A patient is to receive Lidocaine at 3mg/min. Supplied is a one liter bag of D₅W containing Lidocaine 4g. Calculate the infusion rate in mL/hr.

First, identify the doctor's order. Doctor's orders

This is also known as the dose. Second, identify the dose on hand (DOH).

Dose on hand =

4g 1000mL

Supplied is Lidocaine 4g in a one liter (1000mL) bag of D₅W. This can be written as

Now solve for the infusion rate in mL/hr using dimensional analysis.

Doctor's order		Conversion		DOH		Conversion		Wanted Quantity
3mg min	X	1g 1000mg	X	1000mL 4g	X	60min 1hr	=	45	mL hr

The infusion rate would be 45mL/hr.

Remember to set up your problem so that the proper units cancel.

A diabetic is to receive an infusion of insulin at 12 units/hr. The nurse prepares a 250mL bag of NS with 100 units of regular insulin. What is the infusion rate in mL/hr?

First, identify the doctor's order.

Doctor's order =

12units hr

This is also known as the dose.Second, identify the dose on hand (DOH).

Dose on hand =

100units 250mL

Supplied is 100 units of regular insulin in a 250mL bag of NS. This can be written as

Doctor's order		DOH		Wanted Quantity
12units hr	X	250mL 100units	=	30	mL hr

The infusion rate would be 30mL/hr.

Remember to set up your problem so that the proper units cancel.

The doctor orders Heparin at 1800 units/hr. Available is 25,000 units in 250mL of solution. Calculate the infusion rate in mL/hr.

First, identify the doctor's order.

Doctor's order =

1800units hr

This is also known as the dose. Second, identify the dose on hand (DOH).

Dose on hand =

25,000units 250mL

Supplied, are 25,000 units in 250mL of solution. This can be written as

Now solve for the infusion rate in mL/hr using dimensional analysis.

Doctor's order		DOH		Wanted Quantity
1800units hr	X	250mL 25,000units	=	18	mL hr

The infusion rate would be 18mL/hr.

Remember to set up your problem so that the proper units cancel.

Calculating a dose based on weight.

The doctor orders Nipride 3mcg/kg/min to keep SBP < 140mmHg. The pharmacy supplies this in a 250mL bag of D₅W that contains 50mg of the drug. The patient weighs 56kg. Compute the dosage in mcg/min and the infusion rate in mL/hr.

First, identify the doctor's order.

Doctor's order =

3mcg kgmin

The doctor's order is given as 3mcg/kg/min. This can be written as

Second, identify the dose on hand (DOH).

Dose on hand =

50mg 250mL

Supplied is a 250mL bag of D₅W that contains 50mg of the drug. This can be written as

Third, identify the patient's weight.

Patient's weight =

56kg 1

The patient's weight given is 56kg. This can be written as

Now let's first solve for mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
3mcg kgmin	X	56kg 1	=	168mcg min

The dose for this patient would be 168mcg/min. Remember to set up your problem so that the proper units cancel.

Now that you know the dose for the patient, calculate the infusion rate in mL/hr using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
168mcg 1min	X	1mg 1000mcg	X	250mL 50mg	X	60min 1hr	=	50.4	mL hr	= 50	mL hr

The infusion rate would be 50 mL/hr.
Remember to set up your problem so that the proper units cancel.

To check your answer, back solve. You can do this by first solving for mg/hr using the dose calculated for the patient.

Dose		Conversion		Conversion		Wanted Quantity
168mcg 1min	X	1mg 1000mcg	X	60min 1hr	=	10.08	mg hr	= 10	mg hr

Using the dose for the patient based on their weight, they should receive 10 mg/hr.

Using the DOH and the infusion, the patient should receive 10 mg/hr.
Since both answers are equal to each other, your calculation is correct.

Remember to set up your problem so that the proper units cancel.

DOH		Infusion Rate		Wanted Quantity
50mg 250mL	X	50mL hr	=	10	mg hr

Calculating a dose based on weight.

A patient weighing 252 pounds is to begin an infusion of dopamine at 5mcg/kg/min. The drug is supplied in a 250mL bag of NS that contains 400mg. What is the dosage in mcg/min and the infusion rate in mL/hr?

First, identify the doctor's order.

