How to set up an IV rate problem
Every IV rate question is a unit conversion. Something is ordered per unit of time, and the pump or the drip chamber needs it in different units. Two families cover almost all of them: gravity drips in drops per minute, and pump infusions in millilitres per hour. Both are solved by writing down the units you have, the units you need, and multiplying by the factors that get you from one to the other. Nothing here needs to be memorized as a formula if the units are on the page.
Gravity drips: drops per minute
A gravity set is calibrated to deliver a fixed number of drops per millilitre, its drop factor. Macrodrip tubing is 10, 15 or 20 drops/mL; microdrip tubing is 60 drops/mL. The question always gives the drop factor.
drops/min = (volume in mL × drop factor in drops/mL) ÷ time in minutes
Convert the time to minutes before dividing. Then round to a whole number: a drip chamber can't deliver a fraction of a drop, and the nurse counts whole drops against a watch.
Worked example 1: macrodrip
Infuse 1,000 mL of normal saline over 12 hours with a 15 drops/mL set.
minutes = 12 × 60 = 720 min
drops/min = 1,000 × 15 ÷ 720 = 20.83 → 21 drops/min
Worked example 2: microdrip
Infuse 50 mL over 30 minutes with a 60 drops/mL set.
drops/min = 50 × 60 ÷ 30 = 100 drops/min
Notice that 50 mL in 30 minutes is 100 mL/hr, and the answer is 100 drops/min. With a 60 drops/mL set the drops per minute always equal the millilitres per hour, because the 60 in the drop factor cancels the 60 minutes in an hour. That's a useful check, and it's the reason microdrip tubing is used for anything that needs precise low rates.
Pump infusions: mL/hr from a weight-based dose
Vasoactive drips are ordered by dose (mcg/kg/min or mcg/min), but the pump is programmed in mL/hr. The chain from one to the other never changes:
1. concentration of the bag in mcg/mL → 2. dose in mcg/min (× weight if the order is per kg) → 3. × 60 for mcg/hr → 4. ÷ concentration for mL/hr
Step 1 is where the mg-to-mcg conversion happens. A 400 mg bag is 400,000 mcg. Do this conversion once, at the start, and the rest of the chain stays in mcg.
Worked example 3: mcg/kg/min
Dopamine 400 mg in 250 mL is ordered at 5 mcg/kg/min for an 80 kg patient.
concentration = 400 × 1,000 ÷ 250 = 1,600 mcg/mL
dose = 5 × 80 = 400 mcg/min
per hour = 400 × 60 = 24,000 mcg/hr
pump rate = 24,000 ÷ 1,600 = 15 mL/hr
Worked example 4: a flat mcg/min order
Norepinephrine 4 mg in 250 mL is ordered at 8 mcg/min. No weight is given because the order isn't weight-based.
concentration = 4 × 1,000 ÷ 250 = 16 mcg/mL
per hour = 8 × 60 = 480 mcg/hr
pump rate = 480 ÷ 16 = 30 mL/hr
The only difference from example 3 is that step 2 is skipped. If a question gives a weight with a mcg/min order, the weight is a distractor.
Going the other way
Questions also run the chain backwards: the pump is at 15 mL/hr, what dose is the patient getting? Multiply the rate by the concentration to get mcg/hr, divide by 60 for mcg/min, divide by weight for mcg/kg/min. Same four numbers, opposite operations. If you can do the chain forwards you can do it backwards; just keep the units written next to every figure.
Where students lose the points
- Hours left as hours. Drops per minute needs minutes. 8 hours is 480 minutes, and forgetting the × 60 makes the drip rate 60 times too high.
- mg and mcg mixed. The bag is labeled in mg, the order in mcg. Convert the bag at step 1 and never touch mg again.
- Rounding the concentration. 250 mg in 250 mL is exactly 1,000 mcg/mL, but 800 mg in 250 mL is 3,200 mcg/mL, and 4 mg in 250 mL is 16 mcg/mL. Keep the concentration exact; it divides everything downstream.
- Fractional drops. A drip rate is a whole number. 20.83 drops/min is reported as 21. Pump rates, on the other hand, are set to a decimal, so report those to the precision the question asks for (this site grades to 0.1 mL/hr).
- Multiplying by weight on a mcg/min order. Only mcg/kg/min uses the weight. Read the units of the order twice.