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 5 ft 2 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
5 ft 2 in1 ft = 12 in1 in = 2.54 cm
h = cm
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
A patient weighs 60 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
60 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient weighs 107.8 lb. The prescription is 10 mg/kg as a single dose, and the stock contains 125 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
107.8 lb10 mg/kg125 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 5 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
250 mL5 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 20 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min20 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 12-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 bag runs by pump at 75 mL/h. At 07:00, 400 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL400 mL infused75 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 60 units/kg for a patient who weighs 92 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
60 units/kg92 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 88 kg has an order for norepinephrine at 4 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL4 mcg/min88 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 2000 mg as a powder. The practice label says to add 19.2 mL of sterile water; the powder adds 0.8 mL to the volume. The prescribed dose is 600 mg. What volume V do you draw up? Round to one decimal place.
2000 mg19.2 mL+0.8 mL600 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 125 mg. Draw up the dose: what volume V do you give?
500 mg9.2 mL + 0.8 mL125 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 157 cm
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.
Height in inches
5·12 + 2 = 62 in
Inches to centimetres
h = 62·2.54 = 157.5 ≈ 157 cm
Answer
h = 157 cm
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: D = 200 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
10·60 = 600 mg
Per dose
D = 600/3 = 200 mg
Answer
D = 200 mg
4.Dosage calculations
Answer: V = 19.6 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.
Weight in kg
107.8/2.2 = 49 kg
Dose
10·49 = 490 mg
Volume
V = (490/125)·5 = 19.6 mL
Answer
V = 19.6 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.
Time in minutes
5·60 = 300 min
Drip rate
R = 250·60/300 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: t = 3.2 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
42·60/20 = 126 mL/h
Time left
t = 400/126 = 3.175 ≈ 3.2 h
Answer
t = 3.2 h
7.IV fluids & fluid balance
Answer: B = 560 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: 200 + 240 + 100 = 540 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1360 mL
Total output
250 + 400 + 150 = 800 mL
Balance
B = 1360 − 800 = 560 mL
Answer
B = 560 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 8 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 − 400 = 600 mL
Time
t = 600/75 = 8 h
Answer
t = 8 h
That is about 8 h 00 min, so the bag runs out at about 15:00.
9.Pediatric & critical-care dosing
Answer: V = 5.5 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
60·92 = 5 520 units
Volume
V = 5520/1000 = 5.52 ≈ 5.5 mL
Answer
V = 5.5 mL
10.Pediatric & critical-care dosing
Answer: R = 7.5 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
8 000/250 = 32 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 = 240/32 = 7.5 mL/h
Answer
R = 7.5 mL/h
11.Pharmacy calculations
Answer: V = 6 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
19.2 + 0.8 = 20 mL
Concentration
2000/20 = 100 mg/mL
Volume to give
V = 600/100 = 6 mL
Answer
V = 6 mL
12.Pharmacy calculations
Answer: V = 2.5 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.