Doctor's order =

5mcg kgmin

The doctor'ss order is given as 5mcg/kg/min. This can be written as

Second, identify the dose on hand (DOH).

Dose on hand =

400mg 250mL

Supplied is a 250mL bag of NS that contains 400mg. This can be written as

Third, identify the patient's weight.

The patient's weight given is 252lb. This can be written as

Let's first convert the patient's weight from pounds to kilograms.

Patient's weight		Conversion		Wanted Quantity
252lb 1	X	1kg 2.2lb	=	114.5kg

Now let's solve for mcg/min using dimensional analysis.

The dose for this patient would be 573 mcg/min.
Remember to set up your problem so that the proper units cancel.

Now that you know the dose for the patient, calculate the infusion rate in mL/hr using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
573mcg min	X	1mg 1000mcg	X	250mL 400mg	X	60min 1hr	=	21.48	mL hr	= 21	mL hr

The infusion rate would be 21 mL/hr.
Remember to set up your problem so that the proper units cancel.

To check your answer, back solve. You can do this by first solving for mg/hr using the dose calculated for the patient.

Dose		Conversion		Conversion		Wanted Quantity
573mcg min	X	1mg 1000mcg	X	60min 1hr	=	34.38	mg hr	= 34	mg hr

Using the DOH and the infusion, the patient should receive 34 mg/hr.
Since both answers are equal to each other, your calculation is correct.

To finish back solving, solve for mg/hr using the calculated infusion rate and the DOH.

DOH		Infusion Rate		Wanted Quantity
400mg 250mL	X	21mL hr	=	33.6	mg hr	= 34	mg hr

Using the DOH and the infusion, the patient should receive 34 mg/hr.
Since both answers are equal to each other, your calculation is correct.

Remember to set up your problem so that the proper units cancel.

A patient weighing 98 kg is to receive an infusion of dobutamine at 5mcg/kg/min. Available is 500mg in 250mL of solution. What is the dosage in mcg/min and the infusion rate in mL/hr?

First, identify the doctor's order.

Doctor's order =

5mcg kgmin

The doctor's order is given as 5mcg/kg/min. This can be written as

Second, identify the dose on hand (DOH).

Dose on hand =

500mg 250mL

Supplied is 500mg in 250mL of solution. This can be written as

Third, identify the patient's weight.

Patient's weight =

98kg 1

The patient's weight given is 98kg. This can be written as

Now let's first solve for mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
5mcg kgmin	X	98kg 1	=	490mcg min

The dose for this patient would be 490mcg/min. Remember to set up your problem so that the proper units cancel.

Now that you know the dose for the patient, calculate the infusion rate in mL/hr using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
490mcg min	X	1mg 1000mcg	X	250mL 500mg	X	60min 1hr	=	14.7	mL hr	= 15	mL hr

The infusion rate would be 15 mL/hr. Remember to set up your problem so that the proper units cancel.

To check your answer, back solve. You can do this by first solving for mg/hr using the dose calculated for the patient.

Patient's dose		Conversion		Conversion		Wanted Quantity
490mcg min	X	1mg 1000mcg	X	60min 1hr	=	29.4	mg hr	= 29	mg hr

Using the dose for the patient based on their weight, they should receive 29 mg/hr.

To finish back solving, solve for mg/hr using the calculated infusion rate and the DOH.

DOH		Infusion Rate		Wanted Quantity
500mg 250mL	X	15mL hr	=	30	mg hr

Using the DOH and the infusion, the patient should receive 30 mg/hr.

A dose of 6mcg/kg/min is ordered to infuse IV to sustain the blood pressure of an adult weighing 75 kg. The supplied solution contains 500mg in 250mL of D5W. Calculate the dose in mcg/min and the infusion rate in mL/hr.

First, identify the doctor's order.

Doctor's order =

6mcg kgmin

The doctor's order is given as 6mcg/kg/min. This can be written as

Second, identify the dose on hand (DOH).

Dose on hand =

500mg 250mL

The supplied solution contains 500mg in 250mL of D₅W. This can be written as

Third, identify the patients weight.

Patient's weight =

75kg 1

Now let’s first solve for mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
6mcg kgmin	X	75kg 1	=	450	mcg min

The dose for this patient would be 450 mcg/min. Remember to set up your problem so that the proper units cancel.

