Weight-Based Dosing, and Where the Arithmetic Goes Wrong

One multiplication, and that is the whole problem

A weight-based dose is a dose rate times a weight. If the rate is 5 mg/kg and the patient weighs 70 kg, the dose is 350 mg. There is nothing to understand. This is why the failure mode is so peculiar: nobody gets weight-based dosing wrong because the maths defeated them. The published error taxonomies — the ISMP list of error-prone dose designations, the WHO Medication Without Harm programme, the European Medicines Agency's medication-error guidance — describe a completely different set of causes. A microgram written where a milligram was meant. A decimal point that moved, or that was never seen. A weight in pounds pushed into a formula expecting kilograms. A weight that was three weeks old, or the mother's, or an estimate nobody wrote down.

The pound-to-kilogram slip is worth pricing, because it is arithmetically invisible. One kilogram is 2.20462 pounds. A patient who weighs 265 pounds and whose weight is entered as 265 kilograms is dosed 2.205 times over: at a hypothetical 5 mg/kg that is 1 325 mg instead of 601 mg. Nothing in the calculation objects. The multiplication is right, the units on the page look right, and the only signal that anything is wrong is that a human being noticed the number was too big. That is why so much of medication safety is about making numbers hard to misread rather than about making them easier to compute.

Which weight? Total, ideal, or adjusted

Here is the divergence that produces no error message at all. Devine's 1974 equation, written for men, is ideal body weight = 50 kg + 2.3 kg for every inch of height over 60 inches; the companion form for women starts at 45.5 kg with the same slope. Note that it is defined in inches, so a metric height has to be converted first — 178 cm is 70.08 inches, which gives 50 + 2.3 × 10.08 = 73.2 kg. Adjusted body weight then takes the ideal and adds a fraction of the excess, conventionally 40%: adjusted = IBW + 0.4 × (total − IBW). For our 120 kg patient that is 73.2 + 0.4 × 46.8 = 91.9 kg.

Multiply all three by the same hypothetical 5 mg/kg and you get 600 mg, 366 mg and 460 mg. The largest is 64% bigger than the smallest — 234 mg of difference on a single decision that is almost never written down anywhere. Adjusted weight sits 26% above ideal and 31% below total, so it is not a compromise so much as a third answer. And the reason the three exist is genuinely pharmacological, not administrative: a drug that stays in body water and lean tissue will be over-dosed if you count fat, while a lipophilic drug that partitions into fat will be under-dosed if you ignore it. The 0.4 in the adjusted formula is an empirical guess at how much of the extra tissue a particular drug actually reaches.

None of that tells you which weight to use for any given medicine. That answer is published, per drug, in the summary of product characteristics or the label, and it is the prescriber's and the pharmacist's to apply. The point of showing the spread is not to help you pick. It is to show that a calculator which asks only for a weight is answering a narrower question than the one you are actually facing, and that the number it returns is only as good as the weight you fed it.

Body surface area and the Mosteller formula

Some drug classes — cytotoxic chemotherapy above all — are dosed per square metre of body surface area rather than per kilogram, on the historical reasoning that surface area tracks metabolic rate and organ blood flow better than mass does. Body surface area cannot be measured directly on a living person, so it is estimated. Mosteller published the simplest usable estimate in a 1987 letter to the New England Journal of Medicine: BSA in m² = the square root of (height in cm × weight in kg ÷ 3600). Its entire virtue was that it fitted on a pocket calculator, and it has outlived far more elaborate equations for exactly that reason.

Work it for our patient: 178 × 120 = 21 360; divided by 3600 that is 5.933; the square root is 2.436, so 2.44 m². Mosteller also gave an imperial form, the square root of (height in inches × weight in pounds ÷ 3131). For 70 inches and 265 pounds: 70 × 265 = 18 550, divided by 3131 is 5.925, square root 2.434. The two constants, 3600 and 3131, are not two formulas — they are the same formula carrying the inch-to-centimetre and pound-to-kilogram conversions inside the divisor, which is why the two routes agree to within 0.002 m².

The consequence worth knowing is that per-square-metre and per-kilogram dosing are not interchangeable, because surface area rises more slowly than weight. Our 120 kg patient has 2.44 m²; a 70 kg adult of 170 cm has 1.82 m². The heavier patient weighs 71% more but has only 34% more surface. Convert a hypothetical 100 mg/m² into mg/kg and the first patient gets 2.03 mg/kg while the second gets 2.60 mg/kg — from the same prescription. Any calculator, this site's included, that lets you toggle between the two denominators is offering you a choice you should not be making unaided.

