Why dividing pounds by pounds-per-week gives the wrong date
The usual estimate is total loss divided by weekly rate. Lose 13 kg at 0.85 kg a week and you get 15.3 weeks. That answer is wrong, and it is wrong in a predictable direction: it is always too soon.
The reason is that your expenditure depends on your weight. A lighter body has a lower basal rate — 10 kcal a day less for every kilogram, in the Mifflin-St Jeor equation — and it also costs less to move, which the activity multiplier scales up further. At a moderate activity level, each kilogram you lose reduces daily expenditure by about 15.5 kcal. Hold intake constant and your deficit shrinks by the same amount, week after week.
The result is not a straight line but a geometric approach to a plateau. There is a weight at which your chosen intake is exactly maintenance, and your weight glides towards it, quickly at first and ever more slowly. You never quite arrive, which is the mathematical version of the very real experience of the last few kilograms taking longer than the first ten.
Because Mifflin-St Jeor is linear in weight, this curve has an exact closed form rather than needing simulation. That is what this calculator solves, so the projected date accounts for the slowdown from the first week rather than discovering it later.
How the projection works
Three quantities do all the work.
The fixed part of your basal rate. Write Mifflin-St Jeor as BMR = 10W + C, where C = 6.25 × height − 5 × age plus the sex constant. C does not change as you lose weight, so all of the weight dependence sits in the 10W term.
The plateau weight. Set expenditure equal to intake and solve: W* = (intake ÷ PAL − C) ÷ 10. This is the weight at which your planned intake stops being a deficit. Everything about the timeline follows from how far you currently are above it.
The weekly approach rate. Each week you lose a fraction a = 70 × PAL ÷ 7,716 of the gap between your weight and the plateau, where 7,716 kcal per kilogram is the energy density of body-weight change. At PAL 1.55 that is 0.01406, so you close about 1.41% of the remaining gap each week regardless of how big it is.
Put those together and the weight after n weeks is W* + (W₀ − W*) × (1 − a)ⁿ. Invert it with a logarithm and you have the number of weeks to any goal weight above the plateau. A goal at or below the plateau is unreachable at that intake, and the calculator says so rather than returning a very large number.
Worked example: 95 kg to 82 kg on 2,000 kcal a day
A 35-year-old man, 178 cm tall, moderately active (PAL 1.55), currently 95 kg, aiming for 82 kg on a planned intake of 2,000 kcal.
- Fixed term. C = 6.25 × 178 − 5 × 35 + 5 = 1,112.5 − 175 + 5 = 942.5 kcal.
- Starting expenditure. (10 × 95 + 942.5) × 1.55 = 1,892.5 × 1.55 = 2,933 kcal/day, so the opening deficit is 933 kcal.
- First week. 933 × 7 ÷ 7,716 = 0.847 kg.
- Plateau. W* = (2,000 ÷ 1.55 − 942.5) ÷ 10 = (1,290.32 − 942.5) ÷ 10 = 34.78 kg. Far below the goal, so the goal is reachable.
- Weekly fraction. a = 70 × 1.55 ÷ 7,716.18 = 0.014061.
- Weeks. ln((82 − 34.78) ÷ (95 − 34.78)) ÷ ln(1 − 0.014061) = ln(0.78412) ÷ ln(0.985939) = −0.24320 ÷ −0.014161 = 17.2 weeks.
The naive answer was 13 ÷ 0.847 = 15.4 weeks. The adaptive projection adds nearly two weeks — 12% longer — over a modest 13 kg loss. Over a 30 kg loss the gap widens considerably, because the deficit has more time to erode.
Follow the numbers down the curve. At week 8 he is 88.6 kg, expenditure has fallen to 2,833 kcal, and that week's loss is 0.756 kg. By week 16 he is 82.8 kg, expenditure is 2,744 kcal, and the weekly loss is 0.675 kg — 20% slower than week one, on exactly the same diet. If you want to know what intake he should switch to at the end to hold 82 kg, that is the TDEE calculator at his new weight: 2,732 kcal.
Reading the projection honestly
The date is a model output, not a forecast. Three things will move it.
