Resting Metabolic Rate Formulas: Mifflin-St Jeor and More

The common resting metabolic rate formulas are fitted straight lines. Researchers measure the energy of a few hundred people, then find the weights, heights and ages that best predict it. Which line you get depends on who was measured and which inputs were allowed. This page lays the lines side by side, with the original papers, the populations behind them and the errors they carry. The subject is formulas, not personal needs. The health section has the related math, and the total daily energy expenditure page shows what happens after the resting step.

What is BMR?

Basal metabolic rate, BMR, is the amount of energy used to simply stay alive in the absence of any physical activity¹⁰. Strictly, it is measured under standard conditions: awake and lying down, 10 to 12 hours after a meal, after 8 hours of physical rest⁶. Resting metabolic rate, RMR, and resting energy expenditure, REE, are looser terms for the same quantity, more specific to rest¹⁰. The formulas on this page predict that quantity, in kilocalories a day (kcal/day).

BMR is the largest part of the daily energy budget. One reference puts it at about 45 to 70 percent of total energy expenditure in adults, set mainly by sex, body size, body composition and age⁶. A validation study narrows it to 60% to 70% in sedentary adults⁸. The gold standard for measuring it is indirect calorimetry, which is costly and needs trained staff⁸. BMR can be measured only under laboratory conditions and in small groups of representative individuals⁶, so almost everyone uses an equation instead.

The general shape: a line in weight, height and age

The formulas form a family, and the most common shape is a straight line in weight, height and age with one intercept for each sex: RMR = a × weight + b × height − c × age + d.

The coefficients below come from the original papers and from open-access tables that reprint them¹⁷. Weight is in kilograms, height in centimeters and age in years. The result is kcal/day.

Two more families skip height and age. The Schofield equations, which the FAO/WHO/UNU consultation kept in its report, use body weight alone, with separate lines for each age band⁶. The fat-free-mass equations use body composition instead, and they appear below. Four equations were identified as the most commonly used in clinical practice: Harris-Benedict, Mifflin-St Jeor, Owen and the WHO/FAO/UNU set².

What is the Mifflin-St Jeor equation?

Mifflin-St Jeor is a regression fitted to 498 healthy adults, 247 women and 251 men, aged 19 to 78¹. Of them, 264 were normal weight and 234 were obese, and their resting energy was measured by indirect calorimetry¹. The full-precision fit is REE = 9.99 x weight + 6.25 x height - 4.92 x age + 166 x sex - 161, with sex coded 1 for males and 0 for females¹. It explains a share of the variance equal to R2 = 0.71¹. Rounding the coefficients and splitting the equation by sex gave the two familiar lines, and that simplification did not affect its predictive value¹.

The sex term is worth 166 kcal a day between the two forms, because +5 minus −161 is 166¹. Adding relative body weight or body-weight distribution did not significantly improve the prediction¹.

Why Mifflin-St Jeor replaced Harris-Benedict

The Harris-Benedict equations came from a study by Harris and Benedict, published in 1919 by the Carnegie Institution of Washington¹¹. They were derived from indirect calorimetric data in 239 normal subjects³. A 1984 reanalysis added later data and found regression equations similar to the originals³. It put the precision at 14% for a normal subject³. The same paper found the equations unreliable in the malnourished patient³.

Decades after 1919, the Mifflin team measured a new sample and compared. In their data the 1919 equations overestimated measured resting energy by 5%¹. The Mifflin sample included obese adults, who were part of the design from the start¹. Later, a review of the literature on healthy nonobese and obese adults compared the four common equations and found Mifflin-St Jeor the most reliable (systematic review): it predicted RMR within 10% of the measured value in more individuals than any other equation, and it also had the narrowest error range². That result, not fashion, is why calculators moved to it.

Harris-Benedict, Katch-McArdle and FAO: the other formulas

Fat-free-mass equations. Cunningham found in 1980, using 223 subjects from the original Harris and Benedict data, that lean body mass alone predicted resting rate, and proposed BMR (cal/day) = 500 + 22 (LBM)⁵. In that analysis the influences of sex and age added little⁵. His 1991 synthetic review settled on REE = 370 + 21.6 x FFM⁴. This version is usually called the Katch-McArdle formula, and the two are the same equation⁹. It confirms a primary correlation between REE and fat-free mass across a broad range of body weights⁴. A separate fat-mass term was not supported in the general population⁴.