The tenfold error, and why zeros are written the way they are

Two of the oldest rules in prescribing look like typographical fussiness and are not. The first: always write a leading zero before a decimal point. A dose written as .5 mg loses its point on a fax, a photocopy or a bad handwriting day and becomes 5 mg — a tenfold overdose. Written 0.5 mg, the surviving zero tells the reader that a fraction was intended even if the point vanishes. The second rule is the mirror image: never write a trailing zero. A dose written 5.0 mg becomes 50 mg the moment the point is missed, so it is written 5 mg. Both rules appear on the ISMP list of error-prone dose designations, and both exist because the same physical failure — a decimal point that does not survive reproduction — has killed people in both directions.

The same logic drives the ban on abbreviating microgram. Written with the Greek mu, it is one bad photocopy away from mg, and the prefix jump from micro to milli is a factor of a thousand rather than ten. Safety agencies therefore ask for the word to be spelled out. It is worth noticing what all these rules have in common: none of them makes the arithmetic more accurate. They make the inputs harder to misread. That is the honest summary of where weight-based dosing fails — not in the multiplication, but in the reading of what is being multiplied.

Children are not scaled-down adults

The most persistent misconception in dosing is that a child's dose can be obtained by scaling an adult's down in proportion to weight. It cannot, and the geometry alone shows why. Take a 5-year-old of 110 cm and 18 kg against a 175 cm, 70 kg adult. By weight the child is 25.7% of the adult. By Mosteller surface area — 0.742 m² against 1.845 m² — the child is 40.2%. The ratio between those two fractions is 1.56, so scaling by surface area gives that child roughly 1.6 times the dose per kilogram that a proportional weight scaling would.

The mismatch widens as children get smaller. A one-year-old of 75 cm and 10 kg is 14.3% of the adult by weight but 24.7% by surface area — a ratio of 1.73. By fifteen years and 60 kg, the ratio has fallen to 1.06 and the two scalings have almost converged. And surface area is only the geometric part of the story. Organ maturity is the rest: renal clearance, hepatic enzyme activity, protein binding and body water fraction all change through infancy and childhood on their own timetables, which is why paediatric dose ranges are published as their own body of evidence rather than derived from adult ones. The BNF for Children exists precisely because that derivation is not possible.

What this article is not

Everything above is arithmetic. Not one line of it tells you what dose anything should be given at, and that is deliberate: no medicine is named here and no medicine's dose appears here. Dose rates are set per drug by regulators and manufacturers from trial data, published in the label or summary of product characteristics, and applied by a prescriber who knows the patient's renal function, liver function, age, other medicines and clinical state. A pharmacist then checks the whole chain independently. That double check is not bureaucracy — it is the control that catches the decimal point.

The useful thing a calculator can do here is narrow: show you the same weight expressed three ways, so that a number which looked obvious stops looking obvious. If you are a patient or a carer and a dose does not match what you were told, or the units on the box differ from the units on the prescription, the correct move is not to recompute it. It is to stop and ask the pharmacist. They will check it in under a minute, and that is exactly the job.

Frequently asked questions

Which body weight should I use for a dose?

That is not a question this article, or any calculator, can answer for you — it is set per medicine in its label and applied by the prescriber and pharmacist. What the article can tell you is that the choice matters enormously: for one 178 cm, 120 kg patient, total, ideal and adjusted body weights give doses 64% apart at the same rate. If you are looking at a dose and are unsure which weight it was based on, ask the pharmacist, who can see the prescription.

Why does the ideal body weight formula use inches?

Because Devine wrote it in 1974 in the United States, for a clinical population measured in feet and inches. The formula has never been re-derived in metric, so every metric implementation converts the height to inches first and inherits whatever rounding that conversion introduces. It is small — 178 cm is 70.08 inches, so using a flat 70 inches costs about 0.2 kg of ideal body weight — but it is one more place where two calculators can disagree slightly on the same patient without either being wrong.

Is body surface area more accurate than weight?

It is not more accurate, it is a different quantity, chosen for drug classes where the historical evidence tied dose to metabolic scaling rather than mass. Mosteller's estimate itself is a fit, not a measurement, and it has been criticised as a poor proxy in obesity because it treats a heavy patient and a tall one the same way. The practical consequence is that per-square-metre and per-kilogram dosing give systematically different answers in the same person, so the two must never be swapped for convenience.

Can I check my child's dose with a calculator?

You can check that the arithmetic in front of you is internally consistent — that a stated rate times a stated weight gives the stated dose. You cannot check whether the rate is right, because paediatric rates are published per medicine and per age band and are not derived from adult doses. If something looks wrong, the right move is a phone call to the pharmacy or the prescribing team, not a recalculation. They would far rather answer a question than manage a tenfold error.

Why is 5.0 mg considered a dangerous way to write 5 mg?

Because the decimal point is the smallest mark on the page and the first thing lost to a fax, a photocopy, a smudge or a scanner. Drop it from 5.0 mg and you have 50 mg. The ISMP list of error-prone dose designations therefore asks for whole numbers to be written bare — 5 mg — and for fractions to carry a leading zero, 0.5 mg, so that if the point disappears the surviving zero still signals that a fraction was meant. Two opposite typographic rules, one shared cause.