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Hong KongPharmacy calculations
Nearly every PTCE calculation reduces to dimensional analysis: write what you have, multiply by conversion factors arranged so the unwanted units cancel, and read off what remains.
Candidates treat these as seven separate skills. They are one skill applied seven ways.
The one method
Dimensional analysis. Write the quantity you were given, multiply by conversion factors set up so unwanted units cancel diagonally, and whatever units survive are your answer.
It is slower to learn than memorizing formulas and far faster to use, because you never have to remember which formula applies.
A worked example
A child weighs 44 pounds. The dose is 15 mg per kg per day. The suspension is 250 mg per 5 mL. How many mL per day?
- Convert the weight: 44 pounds divided by 2.2 gives 20 kg
- Find the dose: 20 kg times 15 mg per kg gives 300 mg per day
- Convert to volume: 300 mg divided by 250 mg, times 5 mL, gives 6 mL per day
Three steps, each one a unit conversion, and no formula was recalled. That is the method.
The single largest source of calculation errors is a right number with the wrong unit. Carrying the units through the working catches it before you pick an option, and the distractors on these questions are almost always the answer you get by dropping or inverting one conversion.
The conversions to know cold
| From | To |
|---|---|
| 1 teaspoon | 5 mL |
| 1 tablespoon | 15 mL |
| 1 fluid ounce | 30 mL |
| 1 pound | 454 g |
| 1 kg | 2.2 pounds |
| 1 inch | 2.54 cm |
| 1 g | 1000 mg |
| 1 mg | 1000 mcg |
| 1 L | 1000 mL |
These are not worth deriving under time pressure. They are worth knowing the way you know a phone number.
Percentage strength
On a liquid this means grams per 100 mL. A 5 percent solution is 5 g in 100 mL, which is 50 mg per mL.
That single conversion unlocks most dilution and concentration questions.
Estimate before you calculate
Glance at the options first. If three are within a factor of ten of each other and one is wildly out, you have learned something about the scale of the answer before doing any work.
It also catches the decimal-place error, which is the mistake that turns a correct method into a wrong answer.
Common questions
What method should I use for PTCE calculations?
Dimensional analysis - multiply by conversion factors arranged so unwanted units cancel.
Why not memorize formulas?
Dimensional analysis removes the need to remember which formula applies, which is where errors start.
What does a 5 percent solution mean?
5 g in 100 mL, which is 50 mg per mL.
What causes most calculation errors?
A right number with the wrong unit. Writing units at every step catches it.
Should I estimate first?
Yes. Glancing at the options tells you the scale and catches decimal-place errors.