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 newborn weighs 5 lb 7 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
5 lb 7 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tbsp of an oral suspension four times a day for 7 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?
½ tbspfour times a day7 days1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A child weighing 24 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
24 kg7.5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 10 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 40 mg in 1 mL. What volume V do you give? Round to one decimal place.
10 kg12.5 mg/kg40 mg/1 mL
V = mL
5.IV infusion ratesMedium
A drip runs at 30 gtt/min through a set of 60 gtt/mL. How many millilitres V does the patient receive in 12 hours?
30 gtt/min60 gtt/mL12 h
V = mL
6.IV infusion ratesHard
A drip runs at 32 gtt/min through a set of 20 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
32 gtt/min20 gtt/mL450 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 86 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 500 mL bag runs by pump at 60 mL/h. At 16:00, 250 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL250 mL infused60 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 12 500 units of heparin in 250 mL. The order is 18 units/kg/h for a patient who weighs 75 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
12 500 units/250 mL18 units/kg/h75 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 57 kg has an order for norepinephrine at 4 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL4 mcg/min57 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 2 000 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL2 000 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 mL of 25% dextrose by mixing 70% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
70%10%25%1500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.47 kg
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.
Ounces to pounds
7 oz/16 = 0.4375 lb
5 + 0.4375 = 5.438 lb
Pounds to kilograms
m = 5.438/2.2 = 2.472 ≈ 2.47 kg
Answer
m = 2.47 kg
2.Nursing math & unit conversions
Answer: V = 210 mL
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 per dose
½ tbsp = 0.5·15 = 7.5 mL
Whole course
V = 7.5 mL × 4/day × 7 = 210 mL
Answer
V = 210 mL
3.Dosage calculations
Answer: V = 3.6 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 = 7.5·24 = 180 mg
Volume
V = 180/50 = 3.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.6 mL
4.Dosage calculations
Answer: V = 3.1 mL
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 from weight
12.5·10 = 125 mg
Volume
V = (125/40)·1 = 3.125 ≈ 3.1 mL
Answer
V = 3.1 mL
5.IV infusion rates
Answer: V = 360 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
30·60/60 = 30 mL/h
Volume
V = 30·12 = 360 mL
Answer
V = 360 mL
6.IV infusion rates
Answer: t = 4.7 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
32·60/20 = 96 mL/h
Time left
t = 450/96 = 4.688 ≈ 4.7 h
Answer
t = 4.7 h
7.IV fluids & fluid balance
Answer: U = 2.18 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
475 + 175 + 450 + 400 = 1500 mL
Per kilogram per hour
U = 1500/(86·8) = 2.18 mL/kg/h
Answer
U = 2.18 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 4.2 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 − 250 = 250 mL
Time
t = 250/60 = 4.167 ≈ 4.2 h
Answer
t = 4.2 h
That is about 4 h 10 min, so the bag runs out at about 20:10.
9.Pediatric & critical-care dosing
Answer: R = 27 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
18·75 = 1 350 units/h
Concentration
12 500/250 = 50 units/mL
Pump rate
R = 1350/50 = 27 mL/h
Answer
R = 27 mL/h
10.Pediatric & critical-care dosing
Answer: R = 15 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
4·60 = 240 mcg/h
Pump rate
R = 240/16 = 15 mL/h
Answer
R = 15 mL/h
11.Pharmacy calculations
Answer: V = 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
8.2 mL → 500 000 units/mL
Volume to give
V = 2 000 000/500 000 = 4 mL
Answer
V = 4 mL
12.Pharmacy calculations
Answer: V = 1125 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.