Dosage calculation

Weight-based IV infusion (mcg/kg/min to mL/hr)

Critical-care drips like dopamine are ordered in mcg/kg/min but pumps are set in mL/hr. This is the full dimensional-analysis problem: find the bag concentration in mcg/mL, multiply the rate by weight, convert minutes to hours, and divide by concentration so every unit cancels except mL/hr.

The formula

mL/hr = (ordered mcg/kg/min × weight kg × 60) ÷ concentration (mcg/mL)

How to solve it

  1. Convert the bag to mcg/mL: drug mg × 1000 ÷ bag mL.
  2. Multiply the ordered mcg/kg/min by the patient's weight in kg → mcg/min.
  3. Multiply by 60 min/hr → mcg/hr.
  4. Divide by the concentration (mcg/mL) so mcg cancels, leaving mL/hr.

Common mistakes

  • Forgetting the mg→mcg step when finding concentration.
  • Leaving the rate in mcg/min instead of converting to per hour.
  • Cancelling units carelessly — write every unit and confirm only mL/hr remains.
Safety check: High-alert infusions demand an independent double-check of the pump rate. Show every unit so nothing is left uncancelled.

Worked examples

See it solved

A patient weighing 65 kg has dopamine 800 mg in 500 mL. The prescriber orders 5 mcg/kg/min.

Weight65 kg
Ordered rate5 mcg/kg/min
Bag800 mg in 500 mL

What pump rate (mL/hr) delivers this order?

Answer: 12.2 mL/hr

Step-by-step solution

1. Find the bag concentration in mcg/mL
800 mg × ( 1000 mcg ÷ 1 mg ) ÷ 500 mL
= 1600 mcg/mL
2. Dose per minute: multiply the rate by the patient's weight
5 mcg/kg/min × 65 kg
= 325 mcg/min
3. Convert to mcg per hour
325 mcg/min × ( 60 min ÷ 1 hr )
= 19500 mcg/hr
4. Divide by concentration so mcg cancels, leaving mL/hr
19500 mcg/hr × ( 1 mL ÷ 1600 mcg )
= 12.2 mL/hr

A patient weighing 65 kg has dopamine 800 mg in 500 mL. The prescriber orders 5 mcg/kg/min.

Weight65 kg
Ordered rate5 mcg/kg/min
Bag800 mg in 500 mL

What pump rate (mL/hr) delivers this order?

Answer: 12.2 mL/hr

Step-by-step solution

1. Find the bag concentration in mcg/mL
800 mg × ( 1000 mcg ÷ 1 mg ) ÷ 500 mL
= 1600 mcg/mL
2. Dose per minute: multiply the rate by the patient's weight
5 mcg/kg/min × 65 kg
= 325 mcg/min
3. Convert to mcg per hour
325 mcg/min × ( 60 min ÷ 1 hr )
= 19500 mcg/hr
4. Divide by concentration so mcg cancels, leaving mL/hr
19500 mcg/hr × ( 1 mL ÷ 1600 mcg )
= 12.2 mL/hr

A patient weighing 75 kg has nitroglycerin 50 mg in 250 mL. The prescriber orders 10 mcg/kg/min.

Weight75 kg
Ordered rate10 mcg/kg/min
Bag50 mg in 250 mL

What pump rate (mL/hr) delivers this order?

Answer: 225 mL/hr

Step-by-step solution

1. Find the bag concentration in mcg/mL
50 mg × ( 1000 mcg ÷ 1 mg ) ÷ 250 mL
= 200 mcg/mL
2. Dose per minute: multiply the rate by the patient's weight
10 mcg/kg/min × 75 kg
= 750 mcg/min
3. Convert to mcg per hour
750 mcg/min × ( 60 min ÷ 1 hr )
= 45000 mcg/hr
4. Divide by concentration so mcg cancels, leaving mL/hr
45000 mcg/hr × ( 1 mL ÷ 200 mcg )
= 225 mL/hr