Swatinem Blog Resume

The REAL mathematics of fat-loss

— 2 min

There is an interesting TED-talk called The mathematics of weight loss which explains with chemical formulas and maths how bodyfat will be turned into \( CO_2 \) and Water.

The presenter starts with the following chemical formula:

\[ C_{55}H_{104}O_6 + 78O_2 \rarr 55CO_2 + 52H_2O \]

And then goes on to calculate that 84% of of the fat is being exhaled as \( CO_2 \). But that is not really what I am interested in, so lets do the calculation again.

Using the list of atomic weights as presented in the video, we get the following totals for the fat and our total \( CO_2 \) exhaled:

\[ 55 * 12.011 + 104 * 1.008 + 6 * 15.999 = 861.431 \newline 55 * (12.011 + 2 * 15.999) = 2420.495 \newline 2420.495 / 861.431 \approx 2.8 \]

Now that is more interesting! So for every kilogram of fat that my body metabolizes, I breath out 2.8 kg of \( CO_2 \).

Even though not every fat is the same, dietary fat is the equivalent to 9 kcal when it comes to dietary labels, so I will just use that. So one kg of fat equals roughly 9000 kcal. Lets assume that my daily energy expenditure is around 2200 kcal, since I am super sedentary right now; when active I would say that my energy expenditure is more around the 3000 kcal range.

Anyhow. So, I would need between 3 to 4 days of fasting to metabolize one kg of bodyfat. Or fasting for 90 days straight to get rid of the roughly 25 kg of bodyfat that I carry around with me.

When it comes to \( CO_2 \), that means that every day I exhale maybe 700-900 g. Considering that a car that is halfway fun to drive emits around 180 g per km, those numbers are put into a quite interesting relation.

We can round that to maybe 300 kg of \( CO_2 \) a year. Multiplying that up to the approximately 8 mil inhabitants of Austria, that is roughly 2.4 mega tons.

Just by people breathing. Certainly less than 1-2 giga byte, lol.