Why a Taller Person Gets a Higher BMI for the Same Build

Body mass index is one division. Take mass in kilograms, take height in metres, square the height, divide. Two measurements go in, a number with one decimal comes out, and it reads like a property of the body it describes.

Three of the quantities inside that division were chosen rather than measured: the exponent on the height, the constant that makes the imperial version work, and the position of the line at 25. Each choice is defensible. They are nowhere near equal in size.

The three chosen numbers, priced

Every figure below is worked out further down the page, from the profile the calculator opens with: 70 kg at 175 cm, an index of 22.9.

The middle row is the one people ask about, and it is the one that costs nothing: rounding the imperial constant to 703 moves a reading of 30 by three thousandths, which at 1.75 m is nine grams of body mass.

The other two rows are where the number is actually decided, and neither of them is arithmetic you can check by recalculating. They are conventions, and they were adopted for reasons worth knowing.

The same build at five heights

Start with the default profile and rebuild it. Not a heavier person or a lighter one, but the same person scaled, every proportion held, the way a photograph enlarges.

Mass follows volume, and volume rises with the cube of the scaling. Height rises with the scaling itself. The index divides mass by height squared, so the cube and the square cancel down to one surviving factor.

At 1.55 m that build sits in the middle of the healthy band. At 1.95 m the identical build reads 25.5 and crosses the line at 25. The two heights stand in a ratio of 1.2581, and so do the two readings: 25.469 divided by 20.245 is 1.2581 to four places.

That identity is the whole effect. Scale a body by any factor and its index scales by exactly the same factor, because a cube divided by a square leaves one power behind.

Nothing in the table is a claim about real people, who are not enlargements of one another. It is a claim about the formula. Hand it the same shape twice and it returns a bigger number for the bigger copy, every time, with no change in build to justify it.

Why the exponent is two anyway

An index that divided by height cubed would be free of that bias. The paper that named the body mass index looked at exactly this question and chose the square, and it is worth knowing why.

Ancel Keys and colleagues compared several relative-weight indices in 1972 and concluded that weight over height squared was the least bad of them for population work. Least bad is the standard that was actually met, and the paper says so.

The reason the cube loses is that adults are not scaled copies. Across a real population, mass rises closer to the square of height than to the cube, because proportions shift with stature rather than holding constant. The square fits the data; the cube fits the geometry.

So the exponent is a compromise fitted to samples, chosen because it correlated least with height across those samples. It does that job. What it cannot do is stop being a population fit when a single person reads it, and the residual bias in the table above is what is left over.

Where 703 comes from

The imperial form multiplies by 703, and the constant looks arbitrary until you build it. A pound is defined as exactly 0.45359237 kilograms, and an inch as exactly 0.0254 metres. Both are definitions, not measurements.

Take 154 lb at 5 ft 9 in, which is 69 inches. The imperial route gives 703 x 154 / 4761 = 22.7393. Carrying the unrounded constant gives 22.7416, and converting to metric first and dividing gives the same 22.7416.

The gap is 0.0023 of an index unit. Rounding a conversion constant is the one decision in this formula that is genuinely too small to matter, and it is the one that attracts the questions. How many decimals to keep when converting units sets out the general version of that judgement.

The line at 25 has more than one position

The World Health Organization puts the adult healthy band at 18.5 to under 25, overweight at 25 and above, and obesity at 30 and above. The United States adopted the same thresholds in the 1998 clinical guidelines from the National Heart, Lung, and Blood Institute.

A WHO expert consultation then looked at Asian populations, which develop metabolic risk at lower body mass indices, and proposed lower public health action points: 23 rather than 25, and 27.5 rather than 30.

Translate both into kilograms at 1.75 m, where height squared is 3.0625. The action point of 23 lands at 70.44 kg and the cut point of 25 lands at 76.56 kg. Between two boundaries published by the same organisation sits 6.13 kg of the same person.

The boundaries are also round, and risk is not. Nothing changes in a body between 24.9 and 25.0, and the statistics behind the lines rise gradually across the whole range. A round number is chosen because it is easy to remember and easy to agree on across countries, which are properties of a policy instrument rather than of a measurement.

A reading of 24 is inside the healthy band on one table and above the action point on the other. Neither table is wrong. Both mark where a population's risk statistics start to move, so that screening can be aimed somewhere.

What the last displayed digit weighs

The index is reported to one decimal place, and that decimal has a price in kilograms. Multiply 0.1 by height squared and you have it.

At 1.75 m the distance between 24.9 and 25.0 is 306 grams. That is less than a large glass of water, and less than the difference between weighing yourself before and after breakfast.

Read the same table the other way. A two-kilogram swing across a day is ordinary, and at 1.75 m it moves the index by 0.65 — more than six of the steps the display prints. The boundary is crossed and recrossed by an amount smaller than the noise in the measurement.

This is the same argument the converter guides make about decimal places, applied where it bites hardest: a displayed digit is not a measured one, and the last digit here belongs to the scale rather than to the body.

A centimetre of height is worth 793 grams

Height is squared and mass is not, which makes the two inputs unequal. A one per cent error in height moves the index by 1.97 per cent. The same error in mass moves it by exactly one.

Put that in units anyone can act on. At 70 kg and 175 cm, recording 176 cm instead — shoes left on, a slouch, a tape held at an angle — drops the reading from 22.9 to 22.6. To move the index that far with the scale you would have to lose 793 grams.

Two centimetres is worth 1.573 kg, and a two-centimetre disagreement between two measurements of the same person on two occasions is not unusual. Height is the input people record once and reuse for years, and it is the one the formula punishes hardest.

The remedy is small: measure without shoes, heels against a wall, with something flat level on the crown of the head, and keep the height written down next to the reading rather than the reading alone.

What the index is genuinely good at

None of the above makes it useless. Two measurements anyone can take, no equipment beyond a scale and a wall, one division, and a figure that can be compared across decades and across countries. For sorting a large population cheaply into groups worth a closer look, that combination is hard to beat.

What it cannot do is describe a body. It sees total mass and total height, so it cannot tell muscle from fat, and it cannot see where mass sits. The waist-to-height ratio calculator answers the second question, and the body fat calculator estimates the first from circumference measurements.

Two more tools on the shelf inherit the same height term and the same caution. The ideal weight calculator returns a range from formulas fitted to populations rather than to anyone in particular, and the lean body mass calculator splits a weight into tissue the index cannot separate.

Read alongside those, the index is one cheap input among several. Read alone, as a verdict on one body on one morning, it is being asked for something it was never built to supply.

Common mistakes reading a BMI

• Reading it as a measure of fat. Nothing in the formula describes tissue. Two people of the same height and weight score identically whatever they are made of.
• Treating a boundary as a cliff. At 1.75 m the gap between 24.9 and 25.0 is 306 grams, which is inside the day-to-day swing of any bathroom scale.
• Comparing two people of different heights. The taller one carries a built-in advantage of exactly their height ratio, and it says nothing about either build.
• Measuring height in shoes. Because height is squared, an extra 2 cm on a 175 cm frame drops the index from 22.9 to 22.3, which is five printed steps for a measurement error.
• Applying adult cut points to anyone under 20. Children are assessed against age-and-sex growth percentiles, because the normal relationship between mass and height changes throughout growth.
• Recording the number without the height. An index is meaningless without the two measurements behind it, and only those can be rechecked later.