Weight Loss


There is decent evidence that most people's health would benefit from losing weight in a wide variety of ways, especially for people who are obese.

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 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".

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. 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
Legumes & Nuts78%
Non-Root Vegetables65%

Just eye-balling the table above, it seems clear that a major confounding factor here is fiber. All the foods with coefficients above above 95% have virtually no fiber, while all the foods below 80% have ample amounts.

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.

Muscle Mass

Finally, eating more protein relative to other macros helps you build and maintain muscle mass rather than fat mass. Most people view this as inherently desirable and it also raises how many calories you naturally burn (see below).

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)


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)

Though, to be perfectly honest, given the absurdity of the sex-based formulas, I'm somewhat skeptical of these formulas too.

Non-Exercise Activity

Non-exercise activity thermogenesis (NEAT) Levine 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 Levine

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:

  • Eating generally causes NEAT to increase and vice-versa.
  • Overweight people tend to be less active.
  • NEAT has decreased in society over time as obesity has increased.

These observations suggest that variation in NEAT may be crucial to understanding variation in body weight and in theories dealing with bodies having a "set point" - a weight they naturally return to. This has been somewhat confirmed in experimental studies, where it has been shown that there is significant variation between how much people's NEATs change when their calorie intake is modified.

Other Topics

"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 your water weight. 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.





Wikipedia contributors. (2020, August 26). Basal metabolic rate. In Wikipedia, The Free Encyclopedia. Retrieved 19:50, August 27, 2020, from https://en.wikipedia.org/w/index.php?title=Basal_metabolic_rate&oldid=975128276 Merrill, A. Watt, Bernice. (1973). Energy Values of Food ... basis and derivation. United States Department of Agriculture. https://www.ars.usda.gov/ARSUserFiles/80400525/Data/Classics/ah74.pdf Kollias, H. Research Review: A calorie isn't a calorie. Precision Nutrition. https://www.precisionnutrition.com/digesting-whole-vs-processed-foods#:~:text=Protein%20takes%20the%20most%20energy,digest%20and%20absorb%20the%20protein. Levine, J. A. (2002). Non-exercise activity thermogenesis (NEAT). Best Practice & Research Clinical Endocrinology & Metabolism, 16(4), 679-702. Wikipedia contributors. (2020, April 13). Excess post-exercise oxygen consumption. In Wikipedia, The Free Encyclopedia. Retrieved 23:02, August 28, 2020, from https://en.wikipedia.org/w/index.php?title=Excess_post-exercise_oxygen_consumption&oldid=950690897 Robergs, R. A. Kravitz, L. Making Sense of Calorie-burning Claims. https://www.unm.edu/~lkravitz/Article%20folder/caloricexp.html Keytel, L. R., Goedecke, J. H., Noakes, T. D., Hiiloskorpi, H., Laukkanen, R., van der Merwe, L., & Lambert, E. V. (2005). Prediction of energy expenditure from heart rate monitoring during submaximal exercise. Journal of sports sciences, 23(3), 289-297. https://doi.org/10.1080/02640410470001730089