Module 1: Energy and caloriesLesson 3 of 136 min read
Calorie math: percentage vs fixed changes from maintenance
Once a calculator has estimated maintenance calories, there are two common ways to describe a number above or below it. One uses a percentage, such as 15% below. The other uses a fixed amount, such as 500 kcal below. Both are simple arithmetic, but they behave differently as maintenance changes. This lesson works through the math, shows why the calculator's table uses percentages, and explains what the well-known 3,500-kcal shortcut leaves out.
Maintenance is the starting point
Every row in the table starts from one estimate: maintenance calories, also called TDEE. The calculator gets it by multiplying a Mifflin-St Jeor BMR by the multiplier for your ‘Activity level’.
Maintenance is itself an estimate. Any row built on it carries the same uncertainty, whether the row is a percentage or a fixed amount.
Percentage changes
A percentage change multiplies maintenance by a factor. Minus 15% means multiplying by 0.85. Plus 10% means multiplying by 1.10.
The key property is scaling. The same percentage is a bigger number of kcal for a bigger maintenance estimate, and a smaller number for a smaller one. For the man in the example below, −15% is 414 kcal under maintenance. For the woman, the same 15% is only about 238 kcal. The table under ‘Change from maintenance’ shows what each percentage works out to: −20%, −15%, −10%, maintenance, +10% and +15%.
Percentage row
Row = maintenance × (1 + change ÷ 100), rounded to whole kcal. Example: −15% → maintenance × 0.85.
Fixed changes
A fixed change adds or subtracts the same number of kcal for everyone, for example 500. It is easy to remember, which is why it is common.
The catch is that a fixed number is a different share of each person's estimate. To see the share, divide the fixed amount by maintenance. For a large estimate, 500 kcal is a modest slice. For a small estimate, it can be close to a third.
Converting a fixed change into a percentage
Share = fixed change ÷ maintenance × 100. Example: 500 ÷ 2,759 × 100 = 18.1%.
The two side by side
The calculator marks any row that falls below the estimated BMR with the note "below your estimated BMR". BMR does not change with the activity menu, but maintenance does, so the mark can appear or disappear as you switch levels.
The examples below use the same two people as the BMR lesson. The man has a large estimate, the woman a small one.
Worked examples
Man, 80 kg (176.4 lb), 180 cm, 30 years, moderate exercise: BMR 1,780, maintenance 2,759 kcal/day. −15% = 2,759 × 0.85 = 2,345 kcal/day. A fixed 500 below gives 2,259, which is 18.1% below. Woman, 60 kg (132.3 lb), 165 cm, 30 years, little or no exercise: BMR 1,320, maintenance 1,584 kcal/day. −10% = 1,426 and −20% = 1,267, the second marked below her estimated BMR. A fixed 500 below gives 1,084, which is 31.6% below.
What the 3,500-kcal rule assumes
A popular shortcut says that about 500 kcal a day below maintenance leads to about a pound of weight change a week. The arithmetic is 500 × 7 = 3,500 kcal per week, treated as one pound, forever.
In 2011, Hall and colleagues published a mathematical model of body weight change in The Lancet. Their work challenged that shortcut. The model found that weight change slows as a person gets lighter, because energy use changes too. The timescale is long and depends on starting body composition.
For an average adult with overweight, the paper's rule of thumb was different. Each lasting change of 100 kJ (24 kcal) a day in intake leads to an eventual change of about 1 kg (2.2 lb). About half of that change happens in about a year, and about 95% in about three years.
A straight line is the wrong shape
The 3,500-kcal shortcut draws a straight line that never bends. The Hall model describes a curve that flattens over time. The model's own rule of thumb, above, is stated as an eventual change reached over years, not a weekly rate.
What the table does not do
The table is arithmetic on an estimate. It does not say which row anyone should pick, and it does not predict weight over time. Those depend on factors no calculator here measures.
The formulas are for adults. They are not made for pregnancy, people under 18, or medical conditions that change energy needs.
See what each percentage works out to for your own maintenance estimate, and which rows fall below your BMR.
Calorie calculatorQuick check
Three questions. Pick an answer to see why.
Maintenance is 2,759 kcal/day. What is 15% below it?
Show the answer
Answer: 2,345 kcal/day 2,759 × 0.85 = 2,345.
Why can a fixed 500 kcal be a large change for one person and a small one for another?
Show the answer
Answer: It is the same number of kcal but a different share of each maintenance estimate 500 ÷ 2,759 is 18.1%; 500 ÷ 1,584 is 31.6%.
According to Hall and colleagues (2011), roughly how long does it take to reach about half of the eventual weight change from a lasting change in intake?
Show the answer
Answer: About a year About half in a year and about 95% in about three years.
Math, not advice
These guides explain published formulas and reference values. They are not medical advice, and the formulas aren't made for pregnancy, children or medical conditions. Each guide shows the date it was last checked.
Sources
- Hall KD, Sacks G, Chandramohan D, et al. Quantification of the effect of energy imbalance on bodyweight. The Lancet 2011;378:826–837 (Deakin University record)
- Hall KD et al. Quantification of the effect of energy imbalance on bodyweight. Lancet 2011 – PubMed
Last checked October 27, 2026