The body mass index, or BMI, is a division sum. Take someone's weight, divide it by the square of their height, and the number that comes out is it. The number says, in broad strokes, what range a weight falls in for that height, and it says nothing more than that. This note has two things in it: how the sum is done, and what the number does not measure.
1. The formula, and its two traps
The book puts the formula this way: BMI = the weight of the body in kilograms, divided by the square of the height of the body in metres. The unit is kg/m². The formula is short, and there are two places in it where marks are most often lost. First, the weight must be in kilograms and the height must be in metres; a height in centimetres or in feet has to be turned into metres before anything else. A hundred and seventy centimetres is one point seven metres, which is a division by a hundred. Second, it is the height that is squared, never the weight.
calculatorpress the button
Work out a BMI
The boxes come filled with the book's own example, Rahim, 72 kilograms and 1.8 metres. Put other numbers in if you like, and it works just as well if you do not.
A BMI is a broad indication and no more. It measures nothing of muscle, of the build of the bones, of age, of the water in the body, or of whether a person is well. And the adult table does not apply as it stands to anyone still growing; for that, charts by age are used instead. So take this number as a sum to learn, and as that only.
The table below is the book's, and its boundaries are few enough to remember.
BMI (kg/m²)
Class
under 18.5
underweight
18.5 to 24.9
normal weight
25.0 to 29.9
overweight
30.0 to 34.9
obesity, first stage
35.0 to 39.9
obesity, second stage
40 and above
obesity, third stage
2. The sum by hand
There is no calculator in an examination, so the steps are worth doing by hand. Take the book's own example.
step by steppress next
Rahim's BMI, in four steps
Take the two numbers. Rahim weighs 72 kilograms and stands 1.8 metres. Notice that the weight is in kilograms and the height in metres. Had the height been in centimetres or in feet, the very first thing to do would have been to turn it into metres.
Square the height. 1.8 squared is 3.24. It is the height that is squared and not the weight, and this is where the most mistakes are made. Squaring makes the denominator large, which is why a tall person comes out with a lower BMI.
Divide the weight by it. BMI = 72 ÷ 3.24 = 22.2 kg/m². Do not leave the unit off; the weight is in kg and the square of the height in m², so the quotient is kg/m².
Find it in the table. 22.2 falls between 18.5 and 24.9, which the book's table calls a normal weight. But remember what the number has not said: nothing of Rahim's muscle, of the build of his bones, of whether he is well. Only which range the ratio of his weight to his height falls in.
3. What the number is measuring
Because the height is squared in the denominator, a BMI is not a measure of weight. A grid set out side by side makes that plain.
gridtap a cell
Learning to read the grid
Tap a cell. Then go right along its row, and down its column; two different things happen.
height (m) · weight (kg)
45
55
65
75
1.5
20.0
24.4
28.9
33.3
1.6
17.6
21.5
25.4
29.3
1.7
15.6
19.0
22.5
26.0
1.8
13.9
17.0
20.1
23.1
1.5 m and 45 kg: 45 ÷ 2.25 = 20.0, a normal weight.
1.5 m and 55 kg: 55 ÷ 2.25 = 24.4, a normal weight.
1.5 m and 65 kg: 65 ÷ 2.25 = 28.9, overweight.
1.5 m and 75 kg: 75 ÷ 2.25 = 33.3, obesity, first stage.
1.6 m and 45 kg: 45 ÷ 2.56 = 17.6, underweight.
1.6 m and 55 kg: 55 ÷ 2.56 = 21.5, a normal weight.
1.6 m and 65 kg: 65 ÷ 2.56 = 25.4, overweight.
1.6 m and 75 kg: 75 ÷ 2.56 = 29.3, overweight.
1.7 m and 45 kg: 45 ÷ 2.89 = 15.6, underweight.
1.7 m and 55 kg: 55 ÷ 2.89 = 19.0, a normal weight.
1.7 m and 65 kg: 65 ÷ 2.89 = 22.5, a normal weight.
1.7 m and 75 kg: 75 ÷ 2.89 = 26.0, overweight.
1.8 m and 45 kg: 45 ÷ 3.24 = 13.9, underweight.
1.8 m and 55 kg: 55 ÷ 3.24 = 17.0, underweight.
1.8 m and 65 kg: 65 ÷ 3.24 = 20.1, a normal weight.
1.8 m and 75 kg: 75 ÷ 3.24 = 23.1, a normal weight.
Go right along a row and the weight rises and the BMI rises with it, straightforwardly. Go down a column and the height rises and the BMI falls, but not in even steps, because it is the square of the height in the denominator. From 1.5 to 1.8 the height rises by a fifth, while the denominator goes from 2.25 to 3.24, which is a rise of forty four per cent.
Look down the column for 75 kilograms. Four people of one weight, and four different classes. The number is not one of weight, then, but of the relation between weight and height.
the limitstap a chip
What a BMI says, and what it does not
It measures this. This is exactly what a BMI is, and it is nothing else. A third number made out of two.
