4 Intravenous Medication Calculations

Choose the requested rate

IV infusion calculations may ask for a pump rate in $\text{mL/hr}$, a gravity rate in $\text{gtt/min}$, or a medication delivery rate such as $\text{mg/hr}$ or $\text{mcg/kg/min}$. First identify the requested unit, then convert time or dose units as needed. Check that the units in the final answer match the question.

Calculate pump rates

An Infusion pump rate is found by dividing the volume to be infused by the infusion time in hours:

Convert minutes to hours before calculating if the infusion time is given in minutes.

• Example: For $600\,\text{mL}$ over $4\,\text{hr}$, $600\,\text{mL}\div4\,\text{hr}=150\,\text{mL/hr}$.

• Example: For $240\,\text{mL}$ over $90\,\text{min}$, convert the time to $1.5\,\text{hr}$, then calculate $240\,\text{mL}\div1.5\,\text{hr}=160\,\text{mL/hr}$.

An infusion pump rate is generally expressed in $\text{mL/hr}$.

Calculate gravity-flow rates

Gravity tubing delivers drops of a specified size. The Drop factor is the number of drops per milliliter, expressed in $\text{gtt/mL}$, and is printed on the tubing package. Use the drop factor for the actual tubing; do not assume it.

Calculate the Gravity flow rate using:

The units cancel to leave drops per minute. Round the final answer to a whole drop because a fraction of a drop cannot be counted.

Example: Infuse $500\,\text{mL}$ over $4\,\text{hr}$ with tubing labeled $15\,\text{gtt/mL}$.

1. Convert the time: $4\,\text{hr}\times60\,\text{min/hr}=240\,\text{min}$.

2. Calculate: $(500\,\text{mL}\times15\,\text{gtt/mL})\div240\,\text{min}=31.25\,\text{gtt/min}$.

3. Round to $31\,\text{gtt/min}$.

For a microdrip set labeled $60\,\text{gtt/mL}$, the numerical rate in $\text{gtt/min}$ equals the rate in $\text{mL/hr}$. For example, $75\,\text{mL/hr}$ corresponds numerically to $75\,\text{gtt/min}$. Still use the stated drop factor and formula to avoid confusing the units.

Convert medication dose rates

For an order expressed as a medication dose per time, use the Solution concentration to convert the prescribed dose rate to a volume rate. A useful sequence is:

1. Calculate the concentration in the bag by dividing the amount of drug by the total volume.

2. Convert the ordered dose to the same time unit as the requested rate.

3. Divide the required drug amount per time by the concentration to obtain volume per time.

Example: An order is for $18\,\text{mg/hr}$, and the solution contains $90\,\text{mg}$ in $250\,\text{mL}$.

• Concentration: $90\,\text{mg}\div250\,\text{mL}=0.36\,\text{mg/mL}$.

• Volume rate: $18\,\text{mg/hr}\div0.36\,\text{mg/mL}=50\,\text{mL/hr}$.

For a Weight-based order, first multiply the prescribed dose per kilogram by the patient’s weight. Then convert dose units and time units as needed before calculating the volume rate.

Example: An order is for $5\,\text{mcg/kg/min}$ for a $64\,\text{kg}$ patient. The bag contains $400\,\text{mg}$ in $250\,\text{mL}$, and the requested pump rate is in $\text{mL/hr}$.

1. Calculate the dose: $5\,\text{mcg/kg/min}\times64\,\text{kg}=320\,\text{mcg/min}$.

2. Convert dose units and time: $320\,\text{mcg/min}=0.32\,\text{mg/min}$, then $0.32\,\text{mg/min}\times60\,\text{min/hr}=19.2\,\text{mg/hr}$.

3. Calculate the concentration: $400\,\text{mg}\div250\,\text{mL}=1.6\,\text{mg/mL}$.

4. Calculate the volume rate: $19.2\,\text{mg/hr}\div1.6\,\text{mg/mL}=12\,\text{mL/hr}$.

Keep units attached to each value. Convert $\text{mcg}$ to $\text{mg}$ by dividing by $1{,}000$; convert a per-minute rate to a per-hour rate by multiplying by $60$.

Apply safety checks

These examples are for calculation practice, not instructions to administer medication. In practice, verify the order, patient, solution concentration, tubing drop factor, and pump settings, and follow local policy. IV therapy enters the bloodstream directly, so correct calculation and monitoring are important.

Practice and check calculations

Calculate each rate. For gravity questions, round to the nearest whole drop per minute.

1. A $750\,\text{mL}$ infusion is ordered over $6\,\text{hr}$. What is the pump rate in $\text{mL/hr}$?

2. Infuse $1{,}000\,\text{mL}$ over $8\,\text{hr}$ using tubing labeled $15\,\text{gtt/mL}$. What is the gravity rate in $\text{gtt/min}$?

3. Infuse $250\,\text{mL}$ over $90\,\text{min}$ using tubing labeled $20\,\text{gtt/mL}$. What is the gravity rate in $\text{gtt/min}$?

4. An infusion is ordered at $18\,\text{mg/hr}$. The prepared solution contains $90\,\text{mg}$ in $250\,\text{mL}$. What is the pump rate in $\text{mL/hr}$?

5. An infusion is ordered at $5\,\text{mcg/kg/min}$ for a $64\,\text{kg}$ patient. The solution contains $400\,\text{mg}$ in $250\,\text{mL}$. What is the pump rate in $\text{mL/hr}$?

Answers

1. $750\,\text{mL}\div6\,\text{hr}=125\,\text{mL/hr}$.

2. $(1{,}000\,\text{mL}\times15\,\text{gtt/mL})\div480\,\text{min}=31.25\,\text{gtt/min}$, or $31\,\text{gtt/min}$.

3. $(250\,\text{mL}\times20\,\text{gtt/mL})\div90\,\text{min}=55.56\,\text{gtt/min}$, or $56\,\text{gtt/min}$.

4. $90\,\text{mg}\div250\,\text{mL}=0.36\,\text{mg/mL}$; then $18\,\text{mg/hr}\div0.36\,\text{mg/mL}=50\,\text{mL/hr}$.

5. $5\,\text{mcg/kg/min}\times64\,\text{kg}=320\,\text{mcg/min}=19.2\,\text{mg/hr}$. The concentration is $400\,\text{mg}\div250\,\text{mL}=1.6\,\text{mg/mL}$, so $19.2\,\text{mg/hr}\div1.6\,\text{mg/mL}=12\,\text{mL/hr}$.