TDEE formulas: how the BMR equations and activity multipliers fit together

Two steps, every time

The first step estimates resting energy expenditure: what your body burns lying still, awake, after an overnight fast. That number is called basal metabolic rate (BMR) or resting metabolic rate (RMR), depending on how strictly the measurement conditions are defined, and it is the part an equation can predict from your body.

The second step scales that resting number up to a whole day. On this site the scaling factor is one of five activity multipliers: 1.2 for sedentary, 1.375 for lightly active, 1.55 for moderately active, 1.725 for very active and 1.9 for extra active. These values are the convention the calculator uses, not measurements from a study, and they carry everything that is not resting metabolism: work, walking, training and the energy cost of digesting food.

So TDEE = resting estimate x multiplier. Every guide in this category is about one of those two terms, about the vocabulary used to describe them, or about how far the product can be trusted.

Three families of equation

The resting-energy equations used on this site fall into two groups by what they ask of you. Mifflin-St Jeor and Harris-Benedict both take weight, height, age and sex. They differ in their coefficients and in the populations they were built from. Katch-McArdle takes a single input, lean body mass, which you get from your weight and an estimate of your body fat percentage.

That difference in inputs is the whole reason for choosing one family over the other. The weight-height-age-sex equations cannot tell muscle from fat. For people with an ordinary build that matters little. For someone carrying unusually high muscle mass, or unusually high fat mass, a lean-mass equation has information the others do not, provided the body fat estimate it is fed is reasonable. The table below summarises each equation and what its source actually says.

The equations at a glance

W = weight in kg, H = height in cm, A = age in years, LBM = lean body mass in kg. Frankenfield and colleagues' 2005 systematic review compared Mifflin-St Jeor, Harris-Benedict, Owen and WHO/FAO/UNU and found Mifflin-St Jeor the most reliable of the four.

Mifflin-St Jeor

Mifflin and colleagues published their equation in 1990 after measuring resting energy expenditure in 498 healthy adults, 247 women and 251 men, aged 19 to 78. Two of their findings explain most of what you see on modern calculators. First, Harris-Benedict overestimated measured values by about 5 percent in their sample, which is part of why Harris-Benedict tends to give a slightly higher number. Second, fat-free mass was the best single predictor of resting energy expenditure; they reported REE = 19.7 x FFM + 413. That observation is the reason lean-mass equations exist at all, even though Mifflin-St Jeor itself uses weight rather than lean mass so that it works without a body composition measurement.

Fifteen years later, Frankenfield and colleagues reviewed the evidence on four equations and found Mifflin-St Jeor the most reliable: it estimated resting metabolic rate within 10 percent of the measured value in more people than the others, and its errors were the narrowest. The review also flagged a limit worth remembering: older adults and US ethnic minorities were underrepresented in the validation studies, so the evidence is thinner for those groups. Those two papers are the reason the site uses Mifflin-St Jeor as its default.

Harris-Benedict, then and now

Harris and Benedict's biometric study of basal metabolism appeared in the Proceedings of the National Academy of Sciences in December 1918, with the fuller report published as a Carnegie Institution monograph the following year, which is why the equations are usually dated 1919. For most of the twentieth century they were the standard way to estimate resting energy.

In 1984, Roza and Shizgal re-evaluated the equations and published revised coefficients. They described the precision of the revised equations as about plus or minus 14 percent in normally nourished people, and found them unreliable in malnourished patients. That plus or minus 14 percent is worth holding on to: it is a reminder that any single equation gives a central estimate with a wide band around it, not a precise figure.

The revised equation is still built into many calculators and clinical tools, so you will meet it. The Harris-Benedict equation page lays out both coefficient sets and walks a full example; the Mifflin-St Jeor vs Harris-Benedict page explains why most current tools moved to Mifflin.

Katch-McArdle and lean mass

Katch-McArdle is the formula the calculator switches to when you enter a body fat percentage: BMR = 370 + 21.6 x lean body mass in kg. The site does not yet have a verified primary source for its origin, so this hub makes no claim about who derived it or from what data. What can be said is that its logic matches a sourced observation: Mifflin and colleagues found fat-free mass to be the best single predictor of resting energy expenditure.

The catch is that lean mass is only as good as the body fat estimate behind it. A body fat figure that is several points off moves lean mass, and the BMR with it. For someone with an ordinary build, a guessed body fat percentage can easily make Katch-McArdle less accurate than Mifflin-St Jeor, not more. The two pages that cover this, Katch-McArdle vs Mifflin-St Jeor and the TDEE calculator with body fat, explain when the extra input earns its place and how errors in body fat carry through to the final number.

The vocabulary: BMR, RMR, TDEE

Three terms cause most of the confusion in this category, and two of them describe nearly the same thing. BMR and RMR both refer to resting energy expenditure. The difference is the measurement protocol: BMR is measured under stricter conditions, typically after an overnight fast and sleep, lying still in a comfortable room, while RMR is measured under looser conditions. Prediction equations like Mifflin-St Jeor were built from resting measurements, and calculators, this one included, often use the two labels loosely. The BMR vs RMR page explains the measurement differences and when the distinction matters, which is mostly when you compare figures from lab reports or research papers.

