The Ideal Weight Formulas Contradict Each Other by Height

Each of the four classic formulas is defined as a base weight at 5 feet (152.4 cm) plus a fixed increment for every inch above that. We evaluated all four at every whole centimetre from 153 to 200 cm, for both sexes — 96 height-by-sex rows, 384 formula outputs — using the same idealWeights() function behind the ideal weight calculator.

For each output we converted the weight back into the BMI it implies at that height, which is the number that makes the four comparable. A formula that returns 93.1 kg for a 200 cm man is not obviously different from one that returns 82.6 kg until you notice the first implies a BMI of 23.3 and the second 20.7. We also computed the healthy-BMI weight range at each height with healthyBmiRange(), to put the formula disagreement on the same scale as the range clinicians actually use.

Heights below the 5-foot floor are analysed separately at the end, because there the formulas have no defined behaviour and the implementation returns the base weight.

This is arithmetic, not medicine. Every one of these formulas is a straight line in height: add an inch, add a fixed number of kilograms. BMI, meanwhile, divides weight by height squared. A straight line cannot hold a quadratic ratio constant, so the BMI implied by any linear ideal-weight formula must drift as height changes. The only question is which way and how fast.

The answer depends entirely on the per-inch increment. Too small an increment and the implied BMI falls with height; too large and it climbs. The four formulas chose increments between 1.41 and 2.7 kg per inch for men, which is why they end up pointing in opposite directions.

Read down the 155 cm column and then the 200 cm column: the order of the four formulas reverses completely. Miller is the most generous formula for a short adult and the strictest for a tall one; Hamwi is the opposite. If you are 155 cm, Miller tells you to weigh more than Hamwi does; if you are 200 cm, Hamwi tells you to weigh 16 kg more than Miller does.

That reversal is the finding. These are not four noisy estimates of the same quantity — they encode genuinely different beliefs about how weight should scale with height, and averaging them, as many calculators including ours do, splits the difference between positions that contradict each other.

The spread is not flat; it is a V. The four formulas converge to within 1.2 kg at 168 cm for men and 1.4 kg at 173 cm for women, then fan out in both directions — to 6.8 kg at 155 cm and 16 kg at 200 cm.

That shape is a fingerprint of how these formulas were built. Each was fitted to a population whose average height sat near the middle of the range, so they were tuned to agree there. The further you are from average height, the more the choice of formula decides your answer — which is exactly backwards from what you would want, because people at the ends of the height range are the ones a population average serves worst.

Here is the part that reframes the whole question. At the median height in our sweep, the four formulas span 5.3 kg. The weight range corresponding to a normal BMI at the same height spans 19.9 kg — 3.8 times wider.

Take the tallest row: a 200 cm man. The formulas argue between 82.6 and 98.6 kg. The healthy BMI band for that height runs from 74 to 99.6 kg. Every single formula output sits inside that band, along with 25.6 kg of other perfectly healthy weights that no formula names. Picking a winner among the four is choosing a point inside a range where the evidence does not distinguish between points.

This is why clinical guidance moved to a range decades ago and why our ideal weight calculator shows the healthy-BMI range alongside the four formulas rather than presenting a single "ideal" figure. The formulas exist because clinicians needed one number for drug dosing and ventilator settings, not because anyone established that a single weight is optimal for a given height.

BMI does not have separate thresholds by sex, so this asymmetry is a property of the formulas, not of the standard they are being measured against. Across every height, the four formulas point women at a median BMI of 21.1 and men at 22.6, a difference of 1.5 BMI points. At the low end, 19.7 is within 1.2 of the underweight cut-off.

There is a defensible physiological reason to expect a lower BMI at the same height in women — on average, less lean mass — and there is a less defensible one, which is that these equations were written between 1964 and 1983 and inherited the body ideals of their period. This analysis cannot separate the two. What it can say is that a woman comparing her weight to an ideal-weight formula is being held to a stricter standard than a man of the same height, and that neither standard is what a clinician would use today.

Every one of these equations is defined as "base weight at 5 feet, plus an increment per inch above". None of them says what to do below 5 feet. Implementations, including ours, floor the increment at zero and return the base weight — so a shorter adult gets the 5-foot answer.

The consequence is that the shorter you are below 5 feet, the more the formulas overshoot. At 140 cm, Miller (1983) implies a BMI of 28.7— comfortably into the overweight category — as an "ideal" weight. This is not a rounding artefact. It is the formulas being asked a question they were never given an answer for.

We have added a note to the ideal weight calculator so that anyone entering a height below 5 feet is told the four formulas are out of range and pointed to the healthy-BMI weight range instead, which remains valid at any height because it is computed from height directly rather than extrapolated from a base.

This measures the formulas, not health. Nothing here establishes what anyone should weigh. Every finding is about the internal logic of four equations: what they assert, where they contradict each other, and how their outputs compare with the normal BMI band. A formula being internally odd does not make its output unhealthy, and a formula being internally tidy does not make its output right.

BMI is the yardstick here, and BMI is limited.We converted each formula's output into an implied BMI because that is the only common scale available from height and weight alone. BMI cannot distinguish muscle from fat and is a population screening tool, so "implies a BMI of 24.5" is a statement about a ratio, not about body composition. Our analysis of BMI against body-fat percentage covers that gap.

The height range is a choice. We swept 153 to 200 cm because that covers nearly all adults. The drift figures scale with the width of that window: a narrower range would show smaller drift, and the 16 kg maximum spread is specific to 200cm. The direction of each formula's drift, and the fact that they disagree in direction, does not depend on the window.

Sex is binary in these equations. All four formulas define only male and female coefficients, so the analysis inherits that. There is no defined behaviour for anyone who does not fit one of those two sets of coefficients.

Rounding. Weights are rounded to one decimal place and implied BMI to one decimal before the statistics are taken, so a recomputation from unrounded values can differ in the last digit.

The per-inch increments in the second table are the entire method: weight = base + increment x inches above 5 feet, and implied BMI = weight / height in metres squared. Any spreadsheet reproduces the whole analysis from those eight numbers.

To check a single row, the ideal weight calculator reports all four formulas plus the healthy-BMI range for any height, and the BMI calculator converts any of those weights back into a BMI. The ideal weight chart lists the same figures across the height range in one table.

If your rebuild disagrees with anything above, the contact page reaches a person who will check it.