Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
Dosage calculations
Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg
Method
Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
Estimate first and check that the answer is reasonable.
IV infusion rates
Pump rate
mL/h = volume (mL)/time (h)
Drip rate
drops/min = volume (mL) × drop factor / time (min)
Infusion time
time (h) = volume (mL)/rate (mL/h)
Method
Pump rate in mL/h: volume divided by time in hours.
Drip rate in drops/min: volume × drop factor divided by time in minutes.
For time remaining: volume left divided by the rate.
Round as the question or the equipment requires.
IV fluids & fluid balance
Holliday–Segar per hour
4 mL/kg (first 10 kg) + 2 mL/kg (next 10 kg) + 1 mL/kg (each kg above 20)
Holliday–Segar per day
100 / 50 / 20 mL/kg for the same bands
Fluid balance
intake − output
Ice chips
count as half their volume
Urine output
mL/kg/h = mL / (kg × h)
Infusion time
time (h) = volume left (mL) / rate (mL/h)
Volume infused
mL = rate × time
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
2Practice problems
1.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A dose calculation for an injection gives 3.4641 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?
3.4641 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A haemoglobin result is 15.2 g/dL. Express it in g/L Hb.
15.2 g/dL1 L = 10 dL
Hb = g/L
3.Dosage calculationsMedium
A child weighing 28 kg is prescribed 3 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
28 kg3 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 2.48 mg. The ampoule contains 4000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2.48 mg4000 mcg/mL
V = mL
5.IV infusion ratesMedium
Infuse 1500 mL over 5 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute.
1500 mL5 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 25 mg in 250 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
25 mg/250 mL24 mL/h
D = mcg/min
7.IV fluids & fluid balanceMedium
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 150 mL/h. At 07:00, 300 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL300 mL infused150 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 85 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg85 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 58 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL10 mcg/kg/min58 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.66 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.66 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 240 mg. Draw up the dose: what volume V do you give?
1000 mg4.2 mL + 0.8 mL240 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 3.5 mL
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
3.4641 → 4
Only the next digit decides
3.4641 → 6
6 is 5 or more, so round 4 up.
The digits after it (41) are ignored: round once, never step by step.
Round
x = 3.5 mL
Answer
x = 3.5 mL
2.Nursing math & unit conversions
Answer: Hb = 152 g/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Convert
Hb = 15.2 g/dL × 10 dL/L = 152 g/L
Answer
Hb = 152 g/L
3.Dosage calculations
Answer: V = 4.2 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Dose from body weight
D = 3·28 = 84 mg
Volume
V = 84/20 = 4.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 4.2 mL
4.Dosage calculations
Answer: V = 0.62 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Same units
2.48 mg = 2480 mcg
Volume
V = 2480/4000 = 0.62 mL
Answer
V = 0.62 mL
5.IV infusion rates
Answer: R = 75 gtt/min
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Time in minutes
5·60 = 300 min
Drip rate
R = 1500·15/300 = 75 gtt/min
Answer
R = 75 gtt/min
6.IV infusion rates
Answer: D = 40 mcg/min
Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).
Concentration
25000 mcg/250 mL = 100 mcg/mL
Dose per hour
24·100 = 2400 mcg/h
Dose per minute
D = 2400/60 = 40 mcg/min
Answer
D = 40 mcg/min
7.IV fluids & fluid balance
Answer: B = 440 mL
Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Total intake
oral: 120 + 120 = 240 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1140 mL
Total output
300 + 150 + 250 = 700 mL
Balance
B = 1140 − 700 = 440 mL
Answer
B = 440 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 1.3 h
Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Volume left
500 − 300 = 200 mL
Time
t = 200/150 = 1.333 ≈ 1.3 h
Answer
t = 1.3 h
That is about 1 h 20 min, so the bag runs out at about 08:20.
9.Pediatric & critical-care dosing
Answer: V = 6.8 mL
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Units needed
80·85 = 6 800 units
Volume
V = 6800/1000 = 6.8 mL
Answer
V = 6.8 mL
10.Pediatric & critical-care dosing
Answer: R = 17.4 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
10·58 = 580 mcg/min
580·60 = 34800 mcg/h
Pump rate
R = 34800/2000 = 17.4 mL/h
Answer
R = 17.4 mL/h
11.Pharmacy calculations
Answer: V = 6.6 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.66/0.1 = 6.6 mL
Answer
V = 6.6 mL
12.Pharmacy calculations
Answer: V = 1.2 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.