Weight loss timeline calculator

This calculator disagrees with the others, on purpose

Almost every weight-loss timeline on the web runs on one line of arithmetic: a pound of body weight is 3500 calories, so divide your deficit into it and you have your rate. It is simple, it is old, and it produces a straight line that never stops. Extend it far enough and it predicts a negative body weight, which should have been the clue.

The rule’s failure is not the number 3500. Hall and Chow, writing in the International Journal of Obesity, name the real fault: the most serious error of the 3500-kcal rule is its failure to account for dynamic changes in energy balance that occur during an intervention. Your deficit on day 365 is not your deficit on day one, because the body doing the burning is smaller.

The size of the gap

Same person, same deficit, two models. A 40-year-old man, 5 ft 10 in and 220 lb, lightly active (PAL 1.5), eating 500 calories a day below maintenance:

Produced by this site’s own implementation of the model, and reproducible from the test file that ships with it. By year five the old rule has removed more weight than the person started with.

What is actually running

The dynamic model published by Kevin Hall and colleagues in The Lancet in 2011, which is the maths behind the NIH Body Weight Planner. Instead of one division, it steps forward a day at a time and keeps track of four things:

• Fat and lean mass separately. A kilogram of fat carries 39.5 MJ; a kilogram of lean tissue carries 7.6 MJ. Losing the same mass from each costs wildly different amounts of energy, so how the day’s deficit splits between them matters. The split follows Forbes’s rule: the leaner you already are, the more of each deficit comes out of lean tissue.
• Expenditure recalculated daily. Resting metabolism is regressed on your current fat and lean mass, at 13 and 92 kJ per kg per day. Physical activity is charged per kilogram carried, so the same walk costs less every month.
• The thermic effect of food. Eating less means digesting less. Around 10% of the intake you removed comes straight back off your expenditure.
• Adaptive thermogenesis. A further ~14% of the intake change, arriving over about a fortnight, on top of anything body composition explains. This is the term that makes a plateau arrive sooner than the arithmetic suggests.

Your starting body composition is estimated from height, weight, age and sex using the Jackson regressions from the HERITAGE Family Study, and your maintenance calories from the Mifflin-St Jeor equation — the same one the model itself specifies. You can switch to Harris-Benedict in the form; it reads higher, and seeing how much your timeline moves when you do is a useful lesson in how much of this is estimate.

The one-line version, and the check that it works

The Lancet paper states its own rule of thumb: for an average overweight adult, every permanent change of 100 kJ per day in energy intake leads to an eventual body weight change of about 1 kg, with half of that change achieved in about a year.

That sentence is how we know this implementation is right. Feed our code a 100 kJ/day reduction and it settles at 1.27 kg, reaching half of that on day 373. The test that asserts it is in the repository and runs on every build. A calculator that cannot reproduce its own source paper’s headline number is not implementing that paper.

What this model leaves out, and says so

The published model has a second component for the first few weeks: glycogen, the water bound to it, and extracellular fluid driven by dietary sodium. It is not implemented here, because it needs a carbohydrate intake in grams and a sodium intake in milligrams that nobody arriving at a weight-loss calculator has to hand.

The consequence is specific and worth knowing: the first fortnight of the curve above understates the fast drop on the scale that everybody sees in week one. That drop is real, but it is water rather than fat, and it comes back the moment carbohydrate does. After about two weeks the two versions converge, which is why the appendix itself derives the long-run behaviour from the simplified form.

The larger uncertainty is not the model at all. It is whether your calorie deficit is the one you typed in.

Next

• Weight loss percentage calculator — what you have already done, as a percentage.
• Walking calorie calculator — the same projection driven by movement instead of food.
• Macro calculator — turning the calorie target into grams.