Health

What the tools in this category actually do

Working out an index. The BMI Calculator divides weight in kilograms by the square of height in metres. The result is rounded to one decimal, a coloured category appears next to it, and you also get the weight range for your height that matches an index from 18.5 to 24.9. Two unit systems are available: metric, with centimetres and kilograms, and imperial, with feet, inches and pounds, where a pound becomes 0.45359237 kilograms and an inch 2.54 centimetres.

Working out energy. The Daily Calorie Needs calculator follows the Mifflin-St Jeor formula: weight times 10, height times 6.25, age times 5, and then plus 5 for men or minus 161 for women. The resting burn that comes out is multiplied by an activity factor, from 1.2 for desk work up to 1.9 for athletes, and then by a goal factor: 0.85 for losing weight, 1 for holding steady and 1.1 for gaining.

Working out volume. The Volume Calculator covers six shapes: a sphere at 4/3·π·r³, a cylinder at π·r²·h, a cone at 1/3·π·r²·h, a prism at S·h, a pyramid at 1/3·S·h and a rectangular box at a·b·c. A prism and a pyramid need the area of the base rather than its dimensions, so that has to be worked out first. The answer is printed in cubic centimetres and in litres, and the formula is shown with the numbers substituted.

• Body mass index and its categories: BMI Calculator.
• Calories per day for your activity level: Daily Calorie Needs.
• The volume of a shape from its dimensions: Volume Calculator.
• Pounds and inches on input: the BMI Calculator converts them to metric on its own.
• Want to see the weight range for your height: the same BMI Calculator prints the 18.5 to 24.9 band.
• Volume given by the area of the base: the Volume Calculator covers prisms and pyramids.
• Telling resting burn from maintenance and from a goal: Daily Calorie Needs.

Picking the right tool for the job

The question decides the choice outright. An index question goes to the BMI Calculator, which accepts both unit systems and shows the category straight away. An energy question goes to Daily Calorie Needs. A geometry question goes to the Volume Calculator, where six shapes are listed along with the measurements each of them expects.

Inside the index calculation it helps to know what the page expects to receive. Metric input means centimetres and kilograms, imperial means feet, inches and pounds. The values have to land inside a range: height from 0.5 to 2.8 metres and weight from 10 to 700 kilograms, otherwise nothing is calculated. The BMI Calculator handles this neatly, because an empty or absurd input produces no result at all rather than a plausible looking number.

The calorie page takes more parameters: sex, age, height, weight, activity level and goal. Age runs from 10 to 120 years, height from 80 to 260 centimetres and weight from 25 to 500 kilograms. There are five activity levels, from sedentary to athlete, setting a factor between 1.2 and 1.9. The goal is a factor as well, 0.85, 1 or 1.1, which means switching the goal does not touch the calculation itself, only the number that comes out.

• Index and category: BMI Calculator.
• The weight range for your height: the same BMI Calculator.
• Calories for maintenance and for a goal: Daily Calorie Needs.
• Volume from a radius and a height: Volume Calculator.
• Volume from three dimensions: the same Volume Calculator.
• A conversion into litres for a tank: the Volume Calculator turns cubic centimetres into litres itself.
• Two scenarios side by side: BMI Calculator and Daily Calorie Needs show what changes with a different number.

How the lookalike tools differ

Two of the three calculators work on the body and yet measure different things. The BMI Calculator is a ratio of weight to squared height, with no unit of energy anywhere in it. Daily Calorie Needs counts kilocalories per day through the resting burn, the activity factor and the goal adjustment. An index says nothing about how much energy you spend, and a calorie figure says nothing about the proportions of the body.

The calorie calculation contains three separate numbers, and they are mixed up more often than anything else. Resting burn is what the body uses lying completely still. Maintenance is the resting burn times the activity factor, which is a rough estimate of an ordinary day. The goal is maintenance times 0.85, 1 or 1,1 depending on whether you are losing, holding or gaining weight.

There are two ways to enter data in each case, and the answer does not depend on which one you pick. The BMI Calculator offers metric and imperial entry, and the index on the output is the same either way. In the Volume Calculator centimetres, millimetres and metres change the value and the number of litres but never the formula, and a prism differs from a pyramid by nothing more than the factor of one third.

• BMI Calculator gives a dimensionless index, Daily Calorie Needs gives kilocalories per day.
• Resting burn, maintenance and a goal are three numbers from one calculation rather than three separate measures.
• Metric and imperial entry produce the same index in the BMI Calculator.
• Units change the value and the litres in the Volume Calculator but not the formula.
• The BMI Calculator also gives a weight range, while Daily Calorie Needs gives three levels of expenditure.
• Prism and pyramid in the Volume Calculator differ only by a third of the base area.

Common mistakes and edge cases

Body mass index is the most widely used measure and also the most reduced one. It cannot tell muscle from fat: a person with a large muscle mass may land in the category of excess body weight while carrying very little fat. It ignores age, sex and how the fat is distributed, which makes it the wrong tool for teenagers, for pregnancy, for older people and for athletes. The categories used in the BMI Calculator are the boundaries 18.5, 25, 30, 35 and 40 adopted by the World Health Organization for adults.

A calorie target is an estimate rather than a measurement. The Mifflin-St Jeor formula carries an error of dozens of kilocalories on its own, and the activity and goal factors that follow are chosen by eye. A moderate activity level means three to five workouts a week, so if you train less often it is fairer to pick a lower coefficient. Both the BMI Calculator and Daily Calorie Needs are reference points for watching a trend, not a basis for a diet.

Volume is simpler, but two things are worth keeping in mind. A prism and a pyramid need the area of the base, not its dimensions: for a round base calculate S = π·r² first, for a rectangular one S = a·b. And a volume in litres only makes sense for a container that is filled to the brim, because a bottle with a neck holds less than its geometry suggests.

Signs are the last constraint. All three calculators refuse to work with a negative or a zero value: at a zero radius the volume is zero rather than unknown, so no result is shown at all. The BMI Calculator additionally filters out values outside the range, and a height under 50 centimetres or a weight under 10 kilograms is physically possible for a child but carries no meaning as an adult reference.

• An index cannot separate muscle mass from fat, so for an athlete it is effectively too high.
• The boundaries 18.5, 25, 30, 35 and 40 in the BMI Calculator are meant for adults and do not fit children.
• The Mifflin-St Jeor formula carries an error, and the activity factors are picked by eye.
• Daily Calorie Needs works in metric only and accepts a height from 80 to 260 centimetres.
• A prism and a pyramid in the Volume Calculator need the area of the base rather than its dimensions.
• A volume in litres is not the same as the usable capacity of a vessel with a neck or a cut edge.
• With a zero or negative dimension none of the three calculators produces any result.

All three pages are reference calculations based on published formulas. They do not replace a doctor, blood tests or a specialist, and the numbers they print describe a reference point rather than a diagnosis or a prescription.