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.

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

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"))

# 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'))

Results Summary

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'))

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).