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 patient’s temperature is 40.2 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
40.2 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ¾ cup of tea, 3 tbsp of liquid supplement, 1½ tsp of cough syrup, ½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL1 tsp = 5 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 12 kg is prescribed 20 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
12 kg20 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 0.49 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
0.49 mg1000 mcg/mL
V = mL
5.IV infusion ratesMedium
A drip runs at 20 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 2 hours?
20 gtt/min15 gtt/mL2 h
V = mL
6.IV infusion ratesHard
A drip runs at 28 gtt/min through a set of 20 gtt/mL. There are 750 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
28 gtt/min20 gtt/mL750 mL
t = h
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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag was started at 13:30 and runs by pump at 60 mL/h. How many mL V are left in the bag at 15:00?
500 mL60 mL/h13:30 → 15:00
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 15 mL/h. How many units per hour D does the patient receive?
50 units/50 mL15 mL/h
D = units/h
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 12.5 mcg/kg/min for a patient who weighs 96 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL12.5 mcg/kg/min96 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 8.2 mL of diluent. The prescribed dose is 750 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL750 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 300 mL of 8% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%8%300 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 104.4 °F
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Multiply by 9/5
40.2·9/5 = 72.36
Add 32
T = 72.36 + 32 = 104.4 °F
Answer
T = 104.4 °F
2.Nursing math & unit conversions
Answer: V = 247.5 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
¾ cup = 0.75·240 = 180 mL
3 tbsp = 3·15 = 45 mL
1½ tsp = 1.5·5 = 7.5 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 180 + 45 + 7.5 + 15 = 247.5 mL
Answer
V = 247.5 mL
3.Dosage calculations
Answer: V = 9.6 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 = 20·12 = 240 mg
Volume
V = 240/25 = 9.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9.6 mL
4.Dosage calculations
Answer: V = 0.49 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
0.49 mg = 490 mcg
Volume
V = 490/1000 = 0.49 mL
Answer
V = 0.49 mL
5.IV infusion rates
Answer: V = 160 mL
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.
Rate in mL/h
20·60/15 = 80 mL/h
Volume
V = 80·2 = 160 mL
Answer
V = 160 mL
6.IV infusion rates
Answer: t = 8.9 h
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.
Rate in mL/h
28·60/20 = 84 mL/h
Time left
t = 750/84 = 8.929 ≈ 8.9 h
Answer
t = 8.9 h
7.IV fluids & fluid balance
Answer: B = −405 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: 150 + 100 = 250 mL
ice chips: 100/2 = 50 mL
IV infusion: 60·8 = 480 mL
IV antibiotic: 1·50 = 50 mL
total intake = 830 mL
Total output
475 + 425 + 275 + 60 = 1235 mL
Balance
B = 830 − 1235 = −405 mL
Answer
B = −405 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: V = 410 mL
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.
Elapsed time
13:30 → 15:00 = 1.5 h
Volume infused
60·1.5 = 90 mL
Volume left
V = 500 − 90 = 410 mL
Answer
V = 410 mL
9.Pediatric & critical-care dosing
Answer: D = 15 units/h
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.
Concentration
50/50 = 1 units/mL
Units per hour
D = 15·1 = 15 units/h
Answer
D = 15 units/h
10.Pediatric & critical-care dosing
Answer: R = 36 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
12.5·96 = 1200 mcg/min
1200·60 = 72000 mcg/h
Pump rate
R = 72000/2000 = 36 mL/h
Answer
R = 36 mL/h
11.Pharmacy calculations
Answer: V = 1.5 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration from the label
8.2 mL → 500 000 units/mL
Volume to give
V = 750 000/500 000 = 1.5 mL
Answer
V = 1.5 mL
12.Pharmacy calculations
Answer: V = 225 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.