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Desired ÷ Have × Quantity
Identify Desired, Have and Quantity, match the dose units, then calculate the amount to give.
MedMaths Learn pathway
Calculation Methods
Learn three valid ways to organise dosage-calculation arithmetic, then compare them on the same problem.
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Desired ÷ Have × Quantity
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Work through Calculation Methods
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Ratio & Proportion
Set equivalent medication ratios, keep like quantities aligned, cross-multiply and solve the unknown.
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Dimensional Analysis
Use target units and conversion factors so unwanted units cancel and the required unit remains.
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Choosing a Calculation Method
Solve the same relationship three ways and understand why valid methods should produce the same answer.
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Lesson summaries
What each Calculation Methods lesson teaches
A short recap of every lesson in this topic: the key idea, a worked example and the mistake students make most often. Open any lesson for the full step-by-step teaching and its four levels of practice.
Desired ÷ Have × QuantityDesired ÷ Have × Quantity turns an ordered dose and an available strength into the amount to give. Desired and Have must use compatible dose units; Quantity is the amount that contains the Have.
Desired ÷ Have × Quantity turns an ordered dose and an available strength into the amount to give. Desired and Have must use compatible dose units; Quantity is the amount that contains the Have.
Formula
Desired ÷ Have × Quantity = amount to give
Convert Desired and Have to matching dose units before dividing.
Worked example
Order 500 mg; available 250 mg in 5 mL.
- 1Desired = 500 mg.
- 2Have = 250 mg.
- 3Quantity = 5 mL.
- 4500 ÷ 250 × 5 = 10.
10 mL
Common mistake
Swapping Desired and Have, or treating the available volume as Have rather than Quantity.
Desired comes from the order; Have and Quantity stay paired as the available strength.
Ratio & ProportionRatio and proportion writes the available dose-to-quantity relationship and the ordered dose-to-unknown relationship in the same orientation, then solves the unknown.
Ratio and proportion writes the available dose-to-quantity relationship and the ordered dose-to-unknown relationship in the same orientation, then solves the unknown.
Formula
available dose / available quantity = ordered dose / x quantity
Worked example
Order 500 mg; available 250 mg in 5 mL.
- 1250/5 = 500/x.
- 2250x = 2500.
- 3x = 10.
10 mL
Common mistake
Reversing only one side of the proportion so dose no longer lines up with dose and quantity with quantity.
Keep like quantities in the same position before you cross-multiply.
Dimensional AnalysisDimensional analysis keeps units inside the calculation. Equivalent factors are oriented so unwanted units cancel and the target unit remains.
Dimensional analysis keeps units inside the calculation. Equivalent factors are oriented so unwanted units cancel and the target unit remains.
Formula
starting quantity × conversion factor(s) = target quantity
Worked example
Order 500 mg; available 250 mg in 5 mL.
- 1Start with 500 mg.
- 2Multiply by 5 mL / 250 mg.
- 3mg cancels, leaving mL.
- 4500 × 5 ÷ 250 = 10.
10 mL
Common mistake
Flipping a factor so the unwanted unit multiplies instead of cancelling.
Decide the target unit first, then make every unwanted unit cancel on purpose.
Choosing a Calculation MethodD/H × Q, ratio/proportion and dimensional analysis are different ways to organise the same supplied medication relationship. A valid setup using the same inputs should converge on the same mathematical result.
D/H × Q, ratio/proportion and dimensional analysis are different ways to organise the same supplied medication relationship. A valid setup using the same inputs should converge on the same mathematical result.
Worked example
Order 500 mg; available 250 mg in 5 mL.
- 1D/H × Q = 10 mL.
- 2Ratio/proportion = 10 mL.
- 3Dimensional analysis = 10 mL.
All three valid setups produce 10 mL.
Common mistake
Choosing a method to force a preferred answer. The method changes the layout, not the supplied relationship.
Use the method your course requires where specified; otherwise use a valid method you can apply accurately and check.