Calorie Deficit and Weight Change Calculator, With the Floor Built Into the Arithmetic

What daily intake a given amount of weight change over a given number of weeks implies — and, beside it, what the published dynamic model says that intake will actually achieve, which at six months is usually about half. The page refuses rather than answering when the figure would fall below your own estimated basal metabolic rate, or when the rate exceeds 1 kg a week, because a number clamped to a floor looks like an answer.

Last updated 5 Oct 2026

These are measurements of body size. They are not a judgement about you and they are not a diagnosis. They cannot see muscle, bone, where fat sits, or how healthy you are — two people with the same figure can be in very different health. Treat anything here as one rough signal among many, and speak to a doctor or dietitian before making a substantial change to how you eat.

A scenario to test, the intake it implies, and what it will really do

an amount and a number of weeks → kcal/day, with a hard floor at your own basal rate

Sex as the equation uses itUsed only by the Mifflin-St Jeor equation, which carries sex as a single +166 kcal/day term for male against a shared constant of −161. It is a variable in a 1990 regression. The reason it matters here is that it moves your basal rate, and your basal rate is the floor this page will not print below.

Current body weight (kg)Weight in kilograms, as it is now. Two things depend on it: your estimated basal rate, which is the floor, and the check that the amount you are testing is smaller than your whole body weight. Nothing on this page asks for a weight you would like to be, and nothing on it names one.

Height (cm)Height in CENTIMETRES, not metres. The equation’s height coefficient is 6.25 kcal/day per centimetre, so 1.75 typed here instead of 175 lowers your estimated basal rate by about 1,080 kcal/day — which also lowers the floor by 1,080 kcal/day, and that is the dangerous direction for a unit error on this particular page.

Age (years)Adults only; the page refuses below 18. The equation was fitted on adults aged 19 to 78, and a growing body is not a smaller adult body — an energy deficit in childhood or adolescence is a clinical matter and nothing on this page applies to it.

Activity figure for your maintenance estimateThis sets your maintenance intake, which is the number the deficit is subtracted FROM, so it moves the answer more than anything else here. No primary source for the ladder 1.2 / 1.375 / 1.55 / 1.725 / 1.9 could be found; it is convention. The published yardstick it is guessing at is the physical activity level, and the National Academies band that as sedentary 1.0 to 1.39, low active 1.4 to 1.59, active 1.6 to 1.89 and very active 1.9 to 2.5 — against which three of the five rungs sit a whole band below their own label. The BMR and TDEE page sets that out in full and shows what every rung is worth. Choosing a rung too high makes your estimated maintenance too high, which makes the deficit look safer than it is: it is the one input here where optimism is dangerous rather than just wrong.

Custom activity figure (PAL)Only used when the selector says Custom, and locked otherwise. The floor is 1.00 because a total expenditure below the basal rate is not something a living body does. A measured physical activity level from a doubly-labelled-water study belongs here and is the only figure on this page that would be a measurement of you.

Amount of weight change you want to test (kg)This is a scenario to test, not a goal to enter: the page has no notion of a target weight and will not name one, print one, or give you a date on which you would reach one. Put in the amount you are curious about and read what the arithmetic says about it, including the two rows that say how much of it the published dynamic model actually expects. It must be smaller than your current body weight, and it must be above 0 — this page does not model weight gain, which is a different question with a different literature.

Over how many weeksThe horizon for the scenario, from 1 week to 5 years. Longer is where the interesting result is: the linear rule and the published dynamic model agree least over long horizons, and the two rows comparing them at one year and at three years are the most useful numbers on this page. Lengthening this box is also one of only two ways to get a refused scenario answered, the other being to lower the amount.

2,201kcal/dayExample

a 40-year-old man of 90 kg and 175 cm, lightly active at 1.375, testing 6 kg over 24 weeks

The linear rule, the floor, the cap, and the dynamic rule that corrects all three

rate = ΔW / T · deficit = rate × 7,700 / 7 · intake = TDEE − deficit, defined only when intake ≥ BMR and rate ≤ 1 kg/week · BMR = 9.99 W + 6.25 H − 4.92 A + 166 S − 161 · TDEE = BMR × PAL · eventual change = deficit × 4.184 / 100 kg · dynamic change at t years ≈ eventual × (1 − 2^−t)

