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Adding & Subtracting Clinical Quantities
Total several supplied quantities, line up decimals, and subtract one total from another while keeping track of what a negative result means.
MedMaths Learn pathway
Clinical Maths Foundations
Refresh the maths that medication calculations are built on, using the quantities you actually meet on a shift. Already confident with totals, scaling, rates and percentages? Skip straight to Medication Maths Essentials.
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Adding & Subtracting Clinical Quantities
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Work through Clinical Maths Foundations
Follow the order below for a structured pathway, or open any lesson when you need that skill.
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Multiplying & Scaling
Use multiplication for “for each” relationships such as an amount for every kilogram, or a rate held for a number of hours.
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Dividing & Finding the Rate
Share a quantity across a time or a volume to produce a rate or a concentration, and sense-check the size of the result.
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Percentages in Medication Maths
Read a percentage as an amount per 100, move between percentage, decimal and fraction, and keep the concentration bases distinct.
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Working Through Multi-Step Calculations
Decide what has to be worked out first, keep intermediate values intact, and carry units from one stage to the next.
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Lesson summaries
What each Clinical Maths Foundations lesson teaches
A short recap of every lesson in this stage: the key idea, a worked example built from clinical quantities, and the mistake students make most often. Open any lesson for the full step-by-step teaching.
Adding & Subtracting Clinical QuantitiesAdding combines quantities of the same kind into one total; subtracting compares two totals and produces a difference. A fluid balance is exactly that comparison — one total taken away from another — and whether the answer comes out positive or negative records which of the two was larger.
Adding combines quantities of the same kind into one total; subtracting compares two totals and produces a difference. A fluid balance is exactly that comparison — one total taken away from another — and whether the answer comes out positive or negative records which of the two was larger.
Formula
total intake − total output = fluid balance
The order decides the sign. Reversing it gives the same size of answer with the opposite sign.
Worked example
Over one shift a patient receives 250 mL of IV fluid, drinks 300 mL, and receives a further 500 mL. Recorded output for the same period is 900 mL.
- 1Group what belongs together: all three volumes went in.
- 2Total intake: 250 + 300 = 550, and 550 + 500 = 1050 mL.
- 3Output total: 900 mL.
- 4Balance: 1050 − 900 = +150 mL.
A balance of +150 mL — positive, so the intake total was the larger one.
Common mistake
Subtracting the output from each intake volume in turn, which removes it several times over. The output is taken away once, from the finished intake total.
Build both totals first, subtract in the order the question asks for, and treat the sign as part of the answer.
Multiplying & ScalingA value written with a slash is a rate, not a total: 6 mg/kg means 6 mg for each kilogram. It only becomes a dose once it is multiplied by how many of that unit there are. The same move turns a pump rate held for a number of hours into a delivered volume, so weight scaling and rate-and-time scaling are one operation rather than two formulas.
A value written with a slash is a rate, not a total: 6 mg/kg means 6 mg for each kilogram. It only becomes a dose once it is multiplied by how many of that unit there are. The same move turns a pump rate held for a number of hours into a delivered volume, so weight scaling and rate-and-time scaling are one operation rather than two formulas.
Formula
amount per unit × number of units = total
mg/kg × kg leaves mg. mL/hr × hr leaves mL. The matching units cancel.
Worked example
A supplied order is 6 mg/kg for a patient who weighs 45 kg.
- 1Read the slash as “for each”: 6 mg is used for every 1 kg.
- 2Count the units: there are 45 kilograms.
- 36 × 45 = 270.
- 4Units: mg/kg × kg leaves mg.
The calculation gives a dose of 270 mg.
Common mistake
Dividing instead of multiplying, which makes the calculated dose fall as the weight rises. At the same supplied mg/kg figure the dose scales up in direct proportion to weight, so a smaller answer for more kilograms is the signal.
Read the slash as “for each”, multiply by how many there are, and let the cancelling units name the answer.
Dividing & Finding the RateDivision shares one total across something else. Share a volume across hours and the answer is a rate; share an amount of medicine across a volume and the answer is a concentration. Both results describe what belongs to a single unit of whatever you divided by, and the unit asked for tells you which value goes on top.
