Four Ideal Weight Formulas at Every Height: Where They Agree

By Rowan Hale · published October 29, 2026 · updated November 2, 2026

Four formulas are in common use for ideal body weight. At 168 cm they agree within 1.2 kg. At 200 cm they disagree by 16.5 kg. I ran all four at every height from 152 cm to 200 cm to find out where that gap opens up, and the answer is tidier than I expected.

What I ran

I took the four formulas the ideal weight calculator uses and computed every one of them at each centimetre from 152 to 200, for men and for women separately. That is 49 heights, two sexes, four formulas: 392 figures. For each height I recorded the lowest result, the highest, the gap between them, and where all four sat against the healthy BMI range for that height.

The constants are the published ones. Devine adds 2.3 kg per inch over five feet to a 50 kg base for men and 45.5 kg for women. Robinson uses 52 kg and 1.9 kg per inch for men, 49 kg and 1.7 for women. Miller starts higher and climbs slower, at 56.2 kg plus 1.41 per inch for men. Hamwi was written in pounds, 106 lb plus 6 lb per inch for men, which converts to kilograms at the end.

Every figure below comes out of that run. You can check any row against the calculator yourself.

Men: the gap closes at 5 ft 6 in and opens either side

The narrowest point for men sits at 168.1 cm, where the four formulas land within 1.17 kg of each other. That is as close to consensus as these equations ever get. Move away from it in either direction and they separate: 8.3 kg apart at 152 cm, 7.7 kg at 183 cm, 16.5 kg at 200 cm.

The shape of that curve says something about how the formulas were built. All four were fitted around the middle of an adult height distribution, and 168 cm is close to the average height of the men in those reference populations. Away from the middle each equation extrapolates on its own slope, and the slopes were never meant to agree.

Women: the agreement point is taller than the men’s

For women the tightest agreement falls at 172.9 cm, within 1.36 kg. That figure surprised me. Women average several centimetres shorter than men, so you would expect the women’s formulas to converge at a shorter height, not a taller one. They converge about 5 cm higher instead.

The practical effect is that a woman of average height sits further from her formulas’ agreement point than a man of average height does from his. At 160 cm the four results for women spread across 5.0 kg. At 152 cm they spread across 7.9 kg.

Which formula gives the lowest number depends entirely on your height

People ask which of these formulas runs lightest, as though there were a fixed answer. There is not. For men the ranking reorders three times across the range:

• Below 164 cm, Hamwi returns the lowest figure
• From 164 to 166 cm it is Devine
• From 166 to 175 cm it is Robinson
• Above 175 cm it is Miller

Hamwi makes the sharpest move of the four. At 152 cm it gives a man the lowest target of the set, 47.7 kg. At 183 cm it gives him the highest, 80.9 kg. One equation, opposite ends of the pack, because its 6 lb per inch is the steepest slope in use.

For women the order changes twice: Hamwi is lowest below 169 cm, Robinson from there to 184 cm, Miller above that. Miller is the highest result up to 173 cm, and Devine takes over past it.

All four stay inside the healthy BMI band, at every height

Here is the part that puts the disagreement in proportion. I checked all 392 results against the healthy BMI range for their height, 18.5 to 24.9. Not one of them fell outside it. Zero of 49 heights for men, zero of 49 for women.

The formulas quarrel with each other while sitting comfortably inside the same band. At 180 cm the four of them spread across 6.1 kg, inside a healthy range that runs 20.7 kg wide, from 59.9 to 80.7 kg. At 200 cm the spread reaches 16.5 kg inside a band 25.6 kg wide.

That ratio is the useful finding. The formulas never disagree by as much as the healthy range already allows. A 6 kg argument between four equations is a smaller thing than the 21 kg of room the BMI bands give you at the same height.

What to do with your own number

Take the spread at your height as the error bar on any single figure. If you are a 185 cm man, your four results land 8.7 kg apart, and quoting one of them to a decimal place claims a precision nobody has. If you are a 170 cm woman, they land within 1.7 kg, and any of them will do.

None of this tells you what you should weigh. These equations read your height and your sex and stop there, which is the limitation the formulas guide covers in detail. Two people at 185 cm with 15 kg of muscle between them get identical answers. Put your own height through the calculator, note how wide the spread runs, and treat the midpoint as a reference point with a range attached, not as a target.

If you want a figure built from your own body instead of a table, what BMI measures explains where the height-and-weight approach runs out, and a body composition measurement picks up where it stops.

The data

The tables above sample every fifth centimetre. The full run covers all 49 heights at 1 cm steps for both sexes. Every value is reproducible: the formulas are published, the constants are listed at the top of this page, and the calculator on this site applies the same four.

Citing these figures

Quote any of this. The equations are public and the arithmetic is checkable, so the figures belong to anyone who wants to use them in an article, a class handout or a forum answer. A line that lets your reader verify the working:

If you need one number rather than the whole run, the convergence points are the two worth quoting: the four formulas land within 1.2 kg of each other at 168 cm for men and within 1.4 kg at 173 cm for women, then spread to 16.5 kg by 200 cm.