ΔW, T: the amount in kilograms and the horizon in weeks: a scenario to test, not a goal. The rate is rounded to three decimals before anything is done with it, so the figure you can see is the figure that was used; checked over 520,000 amount-and-horizon pairs, the rounded and unrounded rates never disagree about the 1 kg a week cap
7,700: the conventional metric form of Wishnofsky’s 1958 figure of 3,500 kcal per pound. The exact conversion is 7,716 kcal/kg, and the page prints what that 16 kcal is worth so you can see it is negligible beside everything else here. Wishnofsky’s own derivation — a pound of adipose tissue taken as 87 per cent fat, so 395 g, at 9.5 kcal/g — actually gives 3,752 kcal, which he rounded to 3,500: the famous constant was loose from the day it was published
intake ≥ BMR: the floor, and it is part of the formula rather than a warning beside it. When the subtraction would land below the reader’s own estimated basal rate, the expression returns no number and the page explains instead. It is NOT clamped to the floor, because a clamped figure is indistinguishable from an answer
rate ≤ 1 kg/week: the cap. The US CDC describe a gradual, steady pace as about 1 to 2 pounds a week (0.454 to 0.907 kg) and note that people who lose at that pace are more likely to keep it off; 1.0 kg is a rounded-up form of the top of that range, so the cap is generous. Above it the page refuses rather than answering
PAL: the activity figure, which fixes maintenance and therefore the whole answer. Convention, with no primary source found. Choosing it too high raises maintenance, which makes the deficit look safer than it is and raises the apparent headroom above the floor
4.184 / 100: Hall and colleagues, Lancet 2011: a permanent change in intake of 100 kJ a day leads to an eventual body-weight change of about 1 kg, which is about 10 kcal a day per pound. One hundred kilojoules is 23.9 kcal, so one kilocalorie a day is worth 0.04184 kg eventually. This is a STEADY-STATE relation, which is why it needs the time factor beside it
1 − 2^−t: a single exponential anchored on the published statement that about half the eventual change arrives in roughly a year. It reproduces that anchor exactly by construction. It does NOT reproduce the published three-year figure of 95 per cent — it gives 87.5 — and it understates the first few weeks, where glycogen and its water move faster than any steady-state rule describes. The one-year and three-year rows use the published anchors directly and do not depend on it

Worked example

a 40-year-old man of 90 kg and 175 cm, lightly active at 1.375, testing 6 kg over 24 weeks
Maintenance first, because that is what the deficit comes out of. Mifflin-St Jeor: 9.99 × 90 + 6.25 × 175 − 4.92 × 40 + 166 − 161 = 899.1 + 1,093.75 − 196.8 + 5 = 1,801.05 kcal/day basal. At 1.375 that is 1,801.05 × 1.375 = 2,476.44 kcal/day maintenance. The gap between the two, 675 kcal/day, is the entire room this page has: it is the largest deficit that does not take him below his own basal rate.
The scenario. Six kilograms over 24 weeks is 0.25 kg a week, well inside the cap. At 7,700 kcal per kilogram that is 0.25 × 7,700 / 7 = 275 kcal/day. Subtract: 2,476.44 − 275 = 2,201.44 kcal/day, which the headline rounds to 2,201. It clears the floor by 400 kcal/day, so the page answers.
Now the part most calculators stop before. On the published dynamic rule, 275 kcal a day is worth 275 × 4.184 / 100 = 11.51 kg eventually — but eventually is a long way off, with half of it at about a year. By week 24 the single-exponential form of that rule gives 11.51 × (1 − 2^−24/52) = 11.51 × 0.2738 = 3.15 kg. The linear rule said 6. It overpredicted by 2.85 kg, or 90 per cent, on a completely unremarkable six-month plan.
And the error grows. Hold the same 275 kcal/day deficit and the linear rule predicts 13.0 kg at one year against the published anchor of half the eventual figure, 5.75 kg — a factor of 2.26. At three years it predicts 39.0 kg against 95 per cent of the eventual figure, 10.93 kg — a factor of 3.57. The linear rule has no asymptote; the body has one. Beyond about 46 weeks the arithmetic produces something stranger still, and the page says so when it happens: the deficit the linear rule derived from the amount in the box can no longer reach that amount even in infinite time.
Now break it, because the refusals are the point of this page. Ask for 20 kg in six weeks: that is 3.33 kg a week, past the 1 kg cap, and the page prints no number at all. Ask for 10 kg in 12 weeks: 0.833 kg a week is inside the cap, the implied deficit is 917 kcal/day, and the intake would be 2,476.44 − 917 = 1,560 kcal/day — 241 below his basal rate of 1,801.05. The page prints no number for that either. It does not print 1,801. A figure sitting under the inputs he just typed would read as the answer to the question he asked, and 1,801 is not that answer; it is the arithmetic’s refusal wearing a number’s clothes.
Both sides of the floor, since this is where the whole page lives. His headroom is 675.39375 kcal/day exactly. A rate of 0.613 kg a week implies 674.30 kcal/day and the page answers with 1,802 — one kilocalorie above the floor. A rate of 0.614 implies 675.40 and the page refuses, because the intake would be 1,801.04 against a basal rate of 1,801.05. The test is on the unrounded figures, which is the conservative direction, and the margin row exists so that a reader standing one kilocalorie from a refusal can see it. Across a sweep of 36,200 realistic scenarios, 199 landed within 1 kcal/day of the floor and 99 of those would print identical whole numbers for the intake and the basal rate — so the page prints the margin rather than leaving you to subtract two rounded figures and guess.
Two things worth a sentence each. The constant: 3,500 kcal per pound is 7,716 kcal/kg exactly, not 7,700, and for this scenario that rounding is worth 0.013 kg — thirteen grams, against a dynamic correction of 2.85 kg. The constant is not the problem with the linear rule. And the uncertainty: the ±10 per cent band on his maintenance estimate is 495 kcal/day wide, which is larger than the 275 kcal deficit he is planning. The page says so when that happens, because a plan smaller than the error bar on the number it was built from is a plan whose existence cannot be verified by arithmetic — only by standing on a scale for a month.
For maintenance on its own, with the whole activity ladder visible, see the BMR and TDEE page; for dividing an intake into grams of protein, carbohydrate and fat, the macronutrient split page; and for the clinical form of the energy estimate, with five equations and their disagreement, the energy requirement page.

