Percentage solutions: identify what the percentage measures

A 3.5% w/v solution has 3.5 g in every 100 mL of final solution. To calculate the amount for 240 mL, write 240 mL × 3.5 g/100 mL = 8.4 g. The denominator is final solution volume, not simply the volume of solvent poured into the vessel.

If the same 3.5% is w/w, a 240 g final preparation also contains 8.4 g of ingredient. The matching number in this example does not mean 240 g equals 240 mL. Without density or other stated information, do not swap the mass and volume bases.

Because 1 g is 1,000 mg, 1% w/v is 1,000 mg/100 mL = 10 mg/mL. Therefore 0.8% w/v is 8 mg/mL and 3.5% w/v is 35 mg/mL. This shortcut follows from the definition; it is not a rule for w/w or v/v concentrations.

For a hypothetical 0.8% w/v solution, 7.5 mL contains 60 mg. Check by converting to 8 mg/mL first, then multiplying by 7.5 mL. If you interpreted 0.8% as 0.8 mg/mL, your answer would be ten-fold too small.

To calculate a fictional 80 g batch of 2% w/w ointment from pure ingredient and a compatible base, the arithmetic requires 1.6 g ingredient and enough base to reach 80 g total. In this idealized mass-additive example, that is 78.4 g base. Adding 80 g of base would make the batch too large and reduce the intended percentage.

For liquid preparations, volume may not be additive. 'Make to 100 mL' means bring the final preparation to that volume, not necessarily add exactly 100 mL of solvent. A mathematical exercise does not establish solubility, compatibility, stability or an approved compounding procedure.

A question that clearly specifies w/v gives you the basis. If it leaves the basis unclear and the distinction changes the answer, identify the missing information rather than assuming all percentages mean grams per 100 mL. In practice, use the verified product label and preparation instructions.

The archived USP educational calculation proposal linked below describes these concentration conventions. It is not a current compounding standard or a claim that a preparation meets USP requirements. The original exercises here test concentration arithmetic and fit the calculation skills within NABP's broader foundational domain.

Try it before reading the answer

Write your setup, units and check first. These are original practice exercises, not recalled exam items.

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