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 weight conversion gives 107.7748 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
107.7748 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 3 tbsp of liquid supplement, 2½ tsp of cough syrup, 2 cups of tea, 1½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A child weighing 6 kg is prescribed 5 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
6 kg5 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 101 cm tall and weighs 25 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
101 cm25 kg135 mg/m²
D = mg
5.IV infusion ratesMedium
A drip runs at 40 gtt/min through a set of 20 gtt/mL. How many millilitres V does the patient receive in 4 hours?
40 gtt/min20 gtt/mL4 h
V = mL
6.IV infusion ratesHard
A drip runs at 20 gtt/min through a set of 60 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty?
20 gtt/min60 gtt/mL300 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 total intake I in mL.
water: 250 mLjelly: 100 mLmilk: 100 mLIV infusion: 80 mL/h × 8 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 125 mL/h. At 16:30, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL50 mL infused125 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 73 kg. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL0.1 units/kg/h73 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 10 mcg/kg/min for a patient who weighs 102 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL10 mcg/kg/min102 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 3.2 mL of diluent. The prescribed dose is 2 400 000 units. What volume V do you draw up? Round to one decimal place.
3.2 mL → 1 000 000 units/mL2 400 000 units
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 107.5 mg. Draw up the dose: what volume V do you give?
250 mg9.5 mL + 0.5 mL107.5 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 107.8 kg
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
107.7748 → 7
Only the next digit decides
107.7748 → 7
7 is 5 or more, so round 7 up.
The digits after it (48) are ignored: round once, never step by step.
Round
x = 107.8 kg
Answer
x = 107.8 kg
2.Nursing math & unit conversions
Answer: V = 582.5 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
3 tbsp = 3·15 = 45 mL
2½ tsp = 2.5·5 = 12.5 mL
2 cups = 2·240 = 480 mL
1½ fl oz = 1.5·30 = 45 mL
Add
V = 45 + 12.5 + 480 + 45 = 582.5 mL
Answer
V = 582.5 mL
3.Dosage calculations
Answer: V = 3 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 = 5·6 = 30 mg
Volume
V = 30/10 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: D = 113.1 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Body surface area
BSA = √(101·25/3600) = √0.7014 = 0.8375 m²
Dose
D = 135·0.8375 = 113.1 mg
Answer
D = 113.1 mg
5.IV infusion rates
Answer: V = 480 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
40·60/20 = 120 mL/h
Volume
V = 120·4 = 480 mL
Answer
V = 480 mL
6.IV infusion rates
Answer: t = 15 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
20·60/60 = 20 mL/h
Time left
t = 300/20 = 15 h
Answer
t = 15 h
7.IV fluids & fluid balance
Answer: I = 1140 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.
Add the intake
oral: 250 + 100 + 100 = 450 mL
IV infusion: 80·8 = 640 mL
IV antibiotic: 1·50 = 50 mL
I = 1140 mL
Answer
I = 1140 mL
8.IV fluids & fluid balance
Answer: t = 3.6 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 − 50 = 450 mL
Time
t = 450/125 = 3.6 h
Answer
t = 3.6 h
That is about 3 h 36 min, so the bag runs out at about 20:06.
9.Pediatric & critical-care dosing
Answer: R = 7.3 mL/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.
Units per hour
0.1·73 = 7.3 units/h
Concentration
250/250 = 1 units/mL
Pump rate
R = 7.3/1 = 7.3 mL/h
Answer
R = 7.3 mL/h
10.Pediatric & critical-care dosing
Answer: R = 38.3 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
10·102 = 1020 mcg/min
1020·60 = 61200 mcg/h
Pump rate
R = 61200/1600 = 38.25 ≈ 38.3 mL/h
Answer
R = 38.3 mL/h
11.Pharmacy calculations
Answer: V = 2.4 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
3.2 mL → 1 000 000 units/mL
Volume to give
V = 2 400 000/1 000 000 = 2.4 mL
Answer
V = 2.4 mL
12.Pharmacy calculations
Answer: V = 4.3 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.