Your real maintenance may differ from the estimate. The activity multiplier is a bracket, and being one bracket out is worth several hundred calories a day. That translates directly into weeks. Validate the estimate against three weeks of your own weight data before trusting a date months out.
Adherence is not perfect. The projection assumes you hit the intake every single day. Most people average a few hundred calories above their target once weekends and untracked extras are counted, and the timeline stretches accordingly.
Adaptive thermogenesis is not in the model. Sustained restriction lowers expenditure by more than the weight loss alone accounts for, partly through reduced spontaneous movement. The projection therefore remains slightly optimistic even after the weight-dependence is handled.
What the model does capture well is the shape: fast early progress, a gradual flattening, and a plateau you approach but never reach. If your own weight follows that shape, the model is working. If your loss stops abruptly rather than tapering, the usual cause is intake drift rather than metabolism.
One more reading. If the calculator says your goal is unreachable, that is genuinely useful information — it means the intake you planned becomes maintenance before you get there. The fix is a lower intake, more activity, or a goal nearer the plateau, and the calorie deficit calculator will tell you which deficit produces which rate.
The worked example, week by week
| Week | Weight | Expenditure | Loss that week |
|---|---|---|---|
| 0 | 95.0 kg | 2,933 kcal | 0.847 kg |
| 4 | 91.7 kg | 2,882 kcal | 0.800 kg |
| 8 | 88.6 kg | 2,833 kcal | 0.756 kg |
| 12 | 85.6 kg | 2,788 kcal | 0.714 kg |
| 16 | 82.8 kg | 2,744 kcal | 0.675 kg |
| 17.2 | 82.0 kg | 2,732 kcal | 0.664 kg |
The weekly loss falls by 20% between week 0 and week 16 with no change to the diet at all. That decline is the entire reason a linear estimate is too optimistic.
What the projection assumes
- Intake is constant and exact. Every day at the entered figure, with no drift and no untracked calories. This is the assumption that breaks most often.
- Activity level is constant. If you add training as you get fitter, expenditure rises and the real timeline is shorter than projected. If you become less active, it is longer.
- Body-weight change costs 7,716 kcal per kilogram. This is the classic 3,500 kcal per pound figure, which describes fat tissue. Early weight change includes glycogen and water and is much cheaper energetically, so the first week or two usually beats the projection.
- Composition of the loss is ignored. The model tracks weight, not fat. Losing lean mass lowers expenditure faster than the equation predicts, which is one reason protein intake and resistance training matter.
- Age is held fixed. Irrelevant over months, mildly relevant over a multi-year projection.
- No adaptive thermogenesis. Real expenditure during sustained restriction falls somewhat below what body size alone predicts.
Expect the first fortnight to beat the projection
Almost everyone loses more in the first one to two weeks than any energy-balance model predicts, because reducing carbohydrate intake depletes glycogen and each gram of stored glycogen carries about three grams of water with it. That drop is real weight but not fat, and it does not repeat. Judge the model from week three onwards, when the water shift has settled.
How this compares with other projections
This model sits between the two extremes in common use. The linear 3,500 kcal rule ignores the weight dependence entirely and always finishes too early. The NIH Body Weight Planner, built on Kevin Hall's differential-equation model, goes considerably further than this calculator: it tracks fat and lean compartments separately, models glycogen and extracellular fluid, and includes adaptive changes in expenditure. It is the most accurate publicly available tool of its kind, and it will generally return a slightly longer timeline than this one for the same inputs.
What the closed-form model here buys you is transparency. Every number in the projection is recomputable by hand from the formula block above, which means you can see exactly which assumption is driving the answer and change it. That is harder with a simulation whose internals you cannot inspect.
To set the inputs properly, work through them in order: estimate your maintenance with the TDEE calculator, choose a deficit and check it against the safe-rate guidance in the calorie deficit calculator, then bring the resulting intake here to see the date. Once the intake is set, split it into grams with the macro split calculator and check the protein figure against the protein intake calculator — the composition of the diet does not change the timeline much, but it changes how much of the loss is fat.