BMR: What the Equations Actually Estimate

Basal metabolic rate (BMR) is the rate of energy expenditure by a body at complete rest, awake, in a thermally neutral environment, and in the postabsorptive state — usually twelve hours after the last meal. It is the largest single component of daily energy expenditure for most adults, commonly 60–70% of the total. The rest is activity, the thermic effect of food, and, in some people, adaptive thermogenesis.

No equation measures BMR. Each estimates it from variables that correlate with it. The variables differ, the coefficients differ, and the errors differ. A BMR figure without its equation is not a figure.

The three equations in circulation

Mifflin-St Jeor (1990). Derived from indirect calorimetry in 498 adults, this is the equation recommended by the Academy of Nutrition and Dietetics for non-obese and obese adults. It has the smallest standard error of the three — roughly 10% of the predicted value in the original validation, meaning a 2,000 kcal prediction carries a band of about 1,800–2,200.

Men: BMR = 10 × weight(kg) + 6.25 × height(cm) − 5 × age(y) + 5 Women: BMR = 10 × weight(kg) + 6.25 × height(cm) − 5 × age(y) − 161

Harris-Benedict (1919, revised 1984). The original was derived from 239 subjects, mostly young men, using early calorimetry. The 1984 revision adjusted the coefficients. On modern populations it runs about 5% high, which is why it is now mostly of historical interest. The error is not random: the original cohort was leaner and more muscular than a contemporary clinic population, and lean mass is the main determinant of BMR.

Men: BMR = 88.362 + 13.397 × weight(kg) + 4.799 × height(cm) − 5.677 × age(y) Women: BMR = 447.593 + 9.247 × weight(kg) + 3.098 × height(cm) − 4.330 × age(y)

Katch-McArdle. This equation uses lean body mass rather than total weight:

BMR = 370 + 21.6 × lean body mass(kg)

It is more accurate than Mifflin-St Jeor if lean mass is measured properly — by DXA or a four-compartment model. If lean mass is derived from a bioelectrical impedance scale or a skinfold estimate, the error in the input propagates into the output, and the equation can be worse than Mifflin-St Jeor. The equation is only as good as the body-fat figure behind it.

A worked example through all three

The spread is easier to see in calories than to describe. Take a 40-year-old woman, 165 cm, 70 kg, with a measured lean body mass of 50 kg.

Mifflin-St Jeor:
  BMR = 10 × 70 + 6.25 × 165 − 5 × 40 − 161
      = 700 + 1031.25 − 200 − 161
      = 1370 kcal/day

Harris-Benedict (1984):
  BMR = 447.593 + 9.247 × 70 + 3.098 × 165 − 4.330 × 40
      = 447.593 + 647.29 + 511.17 − 173.2
      = 1433 kcal/day

Katch-McArdle (lean mass 50 kg):
  BMR = 370 + 21.6 × 50
      = 370 + 1080
      = 1450 kcal/day

The three figures span 1,370–1,450 kcal, an 80 kcal spread — about 6% of the midpoint. That is the equation-to-equation difference before any measurement error is added. Mifflin-St Jeor is the lowest here; Harris-Benedict is about 4.6% above it; Katch-McArdle is about 5.8% above it. The direction is consistent with the known bias in Harris-Benedict and with this woman’s lean mass being a little above average for her weight.

Now suppose the lean-mass figure was not measured but estimated from a scale reading of 28% body fat. That gives lean mass = 70 × (1 − 0.28) = 50.4 kg, and Katch-McArdle returns 370 + 21.6 × 50.4 = 1,459 kcal. The difference from the DXA-based figure is small here, but bioelectrical impedance can be off by 5–8 percentage points of body fat, which at this weight is 3.5–5.6 kg of lean mass, or 76–121 kcal in the BMR estimate. The input error dominates.

Why the figure moves during a diet

A BMR estimate is a snapshot. During energy restriction, BMR falls for two reasons. The first is mass loss: less tissue means less energy cost, and the Mifflin-St Jeor weight coefficient (10 kcal per kg) captures most of that. The second is adaptive thermogenesis: a reduction in BMR beyond what mass loss predicts, documented in the Minnesota Starvation Experiment and in modern weight-loss trials at roughly 5–15% of the predicted value.

The practical consequence is that a BMR figure calculated at the start of a diet overestimates BMR at the end. If the woman above loses 10 kg, her Mifflin-St Jeor BMR falls by about 100 kcal from mass alone, and adaptive thermogenesis may take another 70–200 kcal. The line is not straight.

A second consequence: the 7,700 kcal per kilogram figure often used to predict weight change describes the energy content of adipose tissue, not body weight. It is wrong early in a diet, when much of the loss is water and glycogen, and wrong late, when maintenance has fallen. It is a simplification in two directions at once.

What people get wrong about BMR

The most common error is to treat a BMR figure as a target. It is not. BMR is the cost of being alive; it is not the amount to eat. Total daily energy expenditure (TDEE) is BMR multiplied by an activity factor, usually 1.2–1.9, and that is the figure a person eats against. Confusing the two produces a plan that is too low by 20–50%.

The second error is to treat the output of a calculator as a measurement. It is a prediction with a band. A BMR calculator that returns 1,370 kcal is saying, in effect, “somewhere near 1,370, probably within 10%.” The band is the useful part.

The third error is to compare equations without comparing inputs. Katch-McArdle is not better than Mifflin-St Jeor in general; it is better when lean mass is measured and worse when it is guessed. The mistake is natural because the equation looks more precise — it has a lean-mass term — and precision of form is not precision of output.

Where the figure comes from, and what it is for

A BMR estimate is a starting point for a TDEE estimate, which is a starting point for an energy target. Each step adds error. The Mifflin-St Jeor BMR has a ~10% standard error; the activity factor has its own error, often larger; and the food intake estimate has error too. A TDEE figure built from these is a hypothesis, not a prescription.

The useful practice is to calculate the figure, state the band, and then adjust against observed weight change over two to three weeks. That is the only feedback loop that closes the error.

This page is not medical advice. If eating or weight is causing distress, or if there is a history of an eating disorder, a clinician or a dietitian is the right route. In the US, the National Eating Disorders Association helpline is available; in the UK, Beat. A BMR equation is not a substitute for either.