Mifflin’s own fat-free-mass line. The Mifflin data found fat-free mass the best single predictor of REE, with R2 = 0.64 and REE = 19.7 x FFM + 413¹. Weight alone did almost as well, with R2 = 0.56 and REE = 15.1 x weight + 371¹. That is the reason weight-based equations work at all: body weight is a rough stand-in for the fat-free mass that does the burning.

FAO/WHO/UNU (Schofield). The FAO/WHO/UNU consultation kept the equations proposed in 1985 by Schofield⁶. They were derived mostly from studies in Western Europe and North America⁶. The adult rows are below, in kcal/day. Each row is a line in body weight alone, and the second number is the standard error of the estimate (the “see” column of the source table):

No validation work focused on individual errors was found for the WHO/FAO/UNU equation².

Worked example: five equations, one woman

Take a 40-year-old woman, 70 kg, 165 cm. For the fat-free-mass lines assume 30% body fat, so 49 kg of fat-free mass; that assumption is ours, not a measurement. The coefficients are the ones in the tables above¹⁴⁵⁶⁷.

Worked example (our arithmetic)

The five answers span 208 kcal a day, from 1,370 to 1,578 (our arithmetic). The first four sit within about 5% of each other, and the 1980 line sits above the rest. The spread is the point. No equation is the truth for this woman. The full spread is about 15% of the lowest value (our arithmetic), the same order as the 14% precision found for Harris-Benedict³.

The same comparison for a 40-year-old man at 80 kg and 180 cm¹⁶⁷:

How much does each input matter?

A fitted line has one slope per input, and the slope is the derivative of the prediction with respect to that input. That makes the comparison simple: look at the coefficients.

Two things stand out. First, Harris-Benedict gives men a weight slope 44% above the women’s one, 13.7516 against 9.5634 (our arithmetic)⁷. Second, the fat-free-mass line has no age term at all. Cunningham found that sex and age added little once lean body mass was in the model⁵, and the Harris-Benedict reanalysis reached a related result: resting expenditure is directly related to the size of the body cell mass and independent of age and sex³.

How accurate are the formulas for one person?

They work on average, and less well for any one person. In a Tehran sample of 284 adults aged 18 to 60, Mifflin-St Jeor was among the equations with the best predictive value at group level, with mean percentage error between −2.2 and 2.4%⁸. At the individual level, the equations with the greatest accuracy still reached only 50 to 53% accuracy against measured values⁸. A study of 427 healthy Saudi adults tested nine equations and found none with an acceptable difference as low as 5% and about 55% accurate prediction at the individual level⁷.

Noteworthy errors and limitations exist when the equation is applied to individuals, and possibly when it is generalized to certain age and ethnic groups². The Tehran authors conclude that race matters when predicting REE⁸.

Choosing a formula: populations and limits

Among general-purpose equations for healthy adults, Mifflin-St Jeor has the strongest evidence: it was the most reliable in the 2005 systematic review². The fat-free-mass equations are the better choice when fat-free mass has actually been measured, because that is the variable the body’s resting rate tracks most closely⁴. They are no better when you must guess the input.

The caveats are about populations, not arithmetic:

• Older adults and ethnic minorities in the United States were underrepresented in both the development and the validation of equations². For such groups a high level of suspicion about accuracy is warranted².
• Very muscular and very overweight people can get identical results from a weight-height-age equation, since these equations do not account for body composition¹¹.
• Malnourished patients are outside the range where the Harris-Benedict equations hold³.
• The FAO table comes mostly from Western European and North American studies⁶.

Where accuracy matters, measurement is the remedy: valid measurement by indirect calorimetry would eliminate estimation error².

Mistakes with the formulas

• Mixing coefficient sets. The Harris-Benedict and Mifflin-St Jeor equations have different intercepts. Using the intercept from one and the slopes from the other gives a number that matches neither paper⁷.
• Wrong units. The equations take kilograms and centimeters. The FAO table lists megajoules and kilocalories in separate columns; for example, 5.40 MJ a day is 1,290 kcal a day⁶.
• Treating the result as exact. An answer like 1,370.25 has six digits and an error in the hundreds, as the five-way comparison shows¹.
• Reading RMR as a needs number. It is one piece of daily expenditure, not an intake⁶.
• Skipping the population. A line fitted to one group may mispredict another⁸.

What next

With a resting rate in hand, the next step is the activity multiplier, covered on the TDEE page. The maximum heart rate formulas are another set of fitted lines with the same pattern: a simple regression, a named population and a standard error. The slopes in the table above are the same idea as the derivative rules on the derivative rules cheat sheet.