# 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.