During the quiet isolation of the global lockdown, I found myself contemplating the invisible systems that sustain us. While we often think of our homes as fortresses of safety, I wondered about the very air we breathe. If a room were truly airtight, how long could a human inhabit it before their own breath turned the sanctuary into a hazard?
This is a back-of-the-napkin exploration of human CO2 production and the timeline of toxicity in a confined space—a simple exercise in systems thinking and environmental estimation.
The Inquiry: When Does Sanctuary Become Toxic?
Most of us spend weeks indoors without a second thought. But from a purely biological perspective, we are constant emitters of CO2. I wanted to quantify the “invisible boundary” of my own room.
Assumptions
- Assuming my room is 4x3x2 m of volume. That’s 24 square meters.
- Assuming air density of air is 1kg per cubic meter (1)(3).
- My room thus has 24kg of air.
- From results of link 1) we produce “0.9 kilograms of carbon dioxide for each day per human” (1).
- CO2 at levels greater then 5% starts to be toxic to humans (2).
- Moist air contains 0.038% of CO2 by volume (1).
Calculation
The question is how long till the room is at toxic level of CO2, assuming ~5% is toxic level. (2) From link (2), people have different tolerance for CO2 toxicity, but we’ll use 5% for this calculation.
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Air in my room contains 0.038% of CO2 by volume. By weight, it’s 0.0006% grams of CO2 per gram of air. (1)
> 0.0006 * 24 = 0.0144 kg of CO2 per kg of air
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If we use 5% toxicity by weight, then 1.2kg of CO2 is considered toxic.
> 24 * 0.05 = 1.2 kg
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Assuming the room is airtight (which it’s not), then in 1.317 days, the room will reach a toxic level of CO2.
> (1.2 - 0.0144) / 0.9 = 1.317
If 5% toxicity is by volume, …
From a caloric intake perspective, …
This is an approximation, helping me decide to open the window every other day rather than keeping it closed all week to keep mosquitoes out and maintain heat.
Note: The density of air is actually 1.225 kg/m3 from Wikipedia (3).
1.3173333333333332
cube_meter = 24
((cube_meter*0.05) - (0.0006*cube_meter))/0.9
1.3173333333333335