In dosage calculation, the units are the problem.

Why dosage math is its own skill

The arithmetic is easy. What makes it hard is that every quantity carries a unit, the units have to cancel correctly, and a plausible-looking answer in the wrong unit is exactly the kind of error that passes a glance. Programmes typically demand 90% or higher on dosage exams for the obvious reason, and many allow limited attempts.

So the failure mode worth training against isn't "can't do the maths". It's a setup that looked right.

Dimensional analysis, and why it is worth the extra line

Three methods get taught — ratio-proportion, the formula method (desired / have × volume), and dimensional analysis. They give the same answer. Dimensional analysis is slower to write and far harder to get silently wrong, because the units themselves tell you whether the setup is valid before you compute anything.

Write every quantity as a fraction with its units, arrange so that unwanted units cancel, and confirm the only unit left standing is the one the question asked for. If milligrams survive to the end of a question asking for millilitres, the setup is wrong — and you know that before you reach for the calculator.

The habit worth building: cancel units first, compute second. If you compute first, a wrong setup produces a confident number and nothing warns you.

Where the marks actually go

• Unit conversion missed or applied twice — g to mg, mcg to mg, L to mL, lb to kg. The single largest category.
• Weight-based dosing in pounds when the order is per kilogram. A 2.2× error is big enough to be dangerous and small enough to look plausible.
• Rate versus volume confusion — mL/hr against total mL, or drops per minute against mL/hr without the drop factor.
• Rounding at the wrong moment. Round once, at the end, to the precision the question specifies. Rounding mid-calculation compounds.
• Answer form. Tablets to the nearest half, drops to whole numbers, mL/hr per your programme's rule. Correct value, wrong form, no mark.
• Ignoring the clinical sanity check. 14 tablets is not an answer. Neither is 0.02 mL. If the number would be absurd at a bedside, the arithmetic is wrong.

How to practise so it sticks

1. Work the problem fully on paper, units written on every line. No mental shortcuts — the shortcut is where the unit gets dropped.
2. Check the units cancel before you evaluate anything.
3. Sanity-check the magnitude against something real: a plausible tablet count, a realistic infusion rate.
4. Then verify the working — photograph it and get the first invalid line named. Knowing "wrong" teaches nothing; knowing "the mcg-to-mg conversion on line two went the wrong way" fixes the category.
5. Log the category, not the question. Your misses will cluster. The cluster is your study plan.

Question types worth drilling separately

Type	The usual trap
Tablet / capsule	Strength per tablet vs total dose ordered
Liquid oral	Concentration expressed per 5 mL rather than per mL
Weight-based	Pounds not converted to kilograms; per-dose vs per-day
IV flow rate (mL/hr)	Total volume over total time, with time in the wrong unit
Drip rate (gtt/min)	Drop factor omitted, or minutes and hours mixed
Reconstitution	Final concentration after diluent, not the powder strength
Safe dose range	Checking the total daily dose against per-dose limits

Being straight with you

This is a practice and verification tool. It is not a clinical decision aid, it is not validated for use at a bedside, and nothing it outputs should be used to prepare or administer a medication. Check every real order against your own institution's references and policy. Its job is to tell you where your homework went wrong, in time for that to matter in an exam rather than in a ward.

Related: checking answers without an answer key covers the substitution and estimation habits that generalise beyond dosage, and the math checker explains the step-level check in more detail.