TDEE is the larger, whole-day number: resting expenditure plus the energy of activity and digestion. The most common mistake in the whole field is using the resting number where the whole-day number belongs, for example setting a diet target as a deficit from BMR. The TDEE vs BMR page is dedicated to separating them.

One worked example, two people

Two hypothetical people run through all three equations. Person A: woman, 35 years, 165 cm, 70 kg, estimated 32% body fat (lean mass 47.6 kg), lightly active (1.375). Person B: man, 28 years, 180 cm, 90 kg, estimated 12% body fat (lean mass 79.2 kg), muscular and moderately active (1.55).

Worked from the formulas in the table above with unrounded intermediate values, then rounded to whole kcal. Person A's Mifflin: 10 x 70 + 6.25 x 165 - 5 x 35 - 161 = 1,395.25. Person B's Harris-Benedict: 88.362 + 13.397 x 90 + 4.799 x 180 - 5.677 x 28 = 1,998.96. Katch-McArdle: 370 + 21.6 x lean mass. These are hypothetical people, not measured cases.

Reading the example

For person A, an ordinary build, the three equations land within 60 kcal of each other at rest and within about 80 kcal at the whole-day level. Harris-Benedict comes out highest, which fits the 5 percent overestimate Mifflin's paper reported, and Katch-McArdle is almost identical to Mifflin because her lean mass is roughly what a weight-based equation assumes for her size.

For person B, a lean and muscular man, the equations spread out. Katch-McArdle is 191 kcal above Mifflin at rest and 295 kcal above it once the 1.55 multiplier is applied. That is the situation the lean-mass formula is designed for: Mifflin sees 90 kg and cannot know that unusually little of it is fat. If his 12 percent body fat estimate is sound, Katch-McArdle is plausibly the better guide for him; if it came from a rough guess, the gap may be partly measurement error.

The more important lesson sits around both people. Roza and Shizgal put the precision of the revised Harris-Benedict equation at about plus or minus 14 percent. Applied to person A's Harris-Benedict figure, that band runs from 1,251 to 1,658 kcal, and all three of her estimates fall inside it. For person B it runs from 1,719 to 2,279 kcal, and again all three estimates fit. The disagreement between equations is smaller than the uncertainty of any one of them. Choosing the equation that gives the number you like does not make the estimate more accurate; testing it against your own weight trend does.

Where to start reading

If the term TDEE is new to you, read What is TDEE first. It defines the number and its parts in plain language and is the foundation everything else builds on. Next, How to calculate TDEE walks the full two-step method by hand with worked examples, which takes the mystery out of the calculator.

If you keep mixing up the terms, the two vocabulary pages are your next stop: TDEE vs BMR for the difference between the resting and whole-day numbers, and BMR vs RMR for the measurement distinction behind two labels for resting expenditure.

If you want to know why the site uses the equation it does, read Mifflin-St Jeor vs Harris-Benedict, then the Harris-Benedict equation page if you want the older formula's coefficients and history in full.

If you know your body fat percentage, or you are noticeably more muscular or carry more fat than average, read Katch-McArdle vs Mifflin-St Jeor, then the TDEE calculator with body fat page for how to estimate body fat well enough to use and when to ignore that input.

And whatever your route, finish with TDEE calculator accuracy. It explains how far any estimate can be trusted and how to turn the formula's output into your own measured number.

Common misreadings

A handful of misunderstandings account for most of the frustration people feel with calorie estimates.

The first is treating BMR as a target. BMR is the resting baseline, not what you burn in a day. Eating at or below it while living a normal, moving life is a much deeper deficit than it sounds.

The second is formula shopping: trying several equations and adopting whichever result is most convenient. As the worked example shows, for most people the equations differ by less than their own uncertainty, so switching between them changes the feel of the number more than its accuracy.

The third is feeding Katch-McArdle a guessed body fat percentage. The formula is only as good as the lean mass it receives, and a poor body fat estimate can make it worse than Mifflin-St Jeor for an average build.

The fourth is treating the activity multiplier as a measurement. The five values are a convention, and the tier you pick usually moves your result more than the choice of equation does. That is why the activity guides in the TDEE by lifestyle category matter as much as anything in this one.

The fifth is reading precision into decimals. A calculator that prints 2,217 kcal is not claiming accuracy to the last calorie; it is showing the arithmetic. Treat any estimate as the centre of a range.

From estimate to your own number

An equation gives you a starting point. Your own body gives you the answer. Eat consistently at the estimated TDEE for about two weeks, weigh yourself each morning under the same conditions, and compare weekly averages. If the average holds steady, the estimate is close to your real maintenance. If it drifts, adjust intake in small steps and keep watching. Keep in mind that weight responds to an intake change slowly, so judge trends over weeks rather than days.

That calibration step matters more than any choice made in this category. Frankenfield's review found the best of the four equations within 10 percent of measured resting expenditure in more people than the others, not in everyone. For anyone outside that band, two weeks of honest data will reveal it, and the formula will have done its job of getting you close enough to start.