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 a small injection gives 0.69114 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.69114 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 3 cups of tea, 1½ tbsp of liquid supplement, 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 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 12 kg and is prescribed 5 mg/kg as a single dose. Find the dose D in mg.
12 kg5 mg/kg
D = mg
4.Dosage calculationsHard
A patient is 144 cm tall and weighs 49 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
144 cm49 kg135 mg/m²
D = mg
5.IV infusion ratesMedium
Infuse 1000 mL over 8 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL8 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 50 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?
50 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 patient weighs 93 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 60 mL/h. At 12:00, 600 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL600 mL infused60 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 62 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg62 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 82 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min82 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.72 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.72 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 60 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 10% ointment? Round to the nearest whole gram.
60 g · 20%0%10%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.69 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 hundredths place
0.69114 → 9
Only the next digit decides
0.69114 → 1
1 is 4 or less, so 9 stays.
The digits after it (14) are ignored: round once, never step by step.
Round
x = 0.69 mL
Answer
x = 0.69 mL
2.Nursing math & unit conversions
Answer: V = 757.5 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 cups = 3·240 = 720 mL
1½ tbsp = 1.5·15 = 22.5 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 720 + 22.5 + 15 = 757.5 mL
Answer
V = 757.5 mL
3.Dosage calculations
Answer: D = 60 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Dose
5·12 = 60 mg
Answer
D = 60 mg
4.Dosage calculations
Answer: D = 189 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 = √(144·49/3600) = √1.96 = 1.4 m²
Dose
D = 135·1.4 = 189 mg
Answer
D = 189 mg
5.IV infusion rates
Answer: R = 31 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
8·60 = 480 min
Drip rate
R = 1000·15/480 = 31.25 ≈ 31 gtt/min
Answer
R = 31 gtt/min
At the bedside you round to the nearest whole drop: 31 gtt/min.
6.IV infusion rates
Answer: t = 5 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
50·60/20 = 150 mL/h
Time left
t = 750/150 = 5 h
Answer
t = 5 h
7.IV fluids & fluid balance
Answer: U = 1.51 mL/kg/h
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 urine
375 + 475 + 275 = 1125 mL
Per kilogram per hour
U = 1125/(93·8) = 1.512 ≈ 1.51 mL/kg/h
Answer
U = 1.51 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 6.7 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
1000 − 600 = 400 mL
Time
t = 400/60 = 6.667 ≈ 6.7 h
Answer
t = 6.7 h
That is about 6 h 40 min, so the bag runs out at about 18:40.
9.Pediatric & critical-care dosing
Answer: V = 5 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
80·62 = 4 960 units
Volume
V = 4960/1000 = 4.96 ≈ 5 mL
Answer
V = 5 mL
10.Pediatric & critical-care dosing
Answer: R = 12.3 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·82 = 205 mcg/min
205·60 = 12300 mcg/h
Pump rate
R = 12300/1000 = 12.3 mL/h
Answer
R = 12.3 mL/h
11.Pharmacy calculations
Answer: V = 7.2 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.72/0.1 = 7.2 mL
Answer
V = 7.2 mL
12.Pharmacy calculations
Answer: m = 60 g
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.