How far the linear rule is out, and how that grows: a 275 kcal/day deficit

The dynamic column is the published steady-state relation (100 kJ/day gives about 1 kg eventually) with a single exponential anchored on the published one-year half-time. The one-year row is therefore exact against the published anchor by construction; the three-year row reads 10.07 kg where the published 95-per-cent anchor gives 10.93, so this approximation understates the tail, and the calculator above prints the published anchors separately for that reason. The 4-week row is the one to trust least — the early weeks include glycogen and the water held with it, which a steady-state rule does not describe, so the real short-term loss is faster than 0.60 kg. What none of that softens is the last row: the linear rule has no asymptote and the body has one, so the ratio between them grows without limit. A reader told they will lose 39 kg in three years on this deficit has been told something arithmetically derived and physiologically impossible.
Held for	Linear rule at 7,700 kcal/kg	Dynamic rule	Linear divided by dynamic	Overshoot
4 weeks	1.00 kg	0.60 kg	1.67×	+67%
3 months	3.25 kg	1.83 kg	1.78×	+77%
6 months	6.50 kg	3.37 kg	1.93×	+93%
1 year	13.00 kg	5.75 kg	2.26×	+126%
2 years	26.00 kg	8.63 kg	3.01×	+201%
3 years	39.00 kg	10.07 kg	3.87×	+287%
for ever	no limit — it keeps going	11.51 kg	unbounded	unbounded

Where the 3,500 kcal per pound rule came from, and what is wrong with it

The thing to take from this table is that the famous constant is the least of the problem. Wishnofsky’s own arithmetic gave 3,752 and he rounded it to 3,500; the metric version loses another 16 kcal/kg; and all of that is rounding noise beside the fact that the rule treats energy expenditure as a fixed property of a person rather than something that falls as they get smaller. That single assumption is worth about 90 per cent at six months and more than 100 per cent at a year.
The claim	Where it comes from	What is actually known
3,500 kcal is a pound of body weight	Wishnofsky M, Am J Clin Nutr 1958;6(5):542–6. A pound of human adipose tissue taken as 87 per cent fat, so 395 g of fat, at 9.5 kcal/g, which is 3,752 kcal — rounded by its own author to 3,500. It assumes adequate protein and equilibrium of glycogen and nitrogen, so that the weight lost is fat; Wishnofsky said as much.	The derivation is about the energy content of a pound of TISSUE, which is a different question from the energy deficit needed to lose a pound of BODY WEIGHT. Hall’s 2008 modelling found the figure approximately matches the energy density of lost weight in people whose initial body fat is above about 30 kg and overstates the deficit needed in leaner people — and that a greater share of the loss is lean tissue as loss continues, which has a lower energy density. So even on its own terms the constant is not a constant.
7,700 kcal is a kilogram	The metric restatement of the same figure. Rounded: 3,500 kcal/lb is 7,716 kcal/kg exactly, at 453.59237 g to the pound.	A 0.21 per cent difference, which this page prints so you can see how small it is. Anyone arguing about 7,700 against 7,716 is arguing about the wrong digit by a factor of several hundred.
So a 500 kcal/day deficit is about half a kilogram a week, indefinitely	The arithmetic of treating 7,700 kcal/kg as fixed and expenditure as unchanged. It appears in textbooks and on government health sites.	This is the part that is wrong, and it is wrong by a lot. Thomas and colleagues, Int J Obes 2013;37(12):1611–13, state that the rule grossly overestimates actual weight loss, having checked it against seven supervised weight-loss experiments. Hall and colleagues, Lancet 2011;378:826–37, give the published worked case: a 100 kg man cutting about 2 MJ a day is predicted by the static rule to lose roughly 22 kg in the first year, which is around 100 per cent more than the dynamic prediction.
What to use instead	Hall KD, Sacks G, Chandramohan D, Chow CC, Wang YC, Gortmaker SL, Swinburn BA, Lancet 2011;378(9793):826–37. Their stated rule of thumb: every permanent change of energy intake of 100 kJ a day leads to an eventual weight change of about 1 kg, or about 10 kcal a day per pound; half of that change in about a year, 95 per cent of it in about three.	Two numbers instead of one — a destination and a speed — and that is the minimum honest description. It is what this page implements, and it is why the page prints an eventual figure and a by-your-horizon figure rather than a single trajectory. The NIH Body Weight Planner is the full dynamic model from the same group if you want a simulation rather than a rule of thumb.