Now that you know the dose for the patient, calculate the infusion rate in mL/hr using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
450mcg min	X	1mg 1000mcg	X	250mL 500mg	X	60min 1hr	=	13.6	mL hr	= 14	mL hr

The infusion rate would be 14 mL/hr.
Remember to set up your problem so that the proper units cancel.

To check your answer, back solve. You can do this by first solving for mg/hr using the dose calculated for the patient.

Dose		Conversion		Conversion		Wanted Quantity
450mcg min	X	1mg 1000mcg	X	60min 1hr	=	27	mg hr

Using the dose for the patient based on their weight, they should receive 27mg/hr.

To finish back solving, solve for mg/hr using the calculated infusion rate and the DOH.

DOH		Infusion Rate		Wanted Quantity
500mg 250mL	X	14mL hr	=	28	mg hr

Using the DOH and the infusion, the patient should receive 28 mg/hr.

The order is to infuse a solution of 50mg in 250mL D₅W at 0.8mcg/kg/min. Calculate the dose in mcg/min and the flow rate in mL/hr of a patient weighing 66 kg.

First, identify the doctor's order

Doctor's order =

0.8mcg kgmin

The doctor's order is given as 0.8mcg/kg/min. This can be written as

Second, identify the dose on hand (DOH).

Dose on hand =

50mg 250mL

The supplied solution contains 50mg in 250mL D5W. This can be written as

Third, identify the patient's weight.

Patient's weight =

66kg 1

Now let's first solve for mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
0.8mcg kgmin	X	66kg 1	=	52.8mcg min	=	53mcg min

The dose for this patient would be 53 mcg/min. Remember to set up your problem so that the proper units cancel.

Now that you know the dose for the patient, calculate the infusion rate in mL/hr using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
53mcg min	X	1mg 1000mcg	X	250mL 50mg	X	60min 1hr	=	15.9	mL hr	= 16	mL hr

The infusion rate would be 16 mL/hr.
Remember to set up your problem so that the proper units cancel.

To check your answer, back solve. You can do this by first solving for mg/hr using the dose calculated for the patient.

Patient's dose		Conversion		Conversion		Wanted Quantity
53mcg min	X	1mg 1000mcg	X	60min 1hr	=	3.18	mg hr	= 3	mg hr

Using the dose for the patient based on their weight, they should receive 3 mg/hr.

Since both answers are equal to each other, your calculation is correct.

Titrations

A medication is ordered at a rate of 1-4mg/min. The solution strength is 2g in 500mL D₅W. What is the infusion rate range in mL/hr? What would the manual infusion rate be in gtt/min for a microdrip IV set (60gtt/mL)?

First, identify the doctor's order.

Doctor's order =

1 - 4mg min

This is also known as the dose.

NOTE: The healthcare provider must change the flow rate of the drug from time to time depending on how the patient is responding and thus must constantly monitor the patient's vital signs in order to titrate the dose (rate of administration) of a drug correctly.

To do this, infusion rate must be calculated at the lower end of the range and then again at the higher end of the range to determine the rate of administration.

Second, identify the dose on hand (DOH).

Dose on hand =

2g 500mL

The solution strength is 2g in 500mL D₅W. This can be written as

Now solve for the infusion rate at the lower end of the range in mL/hr using dimensional analysis.

Doctor's order		Conversion		DOH		Conversion		Wanted Quantity
1mg min	X	1g 1000mcg	X	500mL 2g	X	60min 1hr	=	15	mL hr

The infusion rate at the lower end of the range would be 15mL/hr. Remember to set up your problem so that the proper units cancel.

Now solve for the infusion rate at the higher end of the range in mL/hr using dimensional analysis.

Doctor's order		Conversion		DOH		Conversion		Wanted Quantity
4mg min	X	1g 1000mcg	X	500mL 2g	X	60min 1hr	=	60	mL hr

The infusion rate at the higher end of the range would be 60mL/hr. Remember to set up your problem so that the proper units cancel.

The range is 15-60mL/hr.

Now let's calculate the drip rate (gtt/min) for the lower end of the infusion rate.

Infusion Rate		Drop Factor		Conversion		Wanted Quantity
15mL hr	X	60gtt 1mL	X	1hr 60min	=	15gtt min

The drip rate for the lower end of the infusion rate is

Now let's calculate the drip rate (gtt/min) for the higher end of the infusion rate.

