health weight

Calories In - Calories Out


By far the most popular model of weight loss is the "calories-in-calories-out" (CICO) framework, which maintains that the change in your weight is given by

∆ (weight in pounds) = ((calories eaten) - (calories expended))/3500

This is one of those models that is technically true, but has significant issues in practice, mainly that it completely ignores why people eat and expend different amounts of calories and what exactly it means by "calories in" and "calories out".

The most naive CICO model is to add up the calories on nutrition labels and subtract the calories you burn just by living (BMR) and that you burn by exercising. The rest of this section basically explores how this naive model is insufficient and what adjustments that need to be made.

We'll start with two details in measuring "calories in" (imperfect absorption and digestive energy expenditure) and then talk about details relating to "calories out".

Calories In: Imperfect Absorption

Some nutrients that technically have calories (they burn) just have a hard time being absorbed by the body.

Fortunately, the US Department of Agriculture has done ample research on this subject Energy Values of Food ... basis and derivation. They distinguish between two types of energy content:

  1. gross energy - the energy released by burning the food
  2. fuel value - the gross energy minus the energy that isn't digested (i.e. that ends up in your urine and fecal matter)

The ratio of these two values is the coefficient of digestibility varies a great deal. Some examples (from Table 13):

FoodCoefficient of Digestibility
Eggs, Meat, Dairy97%95%98%
Legumes & Nuts78%90%97%
* 98% of Alcohol's calories are actually digested.

Calories In: Digestive Expenditure

Your body expends ~10% of its energy digesting the food you eat, but some food is harder to digest than others. In particular Kollias:

MacroEnergy Spent Digesting

TODO: Get a better source.

Nutrition Labels

Unfortunately, the FDA provides six different ways for companies to compute the caloric content of the foods they sell for nutrition labels (search for "Caloric content may be calculated by the following methods") Title 21.

One of those methods is to reference the "Table 13" I reference above. Another, though, is to just us 4, 4, and 9 calories per gram of protein, carbohydrate, and fat, respectively. In other words, from a practical point of view, you (the consumer) can't know whether absorption is being accounted for. I don't think any of the methods accounts for the energy spent digesting food.

Calories Out: Basal Metabolic Rate

Your basic metabolic rate (BMR) is essentially the minimum energy your body consumes just staying alive. It is determined largely by how much fat free mass you have, but other variables matter too including sex, fat mass, height, and age Basal metabolic rate. Even after controlling for these there can be significant individual variation in BMR ~13% in either direction.

The most popular formula is the revised Harris-Benedict equation (with kg, mc, years), which is

13.75 * (mass) + 5.00 * (height) + 6.76 * (age) + 66.47

for men and

9.56 * (mass) + 1.85 * (height) + 4.68 * (age) + 655.10

for women. However, an alternative is the Katch-McArdle formula:

370 + 21.6 * (fat free mass)

An in-depth study found that muscle burns about 5.7 (SE=0.1) kcal per pound while fat burns 1.8 kcal (SE=0.2) per pound Specific metabolic rates of major organs and tissues across adulthood, generally confirming earlier estimates of 5.9 and 2.0 kcal, respectively Elia.

Eating more protein relative to other macros helps you build and maintain muscle mass rather than fat mass. In other words, muscle burns more calories than fat, which suggests a naive CICO model will tend to under-prescribe protein for weight loss.

Calories Out: Exercise

There isn't too much to say here. Moving your body takes energy. Generally, oxygen consumption is considered the most accurate way to estimate energy expenditure; though using heart beats can be used as a more convenient approximation.

You burn about 4.9 ± 0.2 calories per liter of oxygen consumed, with the uncertainty being based on whether you're burning carbs or fat Robergs.

When using heart beats, a widely used formula for estimating calories burned per hour Keytel for males is

2.9 * (age) - 0.6 * (weight) + 9.0 * (heart beats per minute) - 790

which implies each heartbeat burns 0.15 calories. For females, the formula is

1.1 * (age) - 0.8 * (weight) + 6.4 * (heart beats per minute) - 293

which suggests each heartbeat burns 0.11 calories.

However, both these equations are clearly wrong. They suggest, for instance, that a young average male would burn 0 calories with a heart rate of 84 bpm and negative calories with lower hearts rates.

If you know your maximal oxygen consumption, they also give another formula.

5.5 * (VO2 max) + 6.5 * (heart beats per minute)

Finally, you can estimate your VO2 max using

15.3 * (max heart rate) / (resting heart rate)


15.3 * (208 - 0.7 * (age)) / (resting heart rate)

TODO: Resistance training vs cardio.

Morning exercise might be better than other times of day Willis.

Calories Out: Non-Exercise Activity

Non-exercise activity thermogenesis (NEAT) Non-exercise activity thermogenesis (NEAT) refers to energy you expend "that is not sleeping, eating or sports-like exercise". NEAT typically accounts for 15% - 50% of human energy expenditure, so this isn't some minor detail in the CICO equation.

