The ideal weight formulas were built for drug dosing

There is a family of formulas that take a height and return a number of kilograms, and they are found everywhere under the heading ideal weight. They were not built for that heading. They were built so a pharmacist could work out how much of a drug to give somebody.

This is the single most useful fact in this set of posts, so it is worth going slowly.

What the formulas are actually for

Some medications distribute mainly through lean tissue rather than through fat. For those, dosing on total body weight can give a dose that does not match what the body will actually do with it. Clinicians therefore need an estimate of lean mass, and they need one that can be produced at a bedside from a number they already have. Height is that number.

The best-known of these estimators is attributed to B. J. Devine and dates from the mid-1970s. It was published in a pharmacy context, for exactly this purpose: a quick height-based figure to put into a dosing calculation for a particular class of drugs. Successor formulas from the 1980s, associated with Robinson and with Miller, adjusted the constants against different data but kept the same shape and the same job.

None of that lineage contains a study asking what a person should weigh. There was never a cohort, never an outcome measured, never a validation of the output as a target of any kind. The formulas were validated, to the extent they were validated at all, against how well the resulting doses worked. Calling the output an ideal is a labelling accident that has been repeated for fifty years.

What this tool does instead, and why that matters

Our tool does not use Devine or any of its successors. It runs the BMI arithmetic backwards. You give it a height; it multiplies the two conventional cut-points, 18.5 and 25, by your height in metres squared, and prints the two products.

For 178 cm:

1. 178 / 100 = 1.78 metres, and 1.78 * 1.78 = 3.1684
2. 18.5 * 3.1684 = 58.6154 kg
3. 25 * 3.1684 = 79.21 kg

That is an algebraic rearrangement and nothing more. It is the set of weights that would produce an index between those two conventional numbers at that height, computed exactly. It inherits, wholesale, every limitation of the index it is derived from — including that the index cannot distinguish what a body is made of, and that the cut-points are conventions fitted to particular reference populations.

So the two figures are the boundaries of an arithmetic band, not a recommendation. The tool is running a formula in reverse; it is not making a suggestion, and it has no information with which it could make one.

Why the framing is worth resisting

A single number presented as an ideal invites a comparison, and the comparison feels like it means something because the number is precise. The precision is real — 58.6154 is exactly right as arithmetic. The authority behind it is not. These are two different properties and they get confused constantly.

What a particular person should weigh is not a question arithmetic can answer. It depends on composition, frame, history, age, what else is going on, and on things a clinician would need to see the person to know. No formula in this family was ever designed to answer it, and the one in this tool is a rearranged population convention.

If you want to know what any of it means for you, that is a question for somebody with your notes in front of them.

Running it

The ideal weight calculator takes a height in centimetres and prints the low and high ends of that band in kilograms, computed on your own device. Both figures come out of multiplying a convention by a squared height, and that is the whole of what they are.

It is informational and it is not medical advice. The interesting thing here was never the output. It is that an entire genre of ideal-weight formula was invented for a completely different job.