BMI Formula

One division, one square. Here is the arithmetic, why it is shaped that way, and the three mistakes that produce a wrong number.

BMI = weight in kilograms ÷ height in metres squared (kg/m²). In imperial units it is 703 × weight in pounds ÷ height in inches squared. A 1.70 m, 68 kg adult therefore reads 68 ÷ 1.70² = 23.5. The category boundaries — 18.5, 25, 30 on the WHO international scale — are fixed cut-points applied to the result; they are not part of the formula.

The two forms of the formula

Metric

BMI = kg ÷ m²

Weight in kilograms, height in metres. 1.70 m is written 1.70, not 170.

Imperial

BMI = 703 × lb ÷ in²

Weight in pounds, height in total inches. 5'10" is 70 inches, not 5.10.

Both return the identical BMI for the same person. The 703 factor is a single constant that converts pounds to kilograms and square inches to square metres together — it is not a correction or a calibration, and there is no second version of it in circulation.

A worked example, step by step

  1. Height: 1.70 m. Square it: 1.70 × 1.70 = 2.89 m².
  2. Weight: 68 kg. Do not convert anything yet — it is already in kilograms.
  3. Divide: 68 ÷ 2.89 = 23.53. Round to one decimal: 23.5.
  4. Classify against your standard: 23.5 is normal on the WHO international scale, overweight on the WHO Asia-Pacific scale (overweight from 23.0) and normal on Japan's JASSO scale.

The same person in imperial units: 5'7" is 67 inches and 68 kg is 149.9 lb. Then 703 × 149.9 ÷ 67² = 703 × 149.9 ÷ 4489 = 23.5. Identical, as it must be.

Why the height is squared

BMI exists to remove height from body weight so that people of different builds can sit on one scale. Body mass scales roughly with the square of height — a person twice as tall is not twice as heavy at the same shape, they are about four times as heavy, because mass grows with volume while height grows in one dimension. Dividing weight by height squared largely cancels that effect and leaves a single height-adjusted number.

That is also the source of the formula's best-known weakness. The exponent of exactly 2 is an assumption about human shape, not a derived constant, and it fits short and average heights better than very tall ones. It is why BMI tends to read slightly high at the top of the height range — one more reason a single number should never be the whole assessment.

The formula was devised in the 1830s by the Belgian mathematician and statistician Adolphe Quetelet, who was describing the distribution of weight in populations. It was renamed the body mass index in 1972 by the American physiologist Ancel Keys, whose study compared it against skinfold measurements and found it the best of the height-weight ratios then available. Both men were working on groups, not individuals — which is still the right way to read it.

The three mistakes that produce a wrong BMI

MistakeWhat it doesCorrect form
Height in centimetresDividing by 170² instead of 1.70² inflates the result 10,000-fold1.70 m, not 170
Height as feet-point-inchesUsing 5.10 for 5'10" treats it as 5.1 feet — 61 inches instead of 70, a 22 cm error that grows with the inch value70 inches (5 × 12 + 10)
Pounds without the 703 factorGives a number in the thousands, or a plausible-looking value that is simply wrong703 × lb ÷ in²

The same BMI is a different weight at every height

This is the part most "ideal weight" answers get wrong. Because weight is multiplied by height squared, every BMI value corresponds to a different weight at each height. There is no single target weight for an adult — only a target BMI, which converts differently for everyone.

The weight corresponding to BMI 23 and BMI 25 at common heights
HeightBMI 23 (Asia-Pacific overweight line)BMI 25 (WHO international overweight line)BMI 25 in pounds
5'2"157 cm57.0 kg62.0 kg137 lb
5'4"163 cm60.8 kg66.1 kg146 lb
5'6"168 cm64.6 kg70.3 kg155 lb
5'8"173 cm68.6 kg74.6 kg164 lb
5'10"178 cm72.7 kg79.0 kg174 lb
6'0"183 cm76.9 kg83.6 kg184 lb
6'2"188 cm81.3 kg88.3 kg195 lb

For the full healthy, overweight and obese range at every height, see the BMI chart.

The cut-points the result is compared against

The formula never changes. What changes is the table you read the answer against — and there are at least eleven published ones.

BMI rangeClassification
< 18.5Underweight
18.5 – < 25Normal weight
25 – < 30Overweight
30 – < 35Obese class I
35 – < 40Obese class II
≥ 40Obese class III (severe obesity)

Source: WHO Expert Consultation, Lancet 2004 — Appropriate body-mass index for Asian populations · WHO — Obesity and overweight fact sheet(WHO technical report series / current global reference)

Which cut-points apply to you

Same arithmetic, eleven different answers. At BMI 23.5 you are normal on the WHO international scale, overweight on the WHO Asia-Pacific scale, and in a class of your own on Japan's JASSO scale, which has no overweight tier at all.

