Module 5 of 14 · 14 min
Compounding formulas
Compounding prescriptions and master formulas rarely match the quantity you need: you scale them, interpret 'aa' and 'qs ad', use commercial products as ingredients and decide whether an amount can even be weighed. These are core PEBC compounding questions.
🧠 QS = 'Quantity to Spare' — whatever is left over after everything else is weighed.
To enlarge or reduce a formula, find one multiplying factor (wanted ÷ formula total) and multiply EVERY ingredient by it. Proportions stay the same, so strengths stay the same.
Latin shorthand: 'aa' (ana) = of each, equal amounts; 'qs' = a sufficient quantity; 'qs ad 100 g' = add enough to make the TOTAL 100 g. A qs ingredient is never scaled directly — it is always 'total minus everything else'.
Parts formulas (1 : 3 : 16) are solved by adding the parts and taking each ingredient's share of the total. When a commercial product is an ingredient (a cream, a tablet), work out how much drug it contributes, then how much of the product supplies the drug you need.
Every balance has a minimum weighable quantity: $\text{MWQ} = \frac{\text{sensitivity requirement}}{\text{acceptable error}}$ (e.g. 6 mg ÷ 5% = 120 mg for a typical Class A/Class III prescription balance — check your reference's value). Below that, use an aliquot: weigh at least the MWQ, dilute with an inert powder, and weigh a portion (also ≥ MWQ) that contains the dose.
🧭 The method
- 1Total the formula and find the factor = wanted ÷ formula total.
- 2Multiply each active ingredient by the factor (or take its share of the parts).
- 3Calculate any 'qs ad' ingredient last: final total − sum of everything else.
- 4For 'aa', split the remaining quantity equally.
- 5Check each weighed amount is ≥ the MWQ; if not, plan an aliquot.
Before each reveal, predict the next step — then check.
A formula for 100 g: menthol 0.25 g, camphor 0.5 g, zinc oxide 10 g, hydrophilic petrolatum qs ad 100 g. Calculate the quantities for 240 g.
- 1
Find the multiplying factor.
$$\text{factor} = \frac{240\,\text{g}}{100\,\text{g}} = 2.4$$ Scale each active ingredient.
$$\text{menthol } 0.25\times 2.4 = 0.6\,\text{g};\quad\text{camphor } 0.5\times 2.4 = 1.2\,\text{g};\quad\text{ZnO } 10\times 2.4 = 24\,\text{g}$$The qs ad ingredient fills up to the total — calculate it last.
$$240 - (0.6 + 1.2 + 24) = 240 - 25.8 = 214.2\,\text{g petrolatum}$$Check every weighed quantity is above the MWQ (120 mg with a 6 mg balance at 5% error).
$$0.6\,\text{g} = 600\,\text{mg} \ge 120\,\text{mg}\ \checkmark$$
Same method — the last steps are yours. Work on paper, then reveal.
Rx: hydrocortisone powder 1%, clotrimazole 1% cream and zinc oxide paste aa qs ad 60 g. How much of each?
- 1
The percentage ingredient is calculated on the TOTAL weight.
$$60\,\text{g}\times 1\% = 0.6\,\text{g hydrocortisone}$$ - 2
Your turn
Now you: what weight is left for the two 'aa' ingredients?
Work it out on paper, then reveal.
$$60 - 0.6 = 59.4\,\text{g}$$ - 3
Your turn
Now you: 'aa' = equal amounts of each.
Work it out on paper, then reveal.
$$\frac{59.4\,\text{g}}{2} = 29.7\,\text{g each}$$
Type your number. Your first try decides when this module comes back for review.
A formula is coal tar 1 part, zinc oxide 3 parts, petrolatum 16 parts. How many grams of zinc oxide are needed for 300 g?
Total the parts, then take zinc oxide's share.
= 45 g
A formula for 5 L contains 120 g of drug. How many grams are needed to make 750 mL?
Same units on top and bottom of the factor: 5 L = 5000 mL.
