How Much Do BMR Formulas Actually Disagree?

We swept a grid of every combination of 7 ages (20 to 80, in ten-year steps), 10 heights (150 to 195 cm, in 5 cm steps), 20 weights (45 to 140 kg, in 5 kg steps), and both sexes. Combinations outside BMI 18.5 to 40 were dropped, because a 45 kg adult at 195 cm is not a body either formula gets used on and keeping such cells would inflate the spread with cases nobody enters. That leaves 1,778 combinations.

For each one we computed the Mifflin-St Jeor BMR and the revised Harris-Benedict (Roza-Shizgal) BMR using the exact functions behind the BMR calculator, then took the signed difference (Harris-Benedict minus Mifflin-St Jeor) in kcal/day and as a percentage of the Mifflin-St Jeor figure. Medians are reported rather than means because the distribution is skewed, and percentiles use nearest-rank with no interpolation, so every value quoted is one an actual combination produced.

This is a sweep of the equations, not a survey of people. It answers "how far apart can these two formulas land across the range of adults they are applied to". It does not weight the cells by how common each body is in any real population, and the "% of combinations" figures should be read as properties of the grid, not as prevalence.

Both equations are linear in weight, height, and age, and both split by sex. They disagree because every coefficient is different:

Three of those differences drive everything below. Harris-Benedict charges men 13.397 kcal per kilogramagainst Mifflin-St Jeor's 10, so for men the gap grows with weight. For women it charges 9.247, slightly less than 10, so for women weight pushes the two formulas back together and eventually past each other. And the female constant is 447.6 against -161, a 609 kcal head start that only gets cancelled out by the lower weight and height coefficients once a woman is reasonably tall and heavy.

So the usual summary — "Harris-Benedict runs a bit high" — is directionally right 78% of the time, and the typical size of the disagreement is 63 kcal/day: roughly one banana. But one combination in ten sits above 164 kcal/day, and the worst case is +270 kcal — a whole meal.

Summary statistics are easy to distrust, so here are four ordinary adults you can check by hand against the coefficient table above.

Note the pattern already visible in four rows: the two heavier, older adults show a wider gap than the two lighter, younger ones of the same sex, even though age barely matters. That is weight doing the work.

The gap roughly quadruples from the normal BMI band to the BMI 35 to 40 band: +26 kcal against +109. This matters more than it looks, because the population most likely to be using a calorie calculator to lose weight is exactly the population where the two formulas disagree most. It is also the region where both equations are on their weakest ground: neither was derived primarily from people at the top of this range, and both treat a kilogram of fat as metabolically identical to a kilogram of muscle.

For men the two formulas differ by +5.6% at the median; for women by +1.4%, which is inside the noise of any real-world adherence. If you are a woman, the choice between these two equations is close to irrelevant. If you are a man, it is worth roughly 96 kcal a day at rest, and more than that once an activity multiplier is applied.

The direction is not fixed for women either. Because the female Harris-Benedict weight coefficient (9.247) is below Mifflin-St Jeor's 10, the two lines cross: a small, older woman gets a much higher Harris-Benedict figure, and a tall, heavy woman gets a lower one.

The median moves by less than half a percentage point across six decades. What does change is the ceiling: the widest gap at age 20 is +10.8%, and at age 80 it is +18.8%. Age does not shift the typical adult; it stretches the worst case. The reason is in the coefficients: Mifflin-St Jeor subtracts 5 kcal per year of age while Harris-Benedict subtracts only 4.330 for women, so the two estimates drift a little further apart with every year lived.

Both extremes are women, at opposite corners of the grid. The widest is a woman of 80 at 150 cm and 45 kg: Harris-Benedict returns +18.8% more, or +156 kcal on a base of only 827. That is the 447.6 constant refusing to shrink for a small body. At the other corner, a woman of 20 at 195 cm and 140 kg gets -98 kcal, -4.2% — there the lower weight and height coefficients have finally overtaken the constant.

Percentage error is the number that matters for a small person. +156 kcal on 827 is a different proposition from +156 kcal on 2,300: at that body size, picking the wrong formula can wipe out or double an intended deficit.

Every calorie calculator asks two things that carry real uncertainty: which BMR equation to use, and how active you are. Debate online concentrates almost entirely on the first. Our grid says that is backwards.

To compare them on one scale we expressed both as a change in maintenance calories. The formula effect is the BMR gap carried through the same activity multiplier (moderately active (3–5 days/week), x1.55). The activity effect is one step up that ladder — from x1.55 to x1.725, a step of 0.175 — applied to the same BMR.

And an activity level is far easier to get wrong than a formula. You either enter your weight correctly or you do not, but "moderately active" is a self-assessment, and the honest error bar on it is at least one notch in either direction. Here is the whole ladder for one of the worked examples, with the formula gap alongside for scale:

For this adult the entire formula debate is worth 74 kcal at rest. The activity dropdown spans 1246 kcal. If you want a better estimate, the productive move is to be honest about the second question, not to hunt for a better equation for the first.

The formula note on our BMR calculator repeated the common claim that Harris-Benedict runs "about 5% higher" than Mifflin-St Jeor. Across this grid the median is +3.8%: the 5% figure describes men (+5.6%) reasonably well and overstates women (+1.4%) by a factor of about 4. We rewrote that note, and the methodology page, to state the measured figures instead.

The BMR calculator already shows both formulas side by side rather than picking one, which this analysis supports: the honest presentation of a 63 kcal disagreement is to show both numbers, not to average them into false precision.

This is a grid, not a population.Every "% of combinations" figure describes the grid defined above, where a 195 cm adult is as common as a 165 cm one. Real heights and weights are not uniformly distributed, so these shares are not prevalence estimates. The medians by sex, age, and BMI band are the more transferable numbers.

Neither formula is the truth. This analysis measures how far two estimates are from each other, which says nothing about how far either is from a measured resting metabolic rate. Indirect calorimetry is the reference standard, and published validation work finds both equations miss individuals by considerably more than they miss each other. A finding that the formulas agree closely for women is not a finding that they are accurate for women.

The activity comparison depends on the step size. We used one notch on this site's five-level ladder, which is a multiplier step of 0.175. Calculators that offer finer-grained activity levels would show a smaller step, and the 2.9x ratio would shrink accordingly. The qualitative conclusion holds for any ladder with steps of this size or larger, which covers every mainstream calculator we are aware of.

Body composition is absent. Both formulas take weight without asking what the weight is made of, so both are expected to misjudge very lean and very high-fat bodies at the same weight. Equations that use lean mass, such as Katch-McArdle, were not included here because they need a body-fat measurement most people do not have. Their disagreement with these two is a separate question.

Rounding. BMR figures are rounded to whole calories and percentages to one decimal place before the statistics are taken, so individual table cells can be a calorie away from an unrounded recomputation.

The analysis is one function. It calls bmr() (Mifflin-St Jeor) and bmrHarrisBenedict() — the same two functions the BMR calculator uses — over the grid, and returns every statistic quoted on this page. Nothing is cached or hand-entered; if the formulas changed, this page would change with them on the next build.

To check any single row, the fastest route is the BMR calculator: enter the age, height, weight, and sex from the table and it reports both formulas. To check a summary statistic, the coefficients in the first table are enough to rebuild the whole grid in a spreadsheet.

If you rebuild it and get a different answer, the contact page reaches a person who will check it.