Infusion Rate		Drop Factor		Conversion		Wanted Quantity
60mL hr	X	60gtt 1mL	X	1hr 60min	=	60gtt min

The drip rate for the lower end of the infusion rate is

The drip rate range is also 15-60 gtt/min.

Calculate dosages using mg/kg and mcg/kg

A patient weighing 160 pounds is to receive a titrated infusion of a medication between 5-10mcg/kg/min. The supplied solution contains 100mg in 40mL of NS. What is the dose range in mcg/min? What is the manual infusion rate range in gtt/min for a microdrip IV set (60gtt/min)? The client stabilizes at 16mL/hr. What is the stabilizing dose in mcg/min?

First, identify the doctor's order.

Doctor's order =

5 - 10mcg kgmin

This is also known as the dose.

NOTE: The healthcare provider must change the flow rate of the drug from time to time depending on how the patient is responding and thus must constantly monitor the patient's vital signs in order to titrate the dose (rate of administration) of a drug correctly.

To do this, infusion rate must be calculated at the lower end of the range and then again at the higher end of the range to determine the rate of administration.

Second, identify the dose on hand (DOH).

Dose on hand =

100mg 40mL

The supplied solution contains 100mg in 40mL of NS. This can be written as

Third, identify the patient's weight.

Patient's weight =

160lb 1

The patient's weight given is 252lb. This can be written as

Let's first convert the patient's weight from pounds to kilograms.

Patient's weight		Conversion		Wanted Quantity
160 lb 1	X	1kg 2.2lb	=	72.7 kg

Using the conversion 1 kg = 2.2 lb we can determine the patients weight to be 72.7 kg.

Now let's solve for the dose at the lower end of the range in mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
5 mcg kgmin	X	72.7kg 1	=	363.5	mcg min	= 364	mcg min

The dose for this patient at the lower end of the range would be 364mcg/min.

Remember to set up your problem so that the proper units cancel.

Now let's solve for the dose at the higher end of the range in mcg/min using dimensional analysis.

Doctor's order		Patient's weight		Wanted Quantity
10 mcg kgmin	X	72.7kg 1	=	727mcg min

The dose for this patient at the higher end of the range would be 727mcg/min.

Remember to set up your problem so that the proper units cancel.

Dose range 364-727 mcg/min

Now that you know the dose range for the patient, calculate the infusion rate in mL/hr at the lower end of the range using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
364mcg min	X	1mg 1000mcg	X	40mL 100mg	X	60min 1hr	=	8.7	mL hr	= 9	mL hr

The infusion rate would be 9 mL/hr at the lower end of the dose range.

Remember to set up your problem so that the proper units cancel.

Now that you know the dose range for the patient, calculate the infusion rate in mL/hr at the higher end of the range using dimensional analysis.

Patient's dose		Conversion		DOH		Conversion		Wanted Quantity
727mcg min	X	1mg 1000mcg	X	40mL 100mg	X	60min 1hr	=	17.4	mL hr	= 17	mL hr

The infusion rate would be 17 mL/hr at the higher end of the dose range.

Remember to set up your problem so that the proper units cancel.

The infusion rate range is 9-17 mL/hr.

Now let,s calculate the manual infusion rate (gtt/min) for the lower end of the infusion rate.

Infusion Rate		Drop Factor		Conversion		Wanted Quantity
9mL hr	X	60gtt 1mL	X	1hr 60min	=	9	gtt min

The drip rate for the lower end of the infusion rate is

Now let's calculate the manual infusion rate (gtt/min) for the higher end of the infusion rate.

Infusion Rate		Drop Factor		Conversion		Wanted Quantity
17mL hr	X	60gtt 1mL	X	1hr 60min	=	17	gtt min

The drip rate for the lower end of the infusion rate is

The manual infusion rate range is also 9-17 gtt/min

Lastly, let's determine the stabilizing dose in mcg/min using the patient's stabilizing rate of 16mL/hr.

Stabilizing Rate		DOH		Conversion		Conversion		Wanted Quantity
16mL hr	X	100mg 40mL	X		X	1hr 60min	=	667.67mcg min	=	667mcg min	1000mcg 1mg

The stabilizing dose for this patient would be 667mcg/min.

Remember to set up your problem so that the proper units cancel.

Answers and step-by-step explanations.

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