How BMI, BMR and body-fat formulas are calculated

Every fitness calculator is an equation someone fitted to a population at some point in the past. Knowing which equation, and which population, tells you how much weight to put on the number it produces. None of this is medical advice, and none of these formulas can assess an individual the way a clinician can.

BMI: a population measure used on individuals

BMI = weight (kg) ÷ height (m)²

The formula dates from the 1830s, devised by Adolphe Quetelet to describe populations, not to assess patients. It became a clinical screening tool in the twentieth century for a practical reason: it needs two measurements anyone can take.

Its limitations follow directly from what it measures, which is mass.

• It cannot distinguish muscle from fat. Muscular athletes are routinely classified as overweight or obese with very low body fat.
• It ignores fat distribution, and abdominal fat carries more metabolic risk than the same mass elsewhere. A waist measurement adds information BMI cannot.
• Squaring height under-corrects for very tall people and over-corrects for very short ones.
• The standard thresholds were derived largely from European populations. Several health authorities apply lower thresholds for people of South Asian and East Asian descent, where metabolic risk appears at a lower BMI.
• Adult categories do not apply to children, who are assessed against age-and-sex percentile charts instead.

It remains useful for what it was designed for — comparing groups — and for tracking your own trend over time. As a verdict on one person on one day, it is weak. The BMI calculator states these bands and their limits.

BMR: Mifflin-St Jeor

Men:   BMR = (10 × kg) + (6.25 × cm) − (5 × age) + 5
Women: BMR = (10 × kg) + (6.25 × cm) − (5 × age) − 161

Published in 1990, this replaced the 1919 Harris-Benedict equation as the usual default because it predicts modern populations more accurately. It estimates basal metabolic rate: the energy used at complete rest for circulation, respiration, temperature regulation and cell maintenance.

Even at its best it is a population fit. Individual metabolic rate varies by roughly ten percent either side of the prediction among people with identical measurements, and more where body composition is unusual, since the equation uses total mass and cannot see how much of it is muscle.

BMR is not a calorie target. Multiplying it by an activity factor gives total daily energy expenditure, and that multiplier is where most of the error enters, because self-reported activity is systematically overestimated. The calorie calculator applies those standard multipliers.

Body fat: the US Navy circumference method

Developed for military screening, this estimates body fat from tape measurements and height, using logarithms of circumference values. Its appeal is that it requires nothing but a tape measure.

Two things are worth knowing. First, the published coefficients are defined for measurements in inches, so a calculator taking centimetres must convert before applying them — using centimetres directly produces nonsense, and this is a common bug in online implementations. Second, accuracy against laboratory methods is typically within three to four percentage points, and worse at the extremes of body composition.

It is also acutely sensitive to technique. A centimetre of difference in where the tape sits changes the result noticeably, which is why consistency between measurements matters far more than precision in any single one. Use it to watch a trend, not to establish a number. The body fat calculator describes the measurement points.

Ideal weight: a dosing formula, repurposed

Men:   50   kg + 2.3 kg per inch over 5 feet
Women: 45.5 kg + 2.3 kg per inch over 5 feet

The Devine formula was published in 1974 to calculate drug dosages. It was never intended as a health target, and it has no evidential basis as one. It also uses height alone, so it cannot account for build or composition at all.

It appears on fitness sites everywhere anyway. A weight range derived from the healthy BMI band is a more defensible reference precisely because it is a range, and the ideal weight calculator shows both.

Due dates: Naegele’s rule

Estimated due date = first day of last period + 280 days

Formulated in the early nineteenth century, this assumes a 28-day cycle with ovulation on day 14. For a longer or shorter cycle the estimate shifts accordingly, which is why a calculator that ignores cycle length is less accurate for a large share of people.

About 4% of births occur on the estimated date. It describes the middle of a window several weeks wide, and an early ultrasound is more accurate and takes precedence when the two disagree.

What all of these have in common

• They are population fits. They describe averages, and any individual can sit some distance from the average without anything being wrong.
• They were derived from specific populations, often decades ago, and frequently not diverse ones.
• They are precise to the decimal and accurate only to a range. A BMR of 1755 kcal is not more trustworthy than “about 1750”.
• A trend in your own numbers, measured the same way each time, carries more information than any single reading.
• None of them diagnoses anything. Weight, body composition and metabolic health interact with sleep, medication, thyroid function, genetics and much else that no tape measure can see.

The reasonable way to use them is as a rough baseline and a direction of travel. If a figure concerns you, it is a reason to talk to a clinician who can look at the whole picture, not a conclusion in itself.