BMI Calculator: How the Index Is Calculated and What It Shows

Body mass index is a single number that relates weight to height. It divides mass by the square of stature, producing a figure that is roughly comparable between a short person and a tall one. That is the entire idea, and understanding what such a ratio can and cannot tell you is more useful than the number itself.

This page is general information about how the index is calculated and what it measures. It is not medical advice, it does not diagnose anything, and no figure here is a target or a recommendation. Anything about your own health, including whether your weight is worth discussing at all, belongs in a conversation with a qualified clinician who can look at you rather than at two numbers.

The calculator returns your BMI, the category it falls in under the standard adult scale, the weights at which the formula would return 18.5 and 24.9 for your height, a line that names which end of that range you sit outside, and BMI prime. Each of those is a restatement of the same ratio, not extra information.

#The formula in both unit systems

Formula: BMI = kg / m^2 in metric units, or BMI = 703 x lb / in^2 in US units, where kg is weight in kilograms, m is height in meters, lb is weight in pounds and in is height in inches.

The metric version is the definition. Weight in kilograms divided by height in meters, squared. A person of 81.6 kg and 1.778 m has a BMI of 81.6 / (1.778 x 1.778).

The US version is the same calculation with a unit conversion folded into a single constant, which is where the 703 comes from. It is not arbitrary and it can be derived.

One pound is 0.45359237 kg and one inch is 0.0254 m. To convert lb per in^2 into kg per m^2, multiply by 0.45359237 and divide by 0.0254 squared:

• 0.0254^2 = 0.00064516
• 0.45359237 / 0.00064516 = 703.0696

So the exact factor is about 703.07, and 703 is the rounded version used in practice. The rounding costs very little: at 180 lb and 70 in the two versions give 25.82 and 25.83.

Height enters squared, which is why the index is far more sensitive to a height error than a weight error. Getting height wrong by an inch moves BMI more than getting weight wrong by three pounds.

#A worked example, done by hand

Take someone 5 ft 10 in tall weighing 180 lb.

1. Convert height to inches: (5 x 12) + 10 = 70 inches.
2. Square it: 70 x 70 = 4,900.
3. Multiply weight by 703: 180 x 703 = 126,540.
4. Divide: 126,540 / 4,900 = 25.8.

The metric route reaches the same place:

1. Height: 70 x 2.54 = 177.8 cm = 1.778 m.
2. Weight: 180 x 0.45359237 = 81.65 kg.
3. Square the height: 1.778^2 = 3.161284.
4. Divide: 81.65 / 3.161284 = 25.8.

The weights that return the range endpoints for 70 inches are about 18.5 x 4,900 / 703 = 128.9 lb and 24.9 x 4,900 / 703 = 173.6 lb. The calculator converts through the exact 0.45359237 kg and 0.0254 m factors rather than the rounded 703, so it shows 128.9 lb and 173.5 lb. The fifth row then names the end you fall outside: at 180 lb it reads "Above the top of the range" and gives 6.5 lb. At 120 lb the same row reads "Below the bottom of the range" and gives 8.9 lb, and anywhere between the two endpoints it reads "Position in the range" and confirms you are within 18.5 to 24.9. That is an arithmetic statement about the formula at this height, nothing more.

BMI prime is BMI divided by 25, so 25.8 / 25 = 1.03, shown to two decimals. Values above 1 sit above the upper end of the standard adult healthy range, and the decimal reads as a proportion.

#Where the index came from

The ratio was devised in the 1830s by Adolphe Quetelet, a Belgian mathematician and astronomer working on the statistical description of populations. He was looking for a way to describe how weight scales with height across large groups of people, and found that dividing by height squared produced a distribution that behaved usefully. He called it the Quetelet index.

It was renamed body mass index in a 1972 paper by Ancel Keys and colleagues, who compared several weight-for-height ratios and concluded that Quetelet's was the best of the simple options for population studies.

The origin matters for interpretation. The index was designed to describe groups, not individuals. A statistic that works well for characterizing the distribution of a population is not automatically informative about any single member of it, and BMI was never validated as a measurement of one person's body composition.

#The standard adult categories

These are the conventional cut points for adults. They are thresholds on a continuous scale, so 24.9 and 25.1 describe nearly identical bodies despite falling in different rows. Treating the boundary as a cliff misreads what a continuous measure does.

BMI is used as a population-level screening measure, which means it is a cheap first filter applied to large numbers of people, not a test that determines anything on its own.

