variable and not particularly reliable, I was surprised to find:

1. There’s a pretty big body of literature of the topic of human body emissions! There’s probably 2-dozen papers on the topic of flatulence alone.
2. Flatulence produces around 2.3x more CO$$_2$$-equivalent emissions than breathing (70% vs 30%), assuming you are a methane producer (~0.3x otherwise).
3. The average American’s farts make up 3.2% of their yearly CO$$_2$$ emissions, and the average person’s farts make up 12.8% of their global CO$$_2$$ emissions (assuming they are a methane producer).

## References

[1]
US Environmental Protection Agency (EPA), 2022.
[2]
F. Suarez, J. Furne, J. Springfield, and M. Levitt, Am J Physiol, vol. 272, no. 5 Pt 1, pp. G1028–33, May 1997.
[3]
K. R. Price, J. Lewis, G. M. Wyatt, and G. R. Fenwick, Food / Nahrung, vol. 32, no. 6, pp. 609–626, 1988.
[4]
M. Li, G. Bekö, N. Zannoni, G. Pugliese, M. Carrito, N. Cera, C. Moura, P. Wargocki, P. Vasconcelos, P. Nobre, N. Wang, L. Ernle, and J. Williams, Science of The Total Environment, vol. 833, p. 155241, 2022.
[5]
H. Ritchie and M. Roser, 2019.
[6]
D. Polag and F. Keppler, Atmospheric Environment, vol. 214, p. 116823, 2019.