What the two limits on this page are, and what they are not

Two of these four are enforced in the expression language rather than written in prose, which is the only place a limit actually holds. The engine behind this page returns no value at all when either is breached, so there is no code path on which a clamped intake can reach the screen — and the project’s test suite carries cases on both sides of each limit, one kilocalorie apart at the floor, so a future edit that softened either one would fail rather than ship.
Limit	Where it comes from	What the page does when it is reached
Intake must not fall below the reader’s own estimated basal metabolic rate	Not from a guideline: it is the reader’s own Mifflin-St Jeor figure, so it scales with them instead of being a flat number like 1,200 or 1,500 kcal/day. It is strictly tighter than the only clean published floor in the area — the 2013 AHA/ACC/TOS guideline’s eighth recommendation, that diets below 800 kcal/day belong only with medical monitoring and trained providers — because an adult basal rate is almost always well above 800.	Refuses, and explains. It does not clamp. A figure printed at the floor is indistinguishable from a figure printed because it was the answer, and the one thing this page is built to avoid is handing somebody a number to act on that the arithmetic did not actually produce.
Rate must not exceed 1.0 kg a week	A rounded-up form of the top of the pace the US CDC describe: about 1 to 2 pounds a week, 0.454 to 0.907 kg, with the observation that people who lose at that pace are more likely to keep it off. The cap is deliberately slightly looser than the source rather than tighter, and the page flags the 0.907 crossing separately so both figures are visible.	Refuses, and explains. Twenty kilograms in six weeks is 3.33 kg a week and gets a reason rather than a figure.
The ±10 per cent band on maintenance	Frankenfield DC, Clin Nutr 2013;32(6):976–82: Mifflin-St Jeor within 10 per cent of measured resting metabolic rate in 87 per cent of adults with a body mass index below 30 and 75 per cent of those at or above it, unbiased overall.	Reports it, and compares it with the deficit. It is not a limit and the page does not refuse on it — but when the band is wider than the deficit, which is common, the page says so, because a plan smaller than the error bar on the figure it came from cannot be verified by arithmetic.
A goal weight, or a date	Nowhere. The page has no notion of either.	Never printed. There is no target-weight field, no projected date, and no trajectory. The amount box is a scenario to test and the page says so, because a page that tells somebody what they will weigh on a given day is making a promise that the dynamic modelling says it cannot keep.

Why this page refuses, and why a refusal is a better answer than a number

Almost every calorie deficit calculator on the internet will answer any question you ask it. Type twenty kilograms and six weeks and it will divide, multiply by 7,700, subtract from a maintenance estimate, and print a figure — sometimes a negative one, more often one quietly raised to whatever floor the author chose, 1,200 kcal for women and 1,500 for men being the usual pair. That clamped figure is the single most dangerous output in this subject, because it is indistinguishable from an answer. It appears in the same place, in the same typeface, with the same confidence as a figure that was actually computed, and the reader has no way to know that the page stopped doing arithmetic and started protecting itself. This page does not do that. When the intake it would produce falls below your own estimated basal metabolic rate, or when the rate exceeds 1 kg a week, the expression returns no number at all and the page explains which limit was reached and what the two ways past it are. That is not a disclaimer bolted onto the output; it is how the formula is written, and the test suite carries cases on both sides of both limits so that it stays that way.

The floor is your own basal rate rather than a flat number, and that choice matters. A fixed 1,200 kcal/day floor is simultaneously too low for a large adult and arbitrary for a small one. Your estimated basal metabolic rate scales with your weight, height, age and sex, so it is the right shape, and for an adult it is almost always well above the 800 kcal/day below which the 2013 AHA/ACC/TOS guideline says a diet belongs only with medical monitoring and trained providers — which means the floor here is stricter than the only clean published floor in the area. It is also computed from an estimate rather than measured, and the page is explicit about what that costs: the Mifflin-St Jeor equation lands within 10 per cent of a measured resting metabolic rate in about 87 per cent of adults whose body mass index is below 30 and about 75 per cent of those at or above it, so roughly one adult in eight sits outside that band. When the headline comes within 10 per cent of the floor, the page says in as many words that your real basal rate may already be above the figure it has just printed.