Division shares one total across something else. Share a volume across hours and the answer is a rate; share an amount of medicine across a volume and the answer is a concentration. Both results describe what belongs to a single unit of whatever you divided by, and the unit asked for tells you which value goes on top.
Formula
volume ÷ time = rate in mL/hr · amount ÷ volume = concentration in mg/mL
Whatever appears before the slash in the answer unit is the value being shared out.
Worked example
1000 mL is to be given over 6 hours, and a vial is labelled 500 mg in 10 mL.
- 1Rate: mL/hr means volume divided by time, so 1000 ÷ 6 = 166.666…
- 2Round only at the end: 166.7 mL/hr.
- 3Concentration: mg/mL means amount divided by volume, so 500 ÷ 10 = 50.
- 4Every 1 mL therefore contains 50 mg.
166.7 mL/hr, and a concentration of 50 mg/mL.
Common mistake
Inverting the division — dividing 4 by 500 rather than 500 by 4. Estimating the answer first catches it instantly, because the result comes out impossibly small.
Read the answer unit to set up the division, keep recurring decimals whole, and check the result is a believable size.
Working Through Multi-Step CalculationsA longer calculation is several short ones in the right order, not a harder sum. Name the final quantity and its unit, work backwards to find what has to exist before it, then calculate forwards — writing each intermediate value down with its unit so a mistake can be found at the step where it happened.
A longer calculation is several short ones in the right order, not a harder sum. Name the final quantity and its unit, work backwards to find what has to exist before it, then calculate forwards — writing each intermediate value down with its unit so a mistake can be found at the step where it happened.
Worked example
A supplied order is 8 mg/kg for a patient who weighs 35 kg. The available liquid is labelled 140 mg in 5 mL. What volume does the calculation give?
- 1Destination: a volume in mL.
- 2Working backwards, a volume needs a dose and a concentration — the dose is the missing one.
- 3Step 1 — dose: 8 × 35 = 280 mg.
- 4Step 2 — concentration: 140 ÷ 5 = 28 mg/mL.
- 5Step 3 — volume: 280 ÷ 28 = 10 mL.
10 mL, with every intermediate value still visible and labelled.
Common mistake
Rounding an intermediate value and carrying it forward. Using 3.3 in place of 3.333… shifts the final answer, and the error is invisible once the working has been collapsed into one expression.
Plan backwards from the answer, calculate forwards, label every intermediate value, and round at the final step.
Percentages in Medication MathsA percentage is a fraction with 100 underneath, so 25% is 25/100 and 0.25. On a medication label the same idea becomes a concentration, and the letters printed after the percentage say what the 100 refers to — grams per 100 mL, millilitres per 100 mL, or grams per 100 g. Reading those letters is what stops a percentage being misread.
A percentage is a fraction with 100 underneath, so 25% is 25/100 and 0.25. On a medication label the same idea becomes a concentration, and the letters printed after the percentage say what the 100 refers to — grams per 100 mL, millilitres per 100 mL, or grams per 100 g. Reading those letters is what stops a percentage being misread.
Formula
1% w/v = 1 g in 100 mL = 10 mg/mL
For any w/v percentage, mg/mL = percentage × 10, because the conversion is always × 1000 then ÷ 100.
Worked example
A preparation is labelled 2% w/v. What is that concentration in mg/mL?
- 1Read the basis: w/v means grams per 100 mL.
- 2Write it out: 2% w/v = 2 g in 100 mL.
- 3Convert: 2 g = 2000 mg.
- 4Divide: 2000 ÷ 100 = 20 mg/mL.
20 mg/mL — and the shortcut agrees: 2 × 10 = 20.
Common mistake
Reading the percentage straight across as mg/mL, so 1% w/v becomes 1 mg/mL instead of 10 mg/mL. The gram-to-milligram step is the one that gets skipped, and it costs a factor of ten.
Read the basis before the number, write the strength out as an amount per 100, and never assume w/v when the label has not said so.