#Reference tables

BMI for a range of heights and weights, computed with the 703 formula:

The same twenty pounds moves BMI by 3.6 points at 5 ft 2 in and by 2.6 points at 6 ft 2 in, because height is squared in the denominator.

The weight span that the formula maps to 18.5 through 24.9 widens with height:

In metric units, at 165 cm the same endpoints are 50.4 kg and 67.8 kg; at 185 cm they are 63.3 kg and 85.2 kg.

#How to read the result

Read it as a position on a ratio scale, not as a description of your body. BMI tells you how your weight compares to what the formula expects for your height, and that is all the information contained in two measurements.

The endpoints reported by the calculator are the inverse of the same formula. They answer the question "what weight would produce a BMI of 18.5 or 24.9 at this height" and nothing else. They are not goals, they are not prescriptions, and they carry no implication that any particular figure would suit you.

Precision beyond one decimal place is false precision. Ordinary daily fluctuation in body water, food and clothing moves measured weight by a few pounds, which moves BMI by a few tenths.

If you want context for the number, a clinician is the person to ask. They can consider what the index leaves out, which is most of what matters.

#What BMI cannot measure

It cannot distinguish muscle from fat. Both are weight. A person carrying substantial muscle mass registers the same as someone of identical weight and height carrying much less, and the index cannot tell them apart.

It ignores where mass sits. Two people with the same BMI can have very different fat distribution, and distribution is one of the things clinicians care about.

It ignores frame and bone. Broader skeletal builds carry more weight at the same height.

It behaves differently across age. Body composition shifts with age at constant weight, so the same BMI means something different at 25 and at 75.

It behaves differently across ancestral populations. Research has repeatedly found that the relationship between BMI and body composition varies between population groups, and some health systems use adjusted cut points for that reason.

It says nothing about anything else. Activity, fitness, diet, sleep, blood pressure and laboratory results are all invisible to a weight-and-height ratio.

#Groups the standard categories do not fit

Children and adolescents. The adult cut points are not applied. Because body composition changes rapidly during growth, pediatric interpretation uses age- and sex-specific percentile charts instead, and belongs with a pediatric clinician. The age calculator is useful for getting an exact age in years and months, which those charts require.

Pregnancy. Weight change during pregnancy is expected and the index is not interpreted using the standard adult scale. Prenatal care providers handle this directly.

Athletes and heavily muscled people. High lean mass raises weight without the composition the categories assume, so the index can place a very lean person in a higher band.

Older adults. Loss of muscle and bone density with age changes what a given ratio reflects.

People with limb differences or conditions affecting stature or fluid balance. Height and weight may not carry their usual meaning.

#What clinicians look at alongside it

Described neutrally, and not as instructions: in practice BMI is one input among several. Clinical assessment commonly also considers waist measurement, personal and family history, blood pressure, laboratory results, physical examination, activity and function, and the trajectory of weight over time rather than a single reading.

The index survives because it is cheap, reproducible and requires only a scale and a tape measure. That makes it useful for comparing populations and for triaging who might benefit from a closer look. It was not built to replace any of the above.

#What this model leaves out

• Body composition. No estimate of fat, muscle, bone or water.
• Fat distribution. Nothing about where mass is carried.
• Any health measurement. No blood pressure, no laboratory values, no fitness measure.
• Individual variation. No adjustment for build, ancestry, age or sex.
• Change over time. A single reading, with no trend.
• Measurement error. Home scales and self-reported height both drift, and height error is magnified by squaring.

For general information on energy balance arithmetic, the calorie calculator explains the Mifflin-St Jeor equation, and the running pace calculator covers pacing mathematics. Neither is health advice either. The full list of tools is on the calculators index, and the site's disclaimer sets out its limits.

#Common mistakes

Entering height in feet alone. 5.8 is not 5 ft 8 in. Convert to total inches, or use the metric fields.

Squaring the wrong unit. In the metric formula, height must be in meters. Using centimeters gives a number about 10,000 times too small.

Forgetting the 703. Pounds divided by inches squared without the conversion factor produces a meaningless fraction.

Weighing under inconsistent conditions. Compare like with like: same time of day, similar clothing, same scale.

Treating a category boundary as a change of state. The scale is continuous and the cut points are conventions.

Reading the range endpoints as targets. They are the formula run backwards, nothing more.

Applying the adult categories to a child. Pediatric interpretation uses different charts entirely.

Assuming the number describes health. It describes a ratio of two measurements, and that is the beginning of a question rather than an answer.