= 18 g
You compound 150 mL of hydrochlorothiazide 2 mg/mL oral suspension from 25 mg tablets. How many tablets?
Total drug needed ÷ drug per tablet.
= 12 tablets
30 g of 2% ketoconazole cream is mixed with 15 g of 1% hydrocortisone cream and 5 g of plain base. What is the % w/w of ketoconazole in the final mixture?
Mixing in other products dilutes the ketoconazole: grams of drug ÷ new total weight.
= 1.2 %
A prescription balance has a sensitivity requirement of 6 mg. What is the minimum weighable quantity if the error must not exceed 4%?
MWQ = sensitivity ÷ acceptable error (as a decimal). Note the 4%, not the usual 5%.
= 150 mg
You need 8 mg of a drug. Your balance's MWQ is 120 mg (6 mg sensitivity, 5% error). You weigh 120 mg of drug and mix it with lactose to a total of 1800 mg. How many mg of the mixture contain 8 mg of drug?
The mixture is 120 mg drug per 1800 mg. Set up the proportion — and check the aliquot is itself ≥ the MWQ.
= 120 mg
⚠️ Tricky
Rx: drug A 2 g, drug B 5 g, cream base qs ad 60 g. Prepare 150 g. How many grams of cream base are needed?
Scale the drugs, then make the base up to the new total.
= 132.5 g
⚠️ The trap: Reading 'qs ad 60 g' as 'add 60 g of base' and scaling it gives 150 g of base (and a 167.5 g batch).
⚠️ Tricky
Rx: salicylic acid and precipitated sulfur aa 3%, hydrophilic ointment qs ad 90 g. How many grams of hydrophilic ointment are needed?
'aa 3%' means EACH ingredient is 3% of the total.
= 84.6 g
⚠️ The trap: Splitting 3% between the two ingredients (1.5% each) gives 87.3 g.
⚠️ Tricky
You compound 100 mL of ondansetron oral solution 0.8 mg/mL (expressed as ondansetron base) from ondansetron hydrochloride dihydrate powder. How many mg of the powder are needed? (MW base 293.4; MW hydrochloride dihydrate 365.9)
The strength is stated as BASE, but you weigh the salt hydrate.
= 99.77 mg
⚠️ The trap: Weighing 80 mg of the salt (as if it were base) gives a solution about 20% under strength.
⚠️ Tricky
You need at least 75 mL of a 3 mg/mL suspension, made from 20 mg tablets. Only whole tablets may be used, and you adjust the final volume to keep exactly 3 mg/mL. What final volume do you make?
Find the minimum number of WHOLE tablets that supplies the drug for 75 mL, then the volume those tablets make.
= 80 mL
⚠️ The trap: Rounding 11.25 down to 11 tablets gives only 73.33 mL — less than the 75 mL needed.
⚠️ Tricky
Prepare 30 capsules, each containing 0.75 mg of a potent drug, plus 2 extra capsules to allow for loss. Each capsule is filled to 200 mg with lactose. The drug is available only as a 1:10 trituration in lactose. How many mg of the trituration must be weighed?
The 200 mg fill weight is not needed. A 1:10 trituration contains 1 mg of drug in every 10 mg.
= 240 mg
⚠️ The trap: Weighing 24 mg of trituration (the amount of pure drug) gives a tenth of the dose in every capsule.
🕵️ Spot the mistake
A formula: drug A 2 g, drug B 3 g, cream base qs ad 50 g. Prepare 200 g.
A student wrote
⚠️ Traps examiners set
- Scaling a 'qs ad' ingredient directly instead of calculating it as total minus everything else.
- Using different units in the factor (litres over mL).
- Forgetting that adding other products to a cream lowers each drug's % w/w.
- Weighing less than the MWQ instead of using an aliquot (and forgetting the aliquot itself must be ≥ MWQ).
- Splitting 'aa' before subtracting the other ingredients from the total.
💬 Explain it in your own words
Why must the aliquot you finally weigh also be at least the minimum weighable quantity — what would go wrong if only the first weighing met it?