Module 9 of 14 · 14 min
IV infusions & rates
Pumps are programmed in mL/h but orders are written in mcg/kg/min, units/h or mg over minutes; a slip of 60 or 1000 is a tenfold-to-thousandfold error at the bedside and a favourite exam trap.
🧠 "Dose × kg × 60 over concentration" — DK60/C.
A rate is amount per time. Write the order and the bag concentration as fractions, then multiply so every unit cancels except mL/h.
Get the concentration in the same mass unit as the dose: a bag of 400 mg in 250 mL is $1.6\ \text{mg/mL}=1600\ \text{mcg/mL}$.
Gravity sets: $\text{drops/min}=\dfrac{\text{mL/h}\times\text{drop factor (gtt/mL)}}{60}$, rounded to a whole drop.
Titrations step up at fixed intervals: count the increases, not the levels, when working out the time to reach a target.
🧭 The method
- 1Write the concentration of the bag in mg/mL or mcg/mL (match the dose's mass unit).
- 2Find the amount needed per minute (multiply by weight if per kg).
- 3Convert per minute to per hour (× 60).
- 4Divide by the concentration to get mL/h (or reverse the chain to get the dose from a rate).
- 5Sense-check: typical pump rates are 1–250 mL/h.
Before each reveal, predict the next step — then check.
Dopamine 5 mcg/kg/min is ordered for an 80 kg patient. The bag contains 400 mg in 250 mL. What rate (mL/h) should the pump be set to?
- 1
Concentration in mcg/mL (1 mg = 1000 mcg).
$$\frac{400\ \text{mg}\times1000\ \text{mcg/mg}}{250\ \text{mL}}=1600\ \text{mcg/mL}$$ Dose per minute for this patient.
$$5\ \frac{\text{mcg}}{\text{kg}\cdot\text{min}}\times80\ \text{kg}=400\ \text{mcg/min}$$Per hour.
$$400\ \frac{\text{mcg}}{\text{min}}\times60\ \frac{\text{min}}{\text{h}}=24\,000\ \text{mcg/h}$$Divide by the concentration: mcg cancels, leaving mL/h.
$$\frac{24\,000\ \text{mcg/h}}{1600\ \text{mcg/mL}}=15\ \text{mL/h}$$
Same method — the last steps are yours. Work on paper, then reveal.
Dobutamine 2.5 mcg/kg/min for a 70 kg patient; the bag is 250 mg in 250 mL. What is the rate in mL/h?
- 1
Concentration.
$$\frac{250\ 000\ \text{mcg}}{250\ \text{mL}}=1000\ \text{mcg/mL}$$ - 2
Dose per minute.
$$2.5\times70=175\ \text{mcg/min}$$ - 3
Your turn
Now you: convert to mcg per hour.
Work it out on paper, then reveal.
$$175\times60=10\,500\ \text{mcg/h}$$ - 4
Your turn
Now you: divide by the concentration.
Work it out on paper, then reveal.
$$\frac{10\,500\ \text{mcg/h}}{1000\ \text{mcg/mL}}=10.5\ \text{mL/h}$$
Type your number. Your first try decides when this module comes back for review.
1000 mL of normal saline is to run over 8 hours. What is the rate in mL/h?
Volume ÷ time.
= 125 mL/h
The same 1000 mL over 8 hours is given by gravity with a 15 gtt/mL set. How many drops per minute (to the nearest whole drop)?
mL/h × gtt/mL ÷ 60 min/h.
= 31 gtt/min
Heparin 25 000 units in 500 mL is running at 22 mL/h. How many units per hour is the patient receiving?
Find units per mL first.
= 1100 units/h
Norepinephrine 4 mg in 250 mL is running at 15 mL/h in a 75 kg patient. What dose is this in mcg/kg/min?
Reverse the chain: mL/h → mcg/h → mcg/min → per kg. Don't forget the ÷ 60.
= 0.0533 mcg/kg/min
An aminophylline loading infusion of 0.2 mg/kg/min for 30 minutes is ordered for a 70 kg patient, using a bag of 500 mg in 100 mL. At what rate (mL/h) should the pump run during the 30 minutes?
Total mg = rate × weight × minutes; convert to mL, then express per hour (30 min = 0.5 h).
= 168 mL/h
An infusion starts at 2 mcg/min and is increased by 2 mcg/min every 5 minutes until it reaches 10 mcg/min. How many mcg have been infused by the moment the rate first reaches 10 mcg/min?
Levels 2, 4, 6, 8 each run 5 minutes; it reaches 10 after 4 increases (20 min), not 5.
= 100 mcg
⚠️ Tricky
Dopamine 400 mg in 250 mL D5W is ordered at 5 mcg/kg/min for a patient weighing 176 lb (1 kg = 2.2 lb). What pump rate (mL/h)?
Weight to kg and bag to mcg/mL before using dose × kg × 60 ÷ concentration.
= 15 mL/h
⚠️ The trap: Plugging in 176 lb as if it were kg gives 33 mL/h, more than twice the ordered dose.
⚠️ Tricky
Vancomycin 1.25 g is diluted to a final concentration of 5 mg/mL. It must not be infused faster than 10 mg/min. What is the fastest permissible pump rate (mL/h)?
Find the minimum infusion time from the mg/min limit; do not assume the usual 60 minutes.
= 120 mL/h
⚠️ The trap: Running the bag over a routine 60 minutes gives 250 mL/h, which delivers about 21 mg/min — over twice the rate limit.
⚠️ Tricky
Ceftriaxone 1 g in 100 mL is to run by gravity over 30 minutes through a 15 gtt/mL set. The nurse counts drops for 15 seconds at a time. How many drops should she count in each 15-second check?
Work out gtt/min first, then answer the question actually asked: drops per 15 seconds.
= 12.5 drops
⚠️ The trap: Stopping at 50 gtt/min answers a different question; the count in 15 seconds is a quarter of that.
⚠️ Tricky
Lidocaine 0.4% premixed in D5W is ordered at 2 mg/min. What pump rate (mL/h)?
A % strength (w/v) means grams per 100 mL — turn it into mg/mL.
= 30 mL/h
⚠️ The trap: Reading 0.4% as 0.4 mg/mL gives 300 mL/h, a tenfold overdose.
⚠️ Tricky
Insulin regular 100 units in 100 mL NS is started at 0.1 units/kg/h for a 72 kg patient. Before connecting, 20 mL of the bag is used to prime and saturate the tubing and discarded. How many hours will the bag last at this rate?
Only what is left after priming reaches the patient; at 1 unit/mL, units/h = mL/h.
= 11.1 h
⚠️ The trap: Forgetting the 20 mL lost to priming gives 13.9 h, so the bag runs dry nearly 3 h earlier than planned.
🕵️ Spot the mistake
A 50 mL syringe-pump syringe has 20 mL left of morphine 1 mg/mL. The prescriber wants 2 mg/mL. How many mL of morphine 10 mg/mL stock must be added?
A student wrote
⚠️ Traps examiners set
- Forgetting the × 60 (or ÷ 60) between per-minute and per-hour.
- Leaving the bag concentration in mg/mL when the dose is in mcg (1000-fold error).
- Counting titration levels instead of increases when timing a step-up.
- Ignoring the volume of stock added when strengthening a syringe.
- Not rounding gravity drops to a whole number.
💬 Explain it in your own words
If the bag concentration doubles but the mcg/kg/min order stays the same, what happens to the mL/h and why?