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). During a shift a patient takes ½ tsp of cough syrup, 4 tbsp of liquid supplement, 8 fl oz of juice, 1½ cups of tea. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 tbsp = 15 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 80 kg. The prescribed dose is 7.5 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
80 kg7.5 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
A child weighing 14 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 125 mg in 5 mL. What volume V do you give?
14 kg15 mg/kg125 mg/5 mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 200 mL/h, but no pump is available. It runs by gravity through a giving set of 15 gtt/mL. Find the drip rate R in drops per minute.
200 mL/h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 50 gtt/min through a set of 15 gtt/mL. There are 600 mL left in the bag. How many hours t until it is empty?
50 gtt/min15 gtt/mL600 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).
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 17:00 at 100 mL/h. After 3 hours the rate is changed to 75 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL100 mL/h · 3 h75 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 10 mL/h. How many units per hour D does the patient receive?
100 units/100 mL10 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 12 mcg/kg/min for a patient who weighs 109 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL12 mcg/kg/min109 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.66 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.66 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 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%1500 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 = 662.5 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
½ tsp = 0.5·5 = 2.5 mL
4 tbsp = 4·15 = 60 mL
8 fl oz = 8·30 = 240 mL
1½ cups = 1.5·240 = 360 mL
Add
V = 2.5 + 60 + 240 + 360 = 662.5 mL
Answer
V = 662.5 mL
3.Dosage calculations
Answer: D = 300 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.
Total per day
7.5·80 = 600 mg
Per dose
D = 600/2 = 300 mg
Answer
D = 300 mg
4.Dosage calculations
Answer: V = 8.4 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
15·14 = 210 mg
Volume
V = (210/125)·5 = 8.4 mL
Answer
V = 8.4 mL
5.IV infusion rates
Answer: R = 50 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
200/60 = 3.333 mL/min
Drip rate
R = 3.333·15 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: t = 3 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
50·60/15 = 200 mL/h
Time left
t = 600/200 = 3 h
Answer
t = 3 h
7.IV fluids & fluid balance
Answer: B = 625 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: 300 + 200 = 500 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1550 mL
Total output
175 + 275 + 475 = 925 mL
Balance
B = 1550 − 925 = 625 mL
Answer
B = 625 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 12.3 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.
First part
100·3 = 300 mL
1000 − 300 = 700 mL left
Second part
700/75 = 9.333 h
Total time
t = 3 + 9.333 = 12.33 ≈ 12.3 h
Answer
t = 12.3 h
That is about 12 h 20 min, so the bag runs out at about 05:20.
9.Pediatric & critical-care dosing
Answer: D = 10 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
100/100 = 1 units/mL
Units per hour
D = 10·1 = 10 units/h
Answer
D = 10 units/h
10.Pediatric & critical-care dosing
Answer: R = 49.1 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
12·109 = 1308 mcg/min
1308·60 = 78480 mcg/h
Pump rate
R = 78480/1600 = 49.05 ≈ 49.1 mL/h
Answer
R = 49.1 mL/h
11.Pharmacy calculations
Answer: V = 6.6 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 = 0.66/0.1 = 6.6 mL
Answer
V = 6.6 mL
12.Pharmacy calculations
Answer: V = 750 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.