The rate cap comes from the one source in this area that is both clean and usable. The US Centers for Disease Control, whose output is a US Government work and therefore free of the licensing problems that rule out several of the obvious alternatives for this site, describe a gradual, steady pace as about 1 to 2 pounds a week and note that people who lose weight at that pace are more likely to keep it off than people who lose it faster. One to two pounds is 0.454 to 0.907 kg. The cap on this page is 1.0 kg a week, which is deliberately a little looser than the top of that range rather than tighter, and the page flags the 0.907 crossing separately so that both numbers are on the screen. Above 1.0 kg a week there is no published figure this page could point you at, so it stops. A reader asking to lose twenty kilograms in six weeks is asking for 3.33 kg a week, and gets a reason.

Now the arithmetic itself, which is wrong in a way that is well established and almost universally ignored. The rule that 7,700 kcal is a kilogram goes back to a one-page paper by Wishnofsky in 1958: a pound of adipose tissue taken as 87 per cent fat, so 395 grams of fat, at 9.5 kcal per gram, giving 3,752 kcal, which he rounded to 3,500. The metric restatement loses a further 16 kcal/kg, since 3,500 kcal/lb is exactly 7,716 kcal/kg. None of that rounding matters. What matters is the assumption the rule makes when it is used forward in time: that your energy expenditure is a fixed property of you. It is not. As weight falls there is less tissue to maintain and less mass to move, so a constant intake becomes a shrinking deficit and eventually no deficit at all. Thomas and colleagues put it bluntly in 2013, having checked the rule against seven supervised weight-loss experiments: it grossly overestimates actual weight loss. The published worked case, from Hall and colleagues in the Lancet in 2011, is a 100 kg man reducing intake by about 2 MJ a day — the static rule predicts roughly 22 kg in the first year, about 100 per cent more than the dynamic prediction.

What the dynamic modelling offers instead is two numbers rather than one, and this page prints both. The rule of thumb from that Lancet paper is that every permanent change of energy intake of 100 kJ a day leads to an eventual body-weight change of about 1 kg — about 10 kcal a day per pound — with half of that change reached in roughly a year and 95 per cent of it in roughly three. One hundred kilojoules is 23.9 kcal, so a kilocalorie a day is worth about 0.042 kg in the end. That gives a destination and a speed, and it is the minimum honest description of what a deficit does. For the default scenario on this page — a 90 kg man cutting 275 kcal a day for 24 weeks — the linear rule says 6 kg and the dynamic rule says about 3.15 kg, an overshoot of 90 per cent. Hold the same deficit for a year and the gap is a factor of 2.26; for three years, 3.57. And beyond about 46 weeks the arithmetic does something the page flags explicitly, because it is genuinely strange: the deficit the linear rule derived from the amount you entered can no longer reach that amount even if you held it for ever, because the linear rule lets a small deficit accumulate without limit and a body does not.

A note on the opposite error, because being honest about this means admitting the dynamic correction is not the only one. Hall’s 2008 modelling of the energy density of lost weight found that 3,500 kcal per pound approximately matches the energy content of the tissue lost in people whose initial body fat is above about 30 kg, but overstates the deficit required per unit of weight loss in leaner people, and that the average energy density falls as loss continues because a greater share of it is lean tissue. That effect pushes the linear rule toward UNDERpredicting loss, which is the opposite direction from the metabolic adaptation. Both are real. The adaptation is much the larger of the two at any horizon anybody cares about, which is why the net effect is a substantial overprediction — but a page that presented the dynamic correction as the whole story would be doing the same thing it criticises, which is offering one mechanism as though it were the only one.

What this page deliberately does not have. There is no goal-weight field, no projected date, and no trajectory chart. An amount and a horizon are a scenario to test; a goal weight and a date are a promise, and the modelling above says it is a promise this arithmetic cannot keep. There is no 1,200 or 1,500 kcal floor, because a flat number is the wrong shape. There is no body-fat input and no estimate of how much of a loss would be fat, because that depends on composition, protein intake and training, and a figure invented here would be the plausible-but-wrong kind. And there is no encouragement anywhere in the output: a page that praised a deeper deficit or a faster rate would be rewarding exactly the input that pushing further makes worse. If you have ever had a difficult relationship with food or with your own weight, a calculator is a poor instrument and a clinician is a good one; in the UK Beat and in India Vandrevala Foundation both run helplines, and your own doctor is the right first call anywhere.

The other pages that belong beside this one. Your maintenance estimate, with the whole activity ladder visible and the published PAL bands it should be read against, is the BMR and TDEE page — which shares this page’s Mifflin-St Jeor expression exactly, so the basal figures agree to the last decimal. Dividing an intake into grams of protein, carbohydrate and fat, with the published acceptable ranges, is the macronutrient split page. The clinical form of the energy estimate, with five equations compared and their disagreement printed, is the energy requirement page; protein by clinical condition in grams per kilogram per day is the protein requirement page. Fluid is the daily water intake page, and the clinical version the adult fluid requirement page.