Since NEAT is defined as non-exercise, what counts as NEAT depends on what counts as exercise - a distinction that isn't entirely clear. For instance, standing and fidgeting are clearly NEAT; jogging and climbing stairs in the gym are clearly exercise; but what about about climbing a flight of stairs to get to your bedroom? The dividing line is further complicated by the fact that your energy expenditure is typically elevated for hours after you exercise Excess post-exercise oxygen consumption.

Some studies have estimated NEAT based on lifestyle. This is typically computed by dividing (BMR + NEAT) / BMR yielding values of at least 1. One table is Non-exercise activity thermogenesis (NEAT)

Chair-bound or bed-bound1.2
Seated work with no option of moving around and little or no strenuous leisure activity1.4 - 1.5
Seated work with discretion and requirement to move around but little or no strenuous leisure activity1.6 - 1.7
Standing work (e.g., housewife, shop assistant)1.8 - 1.9
Strenuous work or highly active leisure2.0 - 2.4

Some observations Non-exercise activity thermogenesis (NEAT):

  • Eating generally causes NEAT to increase.
  • Overweight people tend to be less active.
  • NEAT has decreased in society over time as obesity has increased.
  • Some experimental studies have shown that there is significant variation between how much people's NEATs change when their calorie intake is modified, and that this is at least partly genetically determined.

TODO: See also Nonexercise activity thermogenesis (NEAT): environment and biology

Water Weight

Unfortunately, when you stand on the scale, the number you see fluctuates far more than your "true" body weight. This is mostly because of changes in the amount of water in your body. See here for more details. The other obvious cause of these fluctuations is because of the non-liquid portion of food you eat that *ahem* passes through without being absorbed.

The Good CICO Model

So, if you control for all the above, is CICO correct?

Pretty much.

A number of experts put together a fairly comprehensive CICO model Quantification of the effect of energy imbalance on bodyweight Supplementary webappendix that can be used by anyone via a user-friendly web UI Body Weight Planner. The model accounts for whether weight gain/loss is primarily fat or lean tissue how that affects caloric expenditure, how different amounts of fat and lean body mass affect exercise caloric expenditure. It also accounts for the thermic effect of feeding.

The model has been validated on the CALERIE study Heilbronn and inpatient data.

In other words, we have a pretty accurate understanding of how a caloric surplus happens, how that surplus is converted into new body weight (typically fat), and how that new body weight affects future energy surpluses.

This does not answer why people eat/exercise as much as they do. But the model does imply this is really the hard part of weight management. For instance, the authors note that dieting usually leads to significant weight loss, weight then typically hits a minimum at the 6-8 month mark, and then most of the weight is regained.

The model claims to shed some light on this, finding that the implied adherence to the weight-loss plan only lasts for a few weeks, after which it gradually falls over over the next several months. However, because it takes so long for weight to change, the perception among dieters is that there is minimal relationship between how harshly they stick to their diet and their change in weight; hence, people think they're just hit plateaus or gain weight despite dieting - the reality is they're adherence is just worse.

Potential Limitations

However, before we take the model above as gospel, its worth exploring some limitations besides just plan adherence. Some are just pragmatic limitations: the model doesn't account for absorption and digestive expenditure differences between food types. You could account for this yourself if you wanted to, but I've never heard of anyone doing so.

Other issues are more fundamental:

  1. The model ignores the subtleties of energy expenditure. Instead they estimate energy expenditure by multiplying someone's resting metabolic rate by someone's physical activity level. This is true by definition, so its not wrong, per se, but how is one supposed to measure it? I'm primarily concerned by NEAT here.
  2. The model assumes someone's history has no effect on their present. I'm not claiming this is wrong, but I've heard many people claim things like being overweight once makes it harder to maintain a lower weight later and that this is a metabolic issue, not an exclusively psychological one. Again, I'm mostly concerned with NEAT here, but I've heard people claim this history can depress BMR too.
  3. The study clams it can accurately predict weight

Individual Variation



So is CICO right? I guess?

Its supporters will tell you it must be right because of thermodynamics. It's really more of a claim about biochemistry through, because thermodynamics doesn't tell our cells to store and extract energy equal to the efficacy of fire. That being said, it is pretty much true.

But even then, the claim is at least somewhat philosophical. No one goes around arguing that weight loss is as simple as "weight in minus weight out" (WIWO), even that is actually true by pure physics (conservation of mass). So, perhaps the important questions are (1) how useful it is and (2) what else is true about weight loss in addition to CICO.

There's no debate that CICO is more useful than WIWO - despite all the above disclaimers, the calories on a box of food are a decent estimate of their effect on your weight during a diet, something that is far less true of the food's raw weight.

That being said CICO as its typically practiced is also fairly incomplete in fairly important ways. I'll examine how this is in detail later, but to give you a taste: in real life a 500 kcal weight loss diet will cause dramatically less than 1 pound of weight loss per week, which is what the naive CICO would predicts, probably mostly due to NEAT issues. Moreover, how much the naive CICO overshoots is largely determined by your genes.

CICO also ignores why people ingest and expend what they do. This isn't an argument against CICO's validity, but is again suggestive that there is more to glean from the literature - i.e. that CICO is incomplete as a model of weight gain/loss.

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