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Calories or Kilojoules?

January 21st, 2013

Like many of us, I’m engaged in a constant struggle to maintain a healthy weight and fitness level, and being an economist, I naturally like to think about this in quantitative terms (I’m not alone in this).

The basic equation is simple[1]: Energy used – energy consumed = fat burnt. But to make sense of this equation, we need units, and that raises the immediate questions:

Calories or kilojoules? and
How much do I have to burn to lose 1kg of fat?

The short answers are: Calories and 9000 Cal[2]

More over the fold

Calories (more precisely, kilogram calories, Cal in SI) are familiar and widely used, but Kilojoules are the Standard International Unit, and are more prominently displayed on food. 1 calorie is approximately equal to 4 kilojoules, which is discouraging, because Australian food labels report kilojoules (calories in small print) while most exercise programs only give you calories. Looking at how the unit are derived, this is the wrong way around.

A calorie is a unit of heat: the amount required to raise the temperature of a kilogram (or litre) of water by 1 degree Kelvin (or Celsius). That makes sense as a measure of food energy, since we burn it. A Kilojoule is a measure of work done: it’s what’s needed to generate one kilowatt of power for one second. So, if you’re concerned with running or cycling, the question of interest is how many kilojoules you can generate in torque, overcoming resistance and so on.

So, we might say that Calories are input and Kilojoules are output. If you want to lose weight, it’s calories burnt that matter. But it turns out, quite by chance, that calories are also a pretty good output measure. That’s because, considered as engines, our bodies are only about 25 per cent efficient, which roughly cancels the ratio of kilojoules to calories. So, one calorie (= 4Kj) consumed translates to about 1Kj of useful work.

That makes sense to me. At top pace, I burn around 1000 Cals an hour. At 25 per cent efficiency, that amounts to an output of 250 watts, which is about right, given that I weigh 70kg, am travelling at 3.5m/s and would decelerate to zero in a couple of seconds if I stopped pushing. (The efficiency figure is just for conversion of food to mechanical energy – there’s a whole lot more to consider in terms of the mechanical efficiency of running. Measurement is much easier in the case of cycling).

On the second question, the energy content of fat is around 37Kj/g, or 9Cal/g. Exercise will also result in fluid loss, but since fat doesn’t contain much water, this is all temporary.

So far, I’ve talked only about the difference between calories in and out, but what about the levels? It’s surprisingly hard to get good estimates, but it appears that a moderately active man of my age should be consuming 2000-2500 Cals/day. I’d say I’m burning an extra 1000/day, but on the other hand, I’d like an energy deficit of 500/day at the moment, since I’m trying lose a few kilos I put on at the end of last year. However, I’m not measuring calorie intake with any precision, relying for the moment on more activity and cutting down on a few obvious items, like alcohol.

fn1. Exploiting it is not so simple. I’m not an expert, but it seems pretty clear that, if you have been at a given weight for a long time, your body will try to keep you there, by slowing down metabolism, sending hunger signals to your brain and so on. Still, having lost 15 kilos over a couple of years, and kept all but 2 or 3 off for a couple of years more, I don’t accept the fatalist view that there’s nothing to be done about this.

fn2. My earlier understanding was 7500, and since posting, I’ve seen some sources to support this. YMMV

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