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1Formulas and methods
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
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.
2Practice problems
1.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 92 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg92 kg1 000 units/mL
V = mL
2.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 94 kg has an order for nitroglycerin at 5 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL5 mcg/min94 kg
R = mL/h
3.Dosage calculationsMedium
A child weighing 36 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
36 kg5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 25000 units of a drug in 250 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
25000 units/250 mL2000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 500 mL over 6 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL6 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 30 gtt/min through a set of 20 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
30 gtt/min20 gtt/mL300 mL
t = h
3Solutions
1.Pediatric & critical-care dosing
Answer: V = 7.4 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
80·92 = 7 360 units
Volume
V = 7360/1000 = 7.36 ≈ 7.4 mL
Answer
V = 7.4 mL
2.Pediatric & critical-care dosing
Answer: R = 1.5 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
5·60 = 300 mcg/h
Pump rate
R = 300/200 = 1.5 mL/h
Answer
R = 1.5 mL/h
3.Dosage calculations
Answer: V = 7.2 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 = 5·36 = 180 mg
Volume
V = 180/25 = 7.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.2 mL
4.Dosage calculations
Answer: R = 20 mL/h
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.
Concentration
25000/250 = 100 units/mL
Pump rate
R = 2000/100 = 20 mL/h
Answer
R = 20 mL/h
5.IV infusion rates
Answer: R = 83 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
6·60 = 360 min
Drip rate
R = 500·60/360 = 83.33 ≈ 83 gtt/min
Answer
R = 83 gtt/min
At the bedside you round to the nearest whole drop: 83 gtt/min.
6.IV infusion rates
Answer: t = 3.3 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.