Unit-safe clinical arithmetic

Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. Every scenario and drug is invented; reference figures are orientation only, not settings, doses or targets.

Companion to the units sections of chapter 10 (kidneys, gut and hormones) and appendix C (reference figures and units) of Human Biology for the Medical Maker, with material from chapter 1, chapter 2 (chemistry), chapter 12 (lifespan), chapter 17 (therapy) and chapter 20 (health software).

The tool behaves the way the book says clinical software should (ch01, ch10, ch20):

A value without a unit is refused. Type 7.0 mmol/L, not 7.0 — the chips under each field add the unit. The tool never guesses a unit from the size of a number.
Ambiguous notation is refused. .5 (write 0.5), 5. and 1,5 are rejected rather than interpreted.
Out-of-bounds input is rejected, not clamped. Each field has a plausibility bound — a data-entry sanity check chosen for this tool, not a clinical range — and a value outside it is refused with the bound shown.
Every result is read back with its unit, and the arithmetic is shown step by step.

How to use it

Analytes — glucose (mmol/L × 18 = mg/dL), creatinine (mg/dL × 88.4 = µmol/L), BUN to urea (BUN mg/dL × 0.357 = urea mmol/L — two different things counted differently), HbA1c (IFCC mmol/mol = (DCCT % − 2.15) × 10.929, an offset rather than a ratio), and any substance from its molar mass (mmol/L = mg/dL × 10 ÷ M). Below each read-back the tool shows what the same number would mean in the other unit, and whether a range check would even notice.
Concentration — % w/v → g/L → mmol/L → theoretical mOsm/L for common solutes or any molar mass and particle count (0.9 % NaCl is 154 mmol/L and about 308 mOsm/L; 5 % glucose is about 278 mmol/L). Also the mass needed to make up a solution and a v/v dilution, both from the book’s exercises.
Pressure — mmHg, kPa, cmH₂O, N/cm², Pa, psi and bar, with the book’s anchors (120 mmHg ≈ 16 kPa; 1 N/cm² = 10 kPa ≈ 75 mmHg).
Clearance — C = U × V ÷ P for creatinine, with concentrations in mmol/L, µmol/L or mg/dL and flow in mL/min, mL/h or L/day, each converted explicitly. Beside it, a "unit-blind program" multiplies the bare numbers as typed. The book’s exercise cases are buttons: (a) 8 mmol/L, 1.5 mL/min, 0.09 mmol/L ≈ 133 mL/min; (b) plasma 0.3 mmol/L → 40 mL/min; (c) the plasma value 90 µmol/L typed where mmol/L was expected → ≈ 0.13 mL/min in the unit-blind program, 1000× too low — and rejected here as implausible.
Infusion drill — not a calculator: you cannot enter your own drug, dose or weight. Pick an invented scenario (or generate one), work out the pump rate in mL/h and type it with its unit. The working shows the book’s four-step chain (µg/kg/min × kg → µg/min → µg/h; mg ÷ mL → µg/mL; µg/h ÷ µg/mL → mL/h). Buttons inject the 10×, 60× and 1000× errors and highlight the step where each enters; a wrong answer that matches one of them is named.
Insulin strength — the same invented volume holds 1, 2, 3 or 5 times as many units at U-100, U-200, U-300 and U-500, and a syringe printed in "units" is really printed in hundredths of a millilitre. Volume is not dose unless the concentration is known.
Body size — Mosteller BSA = √(height cm × weight kg ÷ 3600) for the book’s adult (170 cm, 70 kg ≈ 1.82 m²), ten-year-old (140 cm, 32 kg) and newborn (50 cm, 3.5 kg ≈ 0.22 m²), plus your own; BSA per kilogram plotted against weight; and an invented quantity scaled per kg and per m² to show how far the two normalisations diverge (about 2.4× for the newborn). Newborn blood volume is given as the book’s range, 80–90 mL/kg (about 280–315 mL at 3.5 kg), with the share a sample takes.

Links: Share link copies a URL with every tab’s inputs; each tab has its own address — for example clinical-units/#clearance (or #analytes, #concentration, #pressure, #infusion, #insulin, #body).

Limits

Educational arithmetic only. Calculating or checking doses for real patients belongs to clinicians and pharmacists with their own checks; software that calculates or recommends a dose is a regulated medical device (ch10:679-689, ch17:1183-1185).
Plausibility bounds are this tool’s own data-entry sanity checks — glucose 0.5–50 mmol/L is the book’s example (ch20:661); the others (creatinine 5–5000 µmol/L, urea 0.2–100 mmol/L, HbA1c 3–20 %, clearance inputs, body 25–250 cm and 0.3–350 kg) are deliberately wide. They are not reference ranges and say nothing about what is typical for anybody.
The glucose factor is the book’s rounded 18 (molar mass 180.16 g/mol gives 18.016). Osmolarity is theoretical (ideal dissociation); measured osmolality is lower. 5 % glucose uses anhydrous dextrose, as the book does — a label that means dextrose monohydrate gives about 252 mmol/L.
Creatinine clearance only approximates GFR. Mosteller is one BSA formula among several; "per kilogram" and "per m²" are modelling choices.
Sources: the book (chapter and line references are shown beside each figure); exact pressure definitions (1 mmHg = 133.322 Pa, 1 cmH₂O = 98.0665 Pa) from the SI brochure / NIST SP 811.

Related: half-lives, decay and steady state (the pharmacokinetics behind the infusion drill), solutions and lab maths (molarity, dilutions and buffers), unit converter (dimensional analysis for everything else), isotope patterns and exact mass.