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· 12 min read
Every other pregnancy is dated from an estimate. After IVF, fertilisation is timed to the hour, so gestational age is arithmetic: 266 days from fertilisation, minus the embryo's age at transfer. Here is the derivation for day-3, day-5 and day-6 embryos, why frozen and fresh transfers use the same rule, why an early scan rarely moves an IVF date, and what the two-week offset on a scan report means.
· 13 min read
BMI reads muscular bodies as heavy and cannot see where fat sits at all — which is exactly why the waist measures exist. Here are the published waist and waist-to-height thresholds, a worked case where BMI and waist give opposite answers, an honest account of the contested mortality curves, and the 2025 shift toward defining obesity by adiposity and organ function rather than by a ratio.
· 11 min read
The 18.5 cut-off is a population screening line, not a diagnosis. Here is where it comes from, what the mortality data below it actually show, and the three things it cannot see: body composition, recent change — which is far more informative than the level — and the fact that the same line does not fit every age or every population.
· 3 min read
Blood pressure has two numbers: systolic and diastolic, measured in mmHg. Learn the ACC/AHA categories from normal to hypertensive crisis and what they mean.
· 12 min read
Milk production has a computable cost: volume times energy density divided by the efficiency of conversion. Do the sum and you get about 675 kcal a day, not the 500 that gets quoted. Here is the derivation, why the published increment is deliberately lower, how much the real spread is between mothers, what the water requirement actually rests on, and why cutting calories while feeding is a clinical question.
· 13 min read
The extra energy a pregnancy costs is far smaller than the phrase suggests, and it arrives on a schedule: near zero in the first trimester, modest in the second, real in the third. Here are the published increments from EFSA, FAO/WHO/UNU and the 2023 US reference intakes, what they look like as food, and why protein and folate rise proportionally faster than calories do.
· 3 min read
A normal resting heart rate for adults is usually 60 to 100 beats per minute. Learn what affects it, why athletes run lower, and when a reading may be concerning.
· 13 min read
Running costs roughly 0.73 kcal per pound per mile — one kilocalorie per kilogram per kilometre in the units the physiology is published in — and, this is the counterintuitive part, the figure barely moves with pace. Here is the derivation from the ACSM equation, the corrections that matter, and why grade changes it far more than speed.
· 3 min read
Blood alcohol content measures the concentration of alcohol in your blood. Learn how BAC is estimated with the Widmark formula and why legal limits differ by country.
· 12 min read
Ethanol carries 7 kcal per gram and the arithmetic is exact: volume × ABV × 0.789 × 7. A dry spirit is almost pure alcohol calories; a liqueur is nearly half sugar. Here is the derivation, the table, and the metabolic caveat stated without overclaiming.
· 13 min read
A generator solves a constrained arithmetic problem — hit an energy target, hit the macro splits, stay inside a food list — and it does that well. Here is the arithmetic that makes a plan work, and the honest list of what no generator can see.
· 14 min read
There is a small hard answer — the brain's glucose demand, published as 130 g a day — and a very large soft one. Above the minimum, carbohydrate need scales with training volume in grams per kilogram, not with a percentage.
· 16 min read
Alcohol leaves the body at a roughly constant mass per hour, whatever the concentration. That one property — zero-order elimination, unlike caffeine's exponential decay — explains why doubling the dose doubles the time, why nothing speeds it up, and why every estimate carries a wide error bar. With the Widmark relation worked through, and each market's legal limit stated separately.
· 13 min read
Sleep is regulated by two processes: a pressure that builds with every waking hour, and a clock. Caffeine acts on neither directly — it blocks the receptors that report the pressure. The pressure keeps building behind the block, which is why the crash arrives and why an afternoon dose costs that night's sleep even when you do not feel it.
· 14 min read
The WHO infant standard is prescriptive: it was built from healthy breastfed babies and describes how infants should grow. National references describe how they did grow. In the first year the two disagree by enough to move the same baby forty percentile points, with no change in the baby. Here is the size of the gap, and what the published thresholds for concern actually say.
· 12 min read
A percentile is a rank against a reference population, so the first question is never the arithmetic — it is which population, measured when. The same 5'11" man is the 38th percentile in one national dataset and the 86th in another, and the 91st against a reference of people born a century ago. Here is why, and what a z-score adds.
· 14 min read
Average the parents' heights, shift by a sex constant, and you have a target height. The honest part is what comes next: the published prediction interval is about ±4 inches, wide enough to cover most of the adult population. Here is the formula, the interval, why bone age does better, and why children keep out-growing the target.
· 12 min read
Frame size exists because height alone does not fix skeletal mass, and the published methods are crude proxies with real cut-offs. The bigger story is the ideal-weight formulas: four of them, all built for drug dosing rather than health, disagreeing by up to 27 lb at the same height.
· 10 min read
The correction factor says how far one unit of insulin moves glucose, and the classical estimate is 1800 divided by the total daily dose in mg/dL — or 100 divided by it in mmol/L. Those are the same rule, and here is the arithmetic that proves it, plus why stacking is the error that actually hurts.
· 10 min read
High blood glucose pulls water out of cells and dilutes the sodium in it, so a measured sodium in a hyperglycaemic patient reads lower than the real one. Here is the correction, both of the published factors, a case where they disagree by 4 mmol/L, and the different problem that lipids cause.
· 10 min read
The ratio says how many grams of carbohydrate one unit of insulin covers, and the usual starting estimate is 500 divided by the total daily dose. Here is where that number comes from, how sharply it moves across daily doses, why a 450 version exists, and the three things it quietly assumes.
· 13 min read
Milligrams per kilogram is one multiplication, and that is exactly why it fails: the documented errors are unit slips, misplaced decimal points and the wrong body weight, not hard maths. Here is the arithmetic done properly, the three body weights that give three different answers, and what body surface area changes.
· 2 min read
A pack-year sums up a smoking history in one number. Here is how it is calculated and why doctors use it to judge risk and screening.
· 2 min read
Body surface area estimates your body's external area in square metres. Here is how it is calculated and why clinicians use it to dose medicines.