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’s temperature is 102.2 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
102.2 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A blood glucose result is 6.7 mmol/L. Using 1 mmol/L = 18 mg/dL for glucose, find c in mg/dL to the nearest whole number.
6.7 mmol/L1 mmol/L = 18 mg/dL
c = mg/dL
3.Dosage calculationsMedium
A patient weighs 18 kg. The prescribed dose is 30 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
18 kg30 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient is 139 cm tall and weighs 37 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
139 cm37 kg50 mg/m²
D = mg
5.IV infusion ratesMedium
An infusion is ordered at 60 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.
60 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 15 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min15 gtt/mL300 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 total intake I in mL.
milk: 200 mLjelly: 100 mLIV infusion: 100 mL/h × 12 hIV antibiotic: 1 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 150 mL/h. At 16:30, 150 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL150 mL infused150 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 84 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg84 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 37 mL/h. The patient weighs 76 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL37 mL/h76 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.92 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.92 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 2.3 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 320 mg. Draw up the dose: what volume V do you give?
500 mg2.3 mL + 0.2 mL320 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 39 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
102.2 − 32 = 70.2
Multiply by 5/9
T = 70.2·5/9 = 39 °C
Answer
T = 39 °C
2.Nursing math & unit conversions
Answer: c = 121 mg/dL
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.
Convert
c = 6.7·18 = 120.6 ≈ 121 mg/dL
Answer
c = 121 mg/dL
3.Dosage calculations
Answer: D = 180 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
30·18 = 540 mg
Per dose
D = 540/3 = 180 mg
Answer
D = 180 mg
4.Dosage calculations
Answer: D = 59.76 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 = √(139·37/3600) = √1.429 = 1.195 m²
Dose
D = 50·1.195 = 59.76 mg
Answer
D = 59.76 mg
5.IV infusion rates
Answer: R = 60 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
60/60 = 1 mL/min
Drip rate
R = 1·60 = 60 gtt/min
Answer
R = 60 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
6.IV infusion rates
Answer: t = 1.8 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
42·60/15 = 168 mL/h
Time left
t = 300/168 = 1.786 ≈ 1.8 h
Answer
t = 1.8 h
7.IV fluids & fluid balance
Answer: I = 1600 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.
Add the intake
oral: 200 + 100 = 300 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 1·100 = 100 mL
I = 1600 mL
Answer
I = 1600 mL
8.IV fluids & fluid balance
Answer: t = 2.3 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.
Volume left
500 − 150 = 350 mL
Time
t = 350/150 = 2.333 ≈ 2.3 h
Answer
t = 2.3 h
That is about 2 h 20 min, so the bag runs out at about 18:50.
9.Pediatric & critical-care dosing
Answer: V = 6.7 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
80·84 = 6 720 units
Volume
V = 6720/1000 = 6.72 ≈ 6.7 mL
Answer
V = 6.7 mL
10.Pediatric & critical-care dosing
Answer: D = 16.2 mcg/kg/min
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
500 000/250 = 2000 mcg/mL
Micrograms per minute
37·2000 = 74000 mcg/h
74000/60 = 1233 mcg/min
Per kilogram
D = 1233/76 = 16.23 ≈ 16.2 mcg/kg/min
Answer
D = 16.2 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.92 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/1000 mL = 1 mg/mL
Volume
V = 0.92/1 = 0.92 mL
Answer
V = 0.92 mL
12.Pharmacy calculations
Answer: V = 1.6 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.