BMI overweight and obesity cut-points by country and authority
StandardNormal rangeOverweight fromObesity fromWaist / central obesitySource
WHO international (global)World Health Organization18.5 – 24.925.030.0Primary source
WHO Expert Consultation 2004 (Asian populations)World Health Organization expert consultation, published in The Lancet18.5 – 22.923.027.5Primary source
WHO Asia-Pacific (WPRO / IASO / IOTF)WHO Western Pacific Regional Office, International Association for the Study of Obesity, International Obesity Task Force18.5 – 22.923.025.0Primary source
ChinaNational Health Commission of the PRC — health industry standard WS/T 42818.5 – 23.924.028.0M ≥90cm / W ≥85cmPrimary source
Hong Kong, ChinaDepartment of Health, Centre for Health Protection — adopting the WHO Western Pacific Regional Office classification for Asian adults18.5 – < 23.023.025.0WHtR < 0.5Primary source
SingaporeHealth Promotion Board (HPB), Ministry of Health18.5 – 22.923.027.5M ≥90cm / W ≥80cmPrimary source
JapanJapan Society for the Study of Obesity (JASSO)18.5 – 24.925.0M ≥85cm / W ≥90cmPrimary source
South KoreaKorean Society for the Study of Obesity (KSSO)18.5 – 22.923.025.0M ≥90cm / W ≥85cmPrimary source
India and South AsiaConsensus statement for Asian Indians (Misra et al., JAPI 2009); Indian Council of Medical Research18.0 – 22.923.025.0M ≥90cm / W ≥80cmPrimary source
UK NICE guidance — Asian, Chinese, Middle Eastern and Black African/Caribbean adultsNational Institute for Health and Care Excellence (UK), guideline NG24618.5 – 22.923.027.5WHtR < 0.5Primary source
ADA 2026 standard for Asian populationsAmerican Diabetes Association — Standards of Care in Diabetes 2026, adult overweight and obesity18.5 – 22.923.027.5M ≥90cm / W ≥80cmPrimary source

All 11 standards shown, each read from the issuing authority's own document (linked per row). The WHO 2004 figures of 23.0 / 27.5 are public-health action points, not a redefinition of the international categories.

Frequently asked questions

What is the BMI formula?
BMI = weight in kilograms divided by height in metres squared (kg/m²). In imperial units it is 703 × weight in pounds divided by height in inches squared. Both forms produce the same number.
Why is height squared in the BMI formula?
Because BMI is an attempt to remove height from body weight so that people of different heights sit on one comparable scale. Body weight scales roughly with height squared, so dividing weight by height squared largely cancels that effect. The formula was devised in the 1830s by the Belgian statistician Adolphe Quetelet, who was describing populations rather than diagnosing individuals — which is still the right way to read it.
What weight is BMI 25?
It depends entirely on your height, which is why no single number works. BMI 25 is 25 kg per square metre of height: 64.8 kg at 1.61 m, 72.3 kg at 1.70 m and 81.0 kg at 1.80 m. Any chart quoting one target weight for everyone has ignored the height term.
Is the BMI formula the same in metric and imperial units?
The relationship is the same; only the constant differs. Metric is kg / m². Imperial is 703 × lb / in². The 703 factor converts square inches to square metres and pounds to kilograms in a single step, so both versions return the identical BMI for the same person.

Data sources and how we verify them

Every cut-point, band and formula on this page is taken from the issuing authority's own document, listed below. We do not use second-hand summaries, and we do not fill gaps with numbers no source states.

Cut-points are population-level statistical thresholds, not individual diagnoses. If your value sits near a category line, measure your waist as well and read it alongside body-fat percentage. Last checked: 2026-09-15.

Sources

  1. WHO — Obesity and overweight fact sheet (BMI as kg/m², cut-points 25 and 30)
  2. WHO Expert Consultation — Appropriate body-mass index for Asian populations (Lancet 2004;363:157–163)
  3. Keys A et al. — Indices of relative weight and obesity (J Chronic Dis 1972) — the study that named BMI
  4. CDC — Adult BMI calculator and category ranges (obesity subdivided into three classes)

Every figure above was checked against the original document. This page is general information, not medical advice.

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