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 is 197 cm tall. Using 1 in = 2.54 cm, find the height h in inches. Round to one decimal place.
197 cm1 in = 2.54 cm
h = in
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A maintenance infusion runs at 100 mL/h without a break. How many litres V does it deliver in 24 hours?
100 mL/h24 h
V = L
3.Dosage calculationsMedium
How many milligrams of drug m are in 5 mL of a 20% (w/v) solution?
20% w/v5 mL
m = mg
4.Dosage calculationsHard
The prescription is 660 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
660 units1000 units/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 125 mL/h, but no pump is available. It runs by gravity through a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
125 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 32 gtt/min through a set of 60 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty?
32 gtt/min60 gtt/mL400 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 88 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
88 kg8 hurine: 200 mLurine: 275 mLurine: 300 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 50 mL/h. At 06:30, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL50 mL infused50 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 74 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg74 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 10 mcg/kg/min for a patient who weighs 75 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min75 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. The prescribed dose is 500 mg. What volume V do you draw up? Round to one decimal place.
1000 mg9.6 mL+0.4 mL500 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 30% dextrose by mixing 50% and 10% dextrose. How many mL V of the 50% solution do you need? Round to the nearest whole mL.
50%10%30%500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 77.6 in
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.
Centimetres to inches
h = 197/2.54 = 77.56 ≈ 77.6 in
Answer
h = 77.6 in
2.Nursing math & unit conversions
Answer: V = 2.4 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.
Volume in a day
100 mL/h × 24 h = 2400 mL
In litres
V = 2400/1000 = 2.4 L
Answer
V = 2.4 L
3.Dosage calculations
Answer: m = 1000 mg
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
20% = 20 g/100 mL = 200 mg/mL
Mass of drug
m = 200·5 = 1000 mg
Answer
m = 1000 mg
4.Dosage calculations
Answer: V = 0.66 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.
Volume
V = 660/1000 = 0.66 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.66 mL
5.IV infusion rates
Answer: R = 125 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.
Millilitres per minute
125/60 = 2.083 mL/min
Drip rate
R = 2.083·60 = 125 gtt/min
Answer
R = 125 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
6.IV infusion rates
Answer: t = 12.5 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
32·60/60 = 32 mL/h
Time left
t = 400/32 = 12.5 h
Answer
t = 12.5 h
7.IV fluids & fluid balance
Answer: U = 1.1 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
200 + 275 + 300 = 775 mL
Per kilogram per hour
U = 775/(88·8) = 1.101 ≈ 1.1 mL/kg/h
Answer
U = 1.1 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 9 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 = 450/50 = 9 h
Answer
t = 9 h
That is about 9 h 00 min, so the bag runs out at about 15:30.
9.Pediatric & critical-care dosing
Answer: V = 5.9 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
80·74 = 5 920 units
Volume
V = 5920/1000 = 5.92 ≈ 5.9 mL
Answer
V = 5.9 mL
10.Pediatric & critical-care dosing
Answer: R = 45 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
10·75 = 750 mcg/min
750·60 = 45000 mcg/h
Pump rate
R = 45000/1000 = 45 mL/h
Answer
R = 45 mL/h
11.Pharmacy calculations
Answer: V = 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.
Final volume
9.6 + 0.4 = 10 mL
Concentration
1000/10 = 100 mg/mL
Volume to give
V = 500/100 = 5 mL
Answer
V = 5 mL
12.Pharmacy calculations
Answer: V = 250 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.