Body mass index calculator

What this works out

Body mass index is weight divided by height squared. It is one division, and almost nobody gets it wrong; what people actually want is the second half — the band it falls in, and the weight range that band covers at their own height. That second half is the same formula run backwards, and it is the part most calculators either skip or round in the wrong direction.

So this tool gives both, in kilograms and in pounds, and it says out loud where the answer stops being meaningful. BMI has no term for muscle, no term for where fat sits, and no meaning at all under the age of 20 unless it is read against a growth reference. Those are not caveats bolted on at the end; two of them change what this page will show you.

The method

The height is converted to metres and squared, the weight is divided by it, and that is the index. Imperial input is converted first, with the exact definitions rather than approximations: an inch is 2.54 cm and a pound is 0.45359237 kg, both by international agreement, so nothing is lost in the conversion.

The band is decided on the unrounded figure. This is the decision most likely to look like a bug. A weight of 76.47 kg at 175 cm gives a BMI of 24.9738, which is displayed as 25.0 and reported as healthy weight. Classifying the displayed figure instead would move the effective cut-off to 24.95, which is not a number anybody published. A cut-off is a number, not a display, so the display is what gives way.

Each band’s weight range is rounded inwards — the bottom up to the next tenth, the top down to the previous one. Every weight printed is therefore genuinely inside the band it is listed under, which is not true if you round to nearest. The top has one more rule: when the exclusive cut-off lands exactly on a tenth, it steps down a whole tenth rather than staying put. At 180 cm a BMI of 25 is 81.0 kg to the digit, and 81.0 kg at 180 cm is a BMI of exactly 25, which is overweight — so the healthy range there ends at 80.9 kg. 180 cm is not an exotic height, and without that rule the commonest page on the tool would have printed a weight that is not in the band beside it.

The kilogram and pound ranges are rounded separately, in their own units, because converting one into the other reintroduces the problem: 76.5 kg is 168.65 lb, and rounding that either way puts one of the two figures outside the band.

The lowered cut-offs are action points, not a second classification. The 2004 WHO expert consultation looked at whether Asian populations need different numbers, found that risk of type 2 diabetes and cardiovascular disease rises below a BMI of 25, and deliberately kept the international classification while naming 23.0, 27.5, 32.5 and 37.5 as points at which countries might act. The option here applies the first two, and the bands it produces are labelled by risk rather than by category, because that is what the consultation said.

Below 20, no band is given. BMI in childhood and adolescence is read as a percentile against a reference for age and sex — WHO publishes one for ages 5 to 19 — and a BMI of 21 that is unremarkable at 30 is high at 8 and low at 18. A form holding a height, a weight and an age cannot do that reading, so it does not pretend to. The index itself is still shown, because it is the input.

Before you read on

At 175 cm, a weight of 76.47 kg gives a BMI of 24.9738. The page displays 25.0. Which band is that?

• AOverweight — the screen says 25.0, and 25.0 is the cut-off.

  That would move the real cut-off to 24.95, which is not a number anybody published.

• BHealthy weight — the band is decided on the unrounded figure.

  Yes. A cut-off is a number, not a display.

• CIt sits exactly on the boundary, so either is defensible.

  24.9738 is not on the boundary. It only looks like it after rounding.

Healthy weight. The band is decided on the unrounded 24.9738, not on the 25.0 shown beside it — this is the decision on the page most likely to look like a bug, and it is the right way round. Classifying the displayed figure would quietly move the effective cut-off to 24.95, a number no authority has ever published. A cut-off is a number rather than a display, so the display is what gives way.

A worked example

175 cm, 70 kg, 30 years old, international cut-offs.

BMI = 70 / 1.75^2
    = 70 / 3.0625
    = 22.857142…
    = 22.9 to one decimal place

Body mass index	22.9
Band	Healthy weight
Weight for that band at this height	56.7 – 76.5 kg (125.0 – 168.7 lb)
To reach that band	Inside it already

The full table at that height:

Band	BMI	Weight (kg)	Weight (lb)
Underweight	Under 18.5	56.6 and under	124.9 and under
Healthy weight	18.5 to under 25.0	56.7 – 76.5	125.0 – 168.7
Overweight	25.0 to under 30.0	76.6 – 91.8	168.8 – 202.5
Obesity	30.0 and over	91.9 and over	202.6 and over

Checked at the boundaries, which is where a calculator is worth anything: 56.6 kg is a BMI of 18.4816 and underweight, 56.7 kg is 18.5143 and healthy; 76.5 kg is 24.9796 and healthy, 76.6 kg is 25.0122 and overweight.

The same person on the lowered action points. At 170 cm and 68 kg the index is 23.5. On the international bands that is healthy weight, with a range of 53.5 – 72.2 kg. On the lowered points it is increased risk, with an acceptable range of 53.5 – 66.4 kg — a top end 5.8 kg lower — and the tool reports 1.6 kg (3.5 lb) less to reach it. One body, one number, two readings.

These are the same numbers asserted in this tool’s test file, so if the formula ever changes without this page changing with it, the build fails. The test also feeds both ends of every printed range back through the formula at every half centimetre of adult height, in both units and on both sets of cut-offs, and fails if any of them lands in a different band from the one it was printed under.

What it does not do

It does not measure body fat, and BMI does not either. There is no term for muscle, for where fat is carried, for bone density or for frame, so a trained body reads high and a body that has lost muscle with age can read normal while carrying more fat than it once did. It is a screening measure designed for populations, and on one person it is a starting point rather than a finding.

It gives no band below the age of 20, none during pregnancy or breastfeeding — which it cannot detect, so that one is on you — and it makes no adjustment for older adults, where the relationship between BMI and mortality is known to differ from the one the bands were drawn against. It does not diagnose anything, it does not recommend a target weight, and the range it prints is 17 kg wide at a typical height for exactly that reason. Nothing here is medical advice; a number from this page is a reason to talk to a clinician, not a substitute for it.

It also says nothing about what you eat. Where the real question is how much food a day rather than where one number sits in a band, the daily calorie figure is the more useful one to start from.

BMI = weight / height^2
    = kilograms / metres squared

Imperial input is converted first, and exactly:
  1 in = 2.54 cm            1 lb = 0.45359237 kg

The band is decided on the unrounded BMI:
  under 18.5            underweight
  18.5 to under 25      healthy weight
  25 to under 30        overweight
  30 and over           obesity

On the lowered action points the middle two
cut-offs move to 23 and 27.5.

A band's weight range is the same formula run
backwards:
  weight = BMI x metres squared

and each end is rounded inwards to a tenth -
the bottom up, the top down - so every weight
printed is inside the band it is listed under.