Frequently asked questions

Why did the page refuse to give me a number?

One of two limits was reached, and the message under the inputs says which. Either the rate you asked for — the amount divided by the weeks — came to more than 1.0 kg a week, or the intake the scenario implies would have fallen below your own estimated basal metabolic rate. In both cases the page prints no figure at all rather than raising one to the limit, because a clamped number is indistinguishable from a computed one and gets acted on the same way. There are exactly two ways past either limit: a smaller amount, or more weeks. Eating less is not a third way, and that is the reason the floor is written into the formula rather than into a footnote.

Why does it not just show my basal rate as the answer instead?

Because that figure would be an answer to a question nobody asked. You asked what intake a particular amount over a particular time implies; if the honest reply is that no safe intake does it, printing your basal metabolic rate in the place where the answer goes converts a refusal into an instruction. Readers act on the number in the big typeface. There is also a subtler problem: the floor is computed from an estimate with a published accuracy of roughly ±10 per cent in most adults, so a figure printed exactly at the floor stands a real chance of being below the floor it was meant to respect. The page would be clamping to a number it does not actually know.

Is 7,700 kcal per kilogram wrong?

The constant itself is roughly right as a statement about tissue and badly wrong as a way to predict the future. It traces to Wishnofsky in 1958, who took a pound of adipose tissue as 87 per cent fat, 395 g, at 9.5 kcal/g, got 3,752 kcal and rounded it to 3,500; the exact metric form is 7,716 kcal/kg rather than 7,700, a difference this page prints to show you how small it is. The real problem is using it forward in time with expenditure held fixed. Thomas and colleagues in 2013 said the rule grossly overestimates actual weight loss; the published example from Hall and colleagues in 2011 has a static prediction of roughly 22 kg in the first year against a dynamic prediction about half that. This page prints the linear figure because it is what you were expecting, and prints the dynamic figures next to it because they are what will happen.

What is the dynamic rule, in one sentence I can use?

Every permanent change of 100 kJ a day — about 24 kcal — is worth about 1 kg of eventual body weight, with half of it arriving in roughly a year and 95 per cent in roughly three. That is the rule of thumb Hall and colleagues published in the Lancet in 2011, and in imperial terms it is about 10 kcal a day per pound. Run it backwards and it is sobering: a 500 kcal/day deficit converges on about 21 kg, not on an endless half a kilogram a week, and it takes a year to get halfway there. The NIH Body Weight Planner, from the same group, is the full simulation if you want more than a rule of thumb.

Why is there no goal weight field?

Because a goal weight plus a date is a promise, and the modelling this page is built on says it is a promise the arithmetic cannot keep. The amount box here is a scenario to test: you put in a number, the page tells you what intake the old linear rule implies for it, and then tells you how much of it the dynamic rule actually expects by your horizon. That is a different conversation from being handed a date on which you will weigh something. There is a second reason, which is the rule this whole group of pages is written to: nothing here should produce a target somebody could treat as a score to beat. A goal weight is exactly that, and so is a date.

The page says the uncertainty is bigger than my deficit. What am I supposed to do with that?

Measure instead of estimating, because you can. The ±10 per cent band on a maintenance estimate is around 400 to 500 kcal/day for an average adult once an activity multiplier has been applied, and a sensible deficit is 300 to 500 kcal/day, so the arithmetic genuinely cannot tell a real deficit from a rounding error. What settles it is your own weight over three or four consistent weeks at a steady intake: if it is flat, your maintenance is whatever you were eating, and that single observation is worth more than every equation on this site. Use the figure here to pick a starting point, then let the scale correct it. That is also the only route that gets you a maintenance figure specific to you rather than to a 1990 regression on 498 strangers.

Does a faster rate not just get me there sooner?

Not by as much as the arithmetic suggests, and the page caps it anyway. Three things happen as the rate rises. The deficit has to grow in proportion, so it runs into the basal floor and the page refuses. The share of the loss that is lean tissue rises, which has a lower energy density, so each kilogram comes off for less energy than the constant assumes — and losing lean tissue lowers your expenditure further, which deepens the adaptation that was already working against you. And the CDC’s observation about the 1 to 2 pound range is specifically about keeping the weight off afterwards rather than about getting it off at all. The page will answer up to 1.0 kg a week and has nothing to offer above that, because there is no published figure up there to offer.

Why does it refuse an activity figure of 1.00?

