Health and fitness math

BMI, TDEE, macronutrient splits, and one-rep max estimates are all population-derived approximations applied to individuals. That is not a criticism — they are the best available from data you can collect without a lab. What matters is knowing how wide the error is and what to measure instead when it matters.

What BMI can and cannot tell you

BMI is weight in kilograms divided by height in metres squared, with WHO categories at 18.5, 25, and 30. It requires no equipment and is standardised worldwide, which is why epidemiology still uses it.

It cannot distinguish what the weight consists of or where it sits. Muscle is denser than fat, so a 180 cm athlete at 100 kg registers a BMI of 30.9 — formally obese — while potentially carrying 12 percent body fat. The reverse also occurs: sarcopenic obesity, low muscle with high fat at a normal BMI, is common in older adults and carries worse outcomes than the number implies.

Distribution matters more than total for metabolic risk. Visceral fat around the organs is strongly associated with insulin resistance and cardiovascular disease; subcutaneous fat on hips and thighs much less so. BMI is blind to this, which is why waist circumference adds real information — above 102 cm for men or 88 cm for women indicates elevated risk regardless of BMI. Waist-to-height ratio, ideally under 0.5, outperforms BMI as a predictor in most studies and needs only a tape measure.

The thresholds are also population-specific. They were derived from European-descent cohorts, and the WHO recommends lower cut-offs — commonly 23 and 27.5 — for many Asian populations because metabolic risk appears at lower BMI values.

None of this makes BMI useless. It works well at population scale, and for an individual it is a reasonable screening figure indicating whether a closer look is warranted, and a useful thing to track in yourself over time. It is not a diagnosis or a target.

Energy expenditure and why estimates drift

The Mifflin-St Jeor equation estimates basal metabolic rate from weight, height, age, and sex, and is accurate to within about 10 percent for roughly 80 percent of people — the best available without a body composition measurement. It replaced the 1919 Harris-Benedict equations, which overestimate by around 5 percent in modern populations.

Total expenditure has four components. BMR is 60 to 70 percent. The thermic effect of food is about 10 percent, and varies by macronutrient — protein costs 20 to 30 percent of its own calories to process, carbohydrate 5 to 10 percent, fat near zero. Exercise is usually smaller than people assume, commonly 300 to 500 kcal an hour. And non-exercise activity — fidgeting, walking, standing — varies by up to 2,000 kcal a day between individuals and is the largest source of variation between two people with the same BMR.

The activity multiplier is the weakest input. The bands run 1.2 to 1.9, which on a 1,780 kcal BMR spans 2,136 to 3,382 — a range larger than most intended deficits. Self-assessment errs high consistently, partly because a few gym sessions feel more significant than eight hours of sitting. A desk job with three workouts a week is closer to 1.375 than 1.55.

The defensible approach is to take the lower plausible multiplier, eat at that level for two to three weeks while tracking weight, and adjust from the trend. Weight change over time directly measures energy balance, which no equation can. Two weeks minimum, because water fluctuations of a kilogram can mask the signal over shorter periods.

Then the number moves. Part is mechanical — a lighter body costs less to maintain and move. But adaptive thermogenesis takes expenditure 10 to 15 percent below what the new weight predicts, largely through unconscious reductions in spontaneous movement. This is the plateau, and it is not an adherence failure. Recalculate every 5 to 10 kg, and keep deficits to 20 to 25 percent with adequate protein and resistance training, which preserves lean mass considerably better than a larger deficit.

Macronutrients: two floors and a remainder

Protein and carbohydrate provide 4 kcal per gram, fat 9, alcohol 7. Total calories determine whether you gain or lose; the split determines what you gain or lose, how full you feel, and how well you train.

Fixed percentage splits such as 40/30/30 are arbitrary, because protein requirements scale with body weight rather than calorie intake. A 60 kg person cutting on 1,600 kcal and a 100 kg person bulking on 3,500 do not need the same percentage.

Protein is best set per kilogram of body weight. 0.8 g/kg prevents deficiency in a sedentary adult and is a floor, not an optimum. 1.6 to 2.2 g/kg is where muscle protein synthesis is maximised in most studies for resistance-trained individuals. Up to 3.0 g/kg is worth considering in a substantial deficit, where higher protein preserves lean mass and increases satiety.

Fat has a hard floor of about 0.5 g/kg or 20 percent of calories, whichever is higher. It is required for hormone synthesis and fat-soluble vitamin absorption, and sustained intake below that is associated with reduced hormone levels, poor recovery, and menstrual disruption. Very low fat diets are a common and avoidable error in aggressive cuts.

Carbohydrate is the flexible remainder. It has no strict dietary requirement, since the body can produce glucose from other sources, but muscle glycogen fuels anything above moderate intensity and depleted glycogen shows up directly as reduced training capacity. Set protein from body weight, set fat at or above its floor, and assign the rest to carbohydrate. When that remainder gets very small, reducing the deficit is usually better than cutting fat below its floor.

Estimating strength without testing it

The Epley formula estimates one-rep max as weight times one plus reps over 30. So 225 pounds for 5 reps gives about 262.5. The competing Brzycki formula gives about 253 for the same input; below 10 reps the two agree closely and beyond that they diverge.

Accuracy is good in the 3 to 6 rep range, typically within 5 percent for a trained lifter. Outside it, accuracy degrades: a 12 or 20 rep set is limited by muscular endurance and cardiovascular capacity rather than maximal strength, and estimates can be 10 to 15 percent out.

The set also has to be genuinely close to failure. A set of five with three reps in reserve reflects a much higher true maximum than the calculation gives, which is the usual reason an estimate feels wrong.

The relationship also varies by exercise. Squats and deadlifts allow fewer reps at a given percentage because systemic demand accumulates, so high-rep estimates overstate. Bench press and isolation work hold up across a wider range. Individual variation is real and consistent — if your tested maximum sits reliably above or below the estimate, carry that offset forward as a personal correction.

The main use of the number is percentage-based programming: roughly 95 to 100 percent for 1 to 2 reps, 90 for 4, 85 for 6, 80 for 8, 75 for 10, 70 for 12. A true test is more accurate and costs recovery while carrying the highest injury risk in a training week, which is why most non-competitive lifters should estimate rather than test. Tracking a rolling estimate from your heaviest weekly sets gives a trend, and the trend is what tells you whether the programme is working — a fixed number from three months ago is a poor basis for today percentages.

Frequently asked questions

Calculators referenced in this guide