It does not. Muscle is heavier than fat. Someone who plays a sport regularly may come out in the overweight range with very little fat on them. The number sees how much the weight is; it does not see what the weight is made of.
It does not. One person's bones are naturally heavy and broad and another's are light. A BMI knows nothing of the difference.
It does not. And this is just why the adult table does not apply as it stands to anyone still growing. The proportions of a body change while it grows, so charts by age are used instead.
It does not. Sixty to seventy five per cent of a body is water, and that rises and falls within a single day. A BMI catches none of it.
It does not. What a person eats, how varied it is, whether the vitamins and the minerals are all being had, none of it has any place in the formula.
It does not. How far someone can walk, how many stairs they can climb, how soon they tire, all of it can be measured directly, and all of it tells more than a BMI does.
It does not. Being well is many things together: the pressure of the blood, what is in the blood, sleep, energy, the power to fight off illness. A BMI stands in for none of them. That is why it is called a broad indication; a doctor begins with it and does not end there.
Of the eight, a BMI measures one. The other seven it knows nothing about, and those are the ones that matter more.
That muscle is heavier than fat, and that charts by age are used for those still growing, are both ordinary medical knowledge rather than anything from this section of the book.
Why teach it, then? Because it is easy to work out, and because it is a serviceable tool for taking the broad measure of a whole population's health. It is not a tool for passing judgement on one person. That difference is the real lesson of the section.
cardstap a card
A quick run through
QuestionBMI in full?
AnswerBody Mass Index, which in Bangla is দেহের ভরসূচি.
QuestionThe formula?
AnswerBMI = the weight in kilograms ÷ [the height in metres]²
QuestionThe unit?
Answerkg/m², the weight being in kg and the denominator the square of a length in m.
QuestionThe normal range?
AnswerBy the book's table, 18.5 to 24.9. Below that is underweight, 25 to 29.9 is overweight, and from 30 the stages of obesity.
QuestionThe commonest mistake?
AnswerLeaving the height in centimetres, and squaring the weight. It is the height that is squared, and the height must be in metres.
QuestionWhat does it not measure?
AnswerMuscle, the build of the bones, age, the water in the body, what a person eats, what a body can do: none of it. And the adult table does not apply as it stands to anyone still growing.
check yourself
One question
Someone is 160 centimetres tall and weighs 55 kilograms. What is their BMI?
34.4 is what comes of dividing 55 by 1.6 without squaring it. The squaring has been left out.
Right. The height goes into metres first: 160 cm is 1.6 m. Then 1.6 squared is 2.56, and 55 ÷ 2.56 is 21.5 kg/m², a normal weight by the book's table. Had the centimetres been left as they were, the denominator would have been 25600 and the answer 0.002, which means nothing at all.
That comes of mixing centimetres and metres. Turn the height into metres first.
The denominator is not right. 1.6 squared is 2.56, and 55 ÷ 2.56 is 21.5.
check yourself
Another question
Rahima and Ariba are both 1.5 metres tall; Rahima weighs 47 kilograms and Ariba 60. Rahim weighs 72 kilograms and is 1.8 metres tall. Whose BMI is the highest of the three?
The weight is the greatest, but so is the height, and it is the height that is squared. Work it out.
Right. Rahima: 47 ÷ 2.25 = 20.9. Ariba: 60 ÷ 2.25 = 26.7. Rahim: 72 ÷ 3.24 = 22.2. Rahim weighs the most and still comes out below Ariba, because he is much taller and the squaring makes his denominator far larger, 3.24 against 2.25. Which shows that a BMI is not measuring weight but the relation of weight to height.
The lightest would be expected to come out lowest, and so she does: 20.9.
The three are different: 20.9, 26.7 and 22.2.
check yourself
Last question
Someone who plays a sport regularly comes out at a BMI of 26, which the book's table calls overweight. What follows from that?
The formula has no way of knowing whether the weight is muscle or fat, so that does not follow from the number.
Right. There are two things in the formula, a weight and a height. Whether the weight is muscle or fat, the formula cannot tell. Muscle is heavier than fat, so someone who trains may come out higher with little fat on them. The sum is correct, and the formula is the same for a sportsperson; the fault is not in the arithmetic but in reading more into the number than is in it.
There is nothing wrong with the arithmetic. The mistake is in reading more into it than it holds.
The formula is the same for everyone; the question is not whether it can be worked out but how much the result carries.
At a glance
The formula. BMI = the weight in kilograms ÷ [the height in metres]², in kg/m².
Two traps. It is the height that is squared, and the height must be in metres.
The table. 18.5, 25, 30, 40; four boundaries, and the six classes come with them.
The limits. The number measures nothing but the ratio of weight to height, and the adult table does not apply as it stands to anyone still growing.
If your body, your weight or your eating is worrying you, talk to an older person at home or to a teacher at school; if it is needed they will take you to a doctor.
Source: Science, Classes 9-10 (NCTB), Chapter 1 “A better way of living”, section 1.2.