It does not refuse the figure; it refuses every scenario that follows from it. An activity figure of 1.00 means your maintenance intake equals your basal rate, so the gap between maintenance and the floor is zero and there is no deficit at all that clears it. That is the arithmetic being consistent rather than awkward: if you really expended nothing above your basal rate, there would be no safe room to cut. In practice nobody is at 1.00 — the published physical activity level bands start at 1.0 and the sedentary band runs to 1.39 — so the option exists on the maintenance page to show you a basal figure with nothing done to it, and it exists here mainly so you can see what the floor does when there is no headroom.

Is this medical advice?

No, and it is a long way from it. It is four numbers put through a 1990 regression, multiplied by a convention with no traceable source, and then put through a 1958 constant and a 2011 correction to it. It knows nothing about your health, your medication, your blood results, your history with food, whether you are pregnant, or anything else that would actually matter. A substantial change to how you eat is worth taking to a doctor or a dietitian first. If weight or eating is a painful subject for you, please treat that as a reason to talk to somebody rather than to a calculator — this page is deliberately built to refuse rather than to encourage, but no arithmetic is a substitute for a person.

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References

Wishnofsky M. Caloric equivalents of gained or lost weight. Am J Clin Nutr 1958;6(5):542–6. The origin of the 3,500 kcal per pound rule and therefore of the 7,700 kcal/kg used in the headline arithmetic on this page. The derivation: a pound of human adipose tissue taken as 87 per cent fat, which is 395 g of fat, at 9.5 kcal/g, giving about 3,752 kcal, rounded by the author to 3,500. It assumes adequate dietary protein and equilibrium of glycogen and nitrogen so that the weight lost is fat, and Wishnofsky stated that where those assumptions do not hold a 3,500 kcal deficit does not equal a pound. Cited here as the provenance of a constant this page uses and criticises, not as support for using it predictively.
Hall KD, Sacks G, Chandramohan D, Chow CC, Wang YC, Gortmaker SL, Swinburn BA. Quantification of the effect of energy imbalance on bodyweight. Lancet 2011;378(9793):826–37. The source of the dynamic rule implemented on this page: every permanent change of energy intake of 100 kJ per day leads to an eventual body-weight change of about 1 kg, equivalently about 10 kcal per day per pound of weight change, with about half the change reached in approximately one year and about 95 per cent in approximately three years. Also the source of the worked comparison quoted here: for a 100 kg man reducing intake by about 2 MJ/day the static 3,500 kcal rule predicts roughly 22 kg of loss in the first year, which is around 100 per cent greater than the dynamic prediction. The conversion used on this page is exact: 100 kJ is 100/4.184 = 23.9006 kcal, so 1 kcal/day is 0.04184 kg of eventual change.
Thomas DM, Martin CK, Lettieri S, Bredlau C, Kaiser K, Church T, Bouchard C, Heymsfield SB. Can a weight loss of one pound a week be achieved with a 3500-kcal deficit? Commentary on a commonly accepted rule. Int J Obes 2013;37(12):1611–13. Cited for its central statement — that the 3,500 kcal rule grossly overestimates actual weight loss despite appearing in textbooks and on government health websites — and for the fact that the authors tested it against seven supervised weight-loss experiments and offered validated dynamic tools in its place.
Hall KD. What is the required energy deficit per unit weight loss? Int J Obes 2008;32(3):573–6. Cited for the correction that runs the OTHER way, which this page states rather than hiding: the 3,500 kcal per pound figure approximately matches the predicted energy density of lost weight in subjects whose initial body fat is above about 30 kg, but overestimates the cumulative energy deficit required per unit weight loss in people with lower initial body fat, and the average energy density of the loss falls as loss continues because a greater proportion of it is lean tissue. The metabolic-adaptation effect is the larger of the two at any practical horizon, which is why the net error is an overprediction.
Centers for Disease Control and Prevention, healthy-weight guidance on losing weight: “People who lose weight at a gradual, steady pace — about 1 to 2 pounds a week — are more likely to keep the weight off than people who lose weight quicker.” The source of the rate framing on this page. One to two pounds is 0.454 to 0.907 kg a week; the page’s hard cap of 1.0 kg a week is a rounded-up form of the top of that range and is therefore slightly more permissive than the source, which the page states, and the 0.907 crossing is flagged separately so both figures are visible. Chosen deliberately as a US Government work, which carries no licence restriction for a site that displays advertising.
Jensen MD, Ryan DH, Apovian CM et al. 2013 AHA/ACC/TOS guideline for the management of overweight and obesity in adults. Cited by recommendation and figure only, with no guideline text or table reproduced. Recommendation 5 describes prescribing 1,200–1,500 kcal/day for women and 1,500–1,800 kcal/day for men, or a 500 or 750 kcal/day energy deficit. Recommendation 8 states that very low calorie diets, defined as below 800 kcal/day, should be used only where medical monitoring and trained providers are available and only as part of a high-intensity lifestyle intervention. This page uses the second as the published comparison for its own floor, which is tighter, and the first as the comparison for a deficit above a quarter of maintenance.
Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 1990;51(2):241–7. The equation behind both the maintenance estimate and the floor on this page: REE = 9.99 W + 6.25 H − 4.92 A + 166 S − 161, from 498 healthy adults aged 19–78 measured by indirect calorimetry. The expression is character-for-character identical to the one on this plugin’s energy requirement page and on its BMR and TDEE page, and golden test cases pin all three to 1,601.25 kcal/day for a 70 kg, 175 cm, 40-year-old man so that none of them can drift.
Frankenfield DC. Bias and accuracy of resting metabolic rate equations in non-obese and obese adults. Clin Nutr 2013;32(6):976–82. Source of the ±10 per cent band this page prints on the maintenance estimate and of the two accuracy figures it quotes: Mifflin-St Jeor within 10 per cent of measured resting metabolic rate in 87 per cent of non-obese and 75 per cent of obese adults, unbiased overall at a 95 per cent confidence interval of −26 to +8 kcal/day. Used on this page for something more than colour: it is the reason the page warns when the headline comes within 10 per cent of the floor, because at that point the floor itself is inside its own error band.
Activity multipliers 1.2 / 1.375 / 1.55 / 1.725 / 1.9. PROVENANCE NOTE: no primary source for this ladder could be found. It is convention, it is the largest single determinant of the maintenance figure the deficit is subtracted from, and on this page it is the input where optimism is actively dangerous — a rung too high raises maintenance, which raises the apparent headroom above the basal floor. The published yardstick is the physical activity level, banded by the National Academies’ energy DRI as sedentary 1.0–1.39, low active 1.4–1.59, active 1.6–1.89 and very active 1.9–2.5; three of the five named rungs sit a whole band below their own label. This is set out in full on this plugin’s BMR and TDEE page.
Verification performed for this page rather than taken from a source, recorded so it can be checked. (1) The rate is rounded to three decimal places before the 1 kg a week cap is applied; sweeping every amount from 0.1 to 200.0 kg in 0.1 kg steps against every horizon from 1 to 260 weeks, and again on half-week steps, gives 520,000 and 1,040,000 pairs respectively and not one disagreement between the rounded and unrounded rate about which side of the cap it falls on. (2) The basal floor is tested on UNROUNDED figures, which is the conservative direction. Sweeping 36,200 realistic scenarios, 199 landed within 1 kcal/day of the floor and 99 of those would print identical whole numbers for the intake and the basal rate — which is why the page prints the margin between them as its own row rather than leaving a reader to subtract two rounded figures. (3) For a 90 kg, 175 cm, 40-year-old man at 1.375 the headroom is 675.39375 kcal/day exactly; a rate of 0.613 kg/week answers and 0.614 refuses, and the test suite carries both. (4) The linear-to-dynamic ratio has a floor of about 1.63 under the single-exponential approximation even as the horizon tends to zero, which is a known failure of that approximation in the first weeks rather than a physiological claim, and the page says so for horizons under thirteen weeks. (5) The Lancet paper’s own worked example was reproduced through this page’s engine rather than on paper. Two megajoules a day is 478.0115 kcal/day; driving the page to the nearest rate it will take, 0.435 kg/week, gives a deficit of 478.5 kcal/day, a linear one-year prediction of 22.62 kg against the paper’s roughly 22, and an eventual figure of 20.02 kg against the paper’s 20. The one-year dynamic figure is where the page is conservative and it says so: the published half-the-eventual anchor gives 10.01 kg, while the paper’s own full dynamic model implies about 11 kg, since it describes the static 22 kg as roughly 100 per cent greater than the dynamic prediction. So this page’s one-year anchor runs about 9 per cent below the full model, and its ratio of 2.26 runs above the paper’s roughly 2.0. The error is in the direction of understating loss, which is the direction that does not flatter the plan.
Licensing position taken for this page, recorded deliberately. The rate framing is taken from CDC material, a US Government work, specifically to avoid the bodies this project has ruled out: NICE, whose UK Open Content Licence is UK-only and forbids display beside advertising, and WHO, whose publications are CC BY-NC-SA 3.0 IGO and whose NonCommercial term this advertising-supported site cannot satisfy. The AHA/ACC/TOS guideline is cited by recommendation number and figure, with no text or table reproduced. The Mifflin-St Jeor, Wishnofsky, Hall and Thomas publications are methods and findings reproduced with attribution, which is normal scholarly use. No criteria list or recommendation table appears anywhere on this page.

CalcEngines health calculators are for education and for checking arithmetic that has already been decided elsewhere. They are not medical advice, they do not decide what to give, and they do not replace the judgement of a doctor, nurse, midwife or dietitian who knows the person in front of them. Every figure depends on the values you enter and on the assumptions stated on the page — check it against the prescription, the product label and your local policy before acting on it.