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 36.6 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
36.6 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ tsp of cough syrup, 1½ fl oz of juice, 1½ cups of tea, 4 tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL1 tbsp = 15 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 80 kg and is prescribed 7.5 mg/kg as a single dose. Find the dose D in mg.
80 kg7.5 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 1.64 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1.64 mg2000 mcg/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 90 mL/h, but no pump is available. It runs by gravity through a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
90 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 250 mg of a drug in 250 mL and runs at 8 mL/h. How many milligrams per hour D does the patient receive?
250 mg/250 mL8 mL/h
D = mg/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. Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 125 mL/h. At 10:30, 200 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL200 mL infused125 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 4 mL/h. How many units per hour D does the patient receive?
100 units/100 mL4 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 87 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL10 mcg/kg/min87 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.74 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.74 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 225 mg. Draw up the dose: what volume V do you give?
250 mg1.6 mL + 0.4 mL225 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 97.9 °F
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.
Multiply by 9/5
36.6·9/5 = 65.88
Add 32
T = 65.88 + 32 = 97.88 ≈ 97.9 °F
Answer
T = 97.9 °F
2.Nursing math & unit conversions
Answer: V = 467.5 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
1½ fl oz = 1.5·30 = 45 mL
1½ cups = 1.5·240 = 360 mL
4 tbsp = 4·15 = 60 mL
Add
V = 2.5 + 45 + 360 + 60 = 467.5 mL
Answer
V = 467.5 mL
3.Dosage calculations
Answer: D = 600 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.
Dose
7.5·80 = 600 mg
Answer
D = 600 mg
4.Dosage calculations
Answer: V = 0.82 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.
Same units
1.64 mg = 1640 mcg
Volume
V = 1640/2000 = 0.82 mL
Answer
V = 0.82 mL
5.IV infusion rates
Answer: R = 30 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
90/60 = 1.5 mL/min
Drip rate
R = 1.5·20 = 30 gtt/min
Answer
R = 30 gtt/min
6.IV infusion rates
Answer: D = 8 mg/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.
Concentration
250/250 = 1 mg/mL
Dose rate
D = 1·8 = 8 mg/h
Answer
D = 8 mg/h
7.IV fluids & fluid balance
Answer: I = 1380 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: 180 + 200 + 200 = 580 mL
ice chips: 200/2 = 100 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·100 = 100 mL
I = 1380 mL
Answer
I = 1380 mL
8.IV fluids & fluid balance
Answer: t = 2.4 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 − 200 = 300 mL
Time
t = 300/125 = 2.4 h
Answer
t = 2.4 h
That is about 2 h 24 min, so the bag runs out at about 12:54.
9.Pediatric & critical-care dosing
Answer: D = 4 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 = 4·1 = 4 units/h
Answer
D = 4 units/h
10.Pediatric & critical-care dosing
Answer: R = 26.1 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
10·87 = 870 mcg/min
870·60 = 52200 mcg/h
Pump rate
R = 52200/2000 = 26.1 mL/h
Answer
R = 26.1 mL/h
11.Pharmacy calculations
Answer: V = 0.74 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 = 0.74/1 = 0.74 mL
Answer
V = 0.74 mL
12.Pharmacy calculations
Answer: V = 1.8 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.