Advanced Intravenous Calculations

1. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: medicated IV at 4 mcgper kg per min.

Patient’s weight: 50 kg.

a. Information requested: Micrograms per minute ordered

Calculator result:

b. Information requested: Micrograms per hour ordered

Calculator result:

c. Information requested: Milligrams per hour ordered

Calculator result:

ANS:

a. 200 mcg per minute (4 × 50)

b. 12,000 mcg per hour (200 × 60)

c. 12 mg per hour (12,000 ÷ 1000)

2. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

An IV of 1000 mL of D5W contains 400 mg of dopamine HCl.

a. What is the concentration in milligrams per milliliter? (Remember: per indicates division.) Show the data you would enter on a calculator or use a DA equation.

b. What is the concentration in micrograms per milliliter? (Move the decimal point carefully.) Show the data you would enter on a calculator or use a DA equation.

ANS:

a.

b. 1.6 × 1000 = 1600 mcg per mL

3. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: aminophylline IV infusion, for a patient with asthma.

Infusing: aminophylline at 33 mL per hr

Available: IV of 500 mL of D5W with the contents of the vial shown here

Patient’s weight: 110 kg

The nurse has withdrawn 20 mL of D5W and added the medication to make a total volume of 500 mL.

How many milligrams of aminophylline is the patient receiving per hour?

a. DA equation:

b. Evaluation:

ANS:

a.

b. Equation is balanced. Only mg per hour remain. Note: The equation is solved using the total mL (500 mL) not 20 mL.

4. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: dopamine infusion at 3 mcg per kg per min, for a patient in shock.

Available: dopamine 200 mg per 250 mL D5W.

Patient’s weight: 60 kg

a. Information requested: Micrograms per hour ordered

Calculator result:

b. Information requested: Milligrams per hour ordered

Calculator result:

Milliliters per hour to be administered on infusion pump

c. DA equation:

d. Evaluation:

ANS:

a. 10,800 mcg per hr (3 × 60 × 60)

b. 10.800 mg per hr (10.800) (10.800 ÷ 1000)

c.

d. Equation is balanced. Only mL per hour remain. A shortcut can be used by entering the data in the equation as follows:

5. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: dobutamine 2.5 mcg per kg per min

Available: 500 mL D5W

Patient’s weight: 80 kg

a. Information requested: Micrograms per minute ordered

Calculator result:

b. Information requested: Micrograms per hour ordered

Calculator result:

c. Information requested: Milligrams per minute ordered

Calculator result:

d. Milligrams per hour ordered (Use in final flow rate equation.)

Calculator result:

Milliliters per hour to be administered on infusion pump:

e. DA equation:

f. Evaluation:

ANS:

a. 200 mcg (2.5 × 80)

b. 12,000 mcg (200 × 60)

c. 0.2 mg (0.200) (200 ÷ 1000)

d. 12 mg (12.000) (0.2 × 60)

e.

f. Equation is balanced. Only mL per hour remain.

6. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: Lasix 25 mg direct IV, for a patient with pulmonary edema. SDR: Up to 20 mg per min

For pulmonary edema, push over several minutes.

The nurse plans to administer the medication over a 5-minute period.

Available:

Total number of milliliters for the prepared injection to the nearest tenth of a milliliter:

a. Estimated dose:

b. DA equation:

c. Evaluation:

d. Total minutes for injection:

Total seconds for injection:

e. Total number of calibrations occupied by the dose:

Number of calibrations per second to be pushed:

f. DA equation:

g. Evaluation:

ANS:

a. Estimate: Give less than 4 mL.

b.

c. Equation is balanced. Estimate supports answer.

d. 5 minutes; 300 seconds (5 × 60)

e. 25 calibrations

f.

g. Only calibrations per second remain. Inject volume of 2.5 mL at a rate of 1 calibration every 12 seconds.

7. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: meperidine 30-mg IV push, for a patient with complaints of pain.

Drug reference: Inject over 1 minute.

Available:

Total number of milliliters for the prepared injection to nearest tenth of a milliliter:

a. Estimate:

b. DA equation:

c. Evaluation:

d. Total minutes for injection:

Total seconds for injection:

e. Total number of calibrations occupied by dose:

Number of calibrations per second to be pushed:

f. DA equation:

g. Evaluation:

ANS:

a. Estimate: Give less than 1 mL.

b.

c. Equation is balanced. Estimate supports answer.

d. 1 minute; 60 seconds

e. 6 calibrations

f.

g. Inject volume of 0.6 mL at a rate of 1 calibration every 10 seconds.

8. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: magnesium sulfate 2.5 g per hr IV infusion, for a patient with toxemia

Existing infusion rate when nurse arrives on shift: 75 mL per hr

Available: magnesium sulfate (refer to label) diluted in 500 mL D5W

a. Number of milliequivalents per milliliter stated on label:

b. Number of milligrams per milliliter stated in fine print on right side of label:

c. Total number of grams of magnesium sulfate in 50-mL vial:

Number of grams per hour infusing on the infusion pump:

d. DA equation:

e. Evaluation:

Ordered infusion rate:

f. DA equation:

g. Evaluation:

h. Decision:

ANS:

a. 4 mEq mL

b. 500 mg per mL

c. 25 g

d.

e. Equation is balanced. Only g per hour remains.

f.

g. Equation is balanced. Existing flow rate is too rapid.

h. Flow rate needs to be reduced to 50 mL per hr. Contact prescriber promptly for rate of adjustment. Assess and monitor patient. Document.

9. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: oxytocin drip, 1 milliunit per min

Infusing: oxytocin drip at 6 mL per hr

Available:

a. How many units of Pitocin are contained in 1 mL, according to label?

b. How many milliunits equal 1 unit? How many milliunits equal 10 units? (Recall the meaning of the prefix “milli”.)

c. One mL of Pitocin has been placed in 1000 mL of D5W. What is the concentration of milliunits per milliliter in the IV solution?

DA equation:

d. How many milliunits per hour are being infused?

DA equation:

e. Evaluation:

f. How many milliunits per minute are infusing?

DA equation:

g. Evaluation:

h. Is the existing flow rate correct? (Do the milliunits per minute being infused match the order?) If not, what flow rate should be set?

i. DA equation:

j. Evaluation:

ANS:

a. 10 units

b. 1000 milliunits = 1 unit; 10,000 milliunits = 10 units (1000 × 10)

c.

d.

e. Equation is balanced. Only milliunits per hour remain.

f.

g. Equation is balanced. Only mU per minute remain.

h. Yes. Flow rate is correct.

i. N/A

j. Continue the infusion at 6 mL per hour. Note: Be sure to insert commas when working with large numbers.

10. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Diltiazem hydrochloride IV maintenance drip infusion has been ordered for a patient diagnosed with atrial flutter, who was treated on admission with a bolus IV dose to lower the ventricular pulse rate.

Order: Titrate the diltiazem HC1 at 5-15 mg per hr to maintain a ventricular pulse rate 90 beats per minute (bpm). Increase by increments of 5 mg per hr

Available: diltiazem hydrochloride 100 mg per 100 mL NS

a. With what IV dose in mg per hr will the nurse initiate the infusion?

b. Estimated initial flow rate on an EID:

c. DA equation for flow rate:

d. Evaluation:

The patient’s ventricular pulse rate is 100 bpm at the end of the first hour.

e. IV dose in mg per hr to be administered:

f. Estimated flow rate:

g. DA equation for flow rate:

h. Evaluation:

ANS:

a. 5 mg per hr. Note: When titrating medications, the initial dose must be the lowest dose in the range.

b. 5 mL per hr (100 mg per 100 mL = 1:1)

c.

d. Equation is balanced. Only mL per hour remain.

e. 10 mg per hr. Note: The drug is to be titrated in 5 mg per hr increments.

f. 10 mL per hr

g.

h. Equation is balanced. Only mL per hr remain.

11. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV infusion at 3 mg per minute. Available: Drug Y

1500 mg in 1000 mL of D5NS.

a. How many mg per hr will be administered?

b. How many mg per mL will be in the IV?

DA:

Evaluation:

ANS:

a. 180 mg per hr

b.

DA:

12. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV infusion at 0.5 mg per minute. Available: Drug Y 500 mg in 100 mL. LRS.

a. What will the flow rate be in mL per hr?

b. DA:

c. Evaluation:

ANS:

a.

b. DA:

c. Equation is balanced, only mL/hr remains.

13. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV infusion at 1 mg per minute. Available: Drug Y 250 mg in 250 mL of D5W.

a. What will the flow rate be in mL per hour?

b. DA:

c. Evaluation:

ANS:

a. Estimate: 1 mg per mL of D5W × 60 mg per hr and 60 mL per hr

b. DA:

c. Estimate supports answer.

14. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV infusion with drug Y at 2 mg per minute. Available: Drug Y 1 g in 1000 mL of NS.

a. What will the flow rate be in mL per hr?

b. DA:

c. Evaluation

ANS:

a. 120 mL per hr

b. DA:

c. Equation balanced, only mL per hour remains.

15. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV at 2 mcg per kg per minute

Patient’s weight: 60 kg

a. Micrograms per minute ordered:

b. Micrograms per hour ordered:

c. Milligrams per hour ordered:

ANS:

a. 2 mcg × 60 kg =120 mcg per minute

b. 120 × 60 min = 7200 mcg per hr

c. 7200 ÷ 1000 mcg = 7.2 mg per hr

16. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV at 6 mcg per kg per minute

Patient’s weight: 176 lb

a. Estimated wt. in kg:

b. Actual wt. in kg:

c. mcg per hour ordered

d. mg per hour ordered

ANS:

a. Estimated wt. in kg: 176 ÷ 2 = 88

b. Actual wt. in kg: 176 ÷ 2.2 = 80

c. mcg per hour ordered 6 × 80 × 60 min = 28,800 mcg per hr

d. mg per hr ordered: 28,800 ÷ 1000 = 28.8 mg per hr

17. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: A medicated IV at 3 mcg per kg per minute. Available IV: D5W 1000 mL with 500 mg of Drug Y.

Patient weight: 50 kg

a. What flow rate will you set in mL per hr to the nearest tenth of a mL?

DA:

b. Evaluation:

ANS:

a. Flow rate: 18 mL per hr

DA:

b. Evaluation: Equation verified twice with calculator.

18. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: Dobutamine hydrochloride IV infusion 0.5 mcg per kg per minute,

for a patient with cardiac decompensation.

Patient weight: 70 kg.

Available dobutamine: 250 mg in 500 mL

a. How many mg per mL of drug are contained in the IV?

b. How many mcg per mL of drug are contained in the IV?

c. What flow rate will you set in mL per hr to the nearest tenth of a mL?

DA:

d. Evaluation:

ANS:

a.

b. 0.5 X 1000 = 500 mcg/mL

c. 4.2 mL per hr

DA:

d. Evaluation: Equation verified twice with calculator.

19. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: Dopamine infusion at 10 mcg per kg per minute. Available: Dopamine 400 mg premixed in 500 mL of D5W.

Patient weight: 60 kg (45 mL per hr)

a. How many mg per mL are contained in the solution?

b. How many mcg per mL are contained in the solution?

c. How many mL per hr will the flow rate be set?

DA:

d. Evaluation:

ANS:

a. mg per mL:

b. mcg per mL: 0.8 mg = 800 mcg per mL

c. 45 mL per hr

d. Equation balanced, only 1 mL per hour remain. Equation verified twice with calculator.

20. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

Ordered: Dopamine infusion at 5 mcg per kg per min. Available: Dopamine 200 mg in 250 mL of D5W.

Patient weight: 80 kg

a. How many mcg per mL are contained in the solution?

b. How many mL per hr will the flow rate be set?

DA:

c. Evaluation

ANS:

a. 800 mcg per mL; 0.8 mg per mL

b. 30 mL per hr

DA:

c. Evaluation: Equation verified twice with calculator.

21. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

(11 to 15)

IV Push (Bolus) Rx
and Time For
Available
Dilution
Total mL to Be Given
mL per Minute
a.
Morphine sulfate IV 2 mg over 2 minutes
for pain
Morphine sulfate 10 mg per mL
3 mL syringe
1 mg per mL of NS

b.
Hydromorphone HCl (Dilaudid) IV 0.5 mg over 5 minutes for pain
Dilaudid 2 mg ampule
5 mL syringe
5 mL SW or NS

c.
Naloxone HCl (Narcan) 1 mg IV for opioid overdose
Rate: Each 0.4 mg or fraction thereof over 15 seconds
Naloxone
400 mcg per mL
3 mL syringe
Dilute up to 2 mL

d.
Furosemide (Lasix) 30 mg IV for edema. Give over 2 minutes
Furosemide 10 mg per mL
3 mL syringe
May be given undiluted

e.
Phenobarbital sodium 120 mg IV for status epilepticus. May repeat times 3. Give 60 mg per minute
Phenobarbital sodium 120 mg per 3 mL
10 mL syringe
Dilute to 10 mL with SW

ANS:

IV Push (Bolus) Rx
and Time For
Available
Dilution
Total mL to Be Given
mL per Minute
a.
Morphine sulfate IV 2 mg over 2 minutes
for pain
Morphine sulfate 10 mg per mL
3 mL syringe
1 mg per mL of NS
2.2 mL
1.1 mL per minute
b.
Hydromorphone HCl (Dilaudid) IV 0.5 mg over 5 minutes for pain
Dilaudid 2 mg ampule
5 mL syringe
5 mL SW or NS
5 mL
1 mL per minute
c.
Naloxone HCl (Narcan) 1 mg IV for opioid overdose
Rate: Each 0.4 mg or fraction thereof over 15 seconds
Naloxone
400 mcg per mL
3 mL syringe
Dilute up to 2 mL
2 mL
2 mL per 3 minutes or 0.67 mL rounded to 0.7 ml 1st and 2nd minute and 0.6 mL 3rd minute
d.
Furosemide (Lasix) 30 mg IV for edema. Give over 2 minutes
Furosemide 10 mg per mL
3 mL syringe
May be given undiluted
3 mL
3 mL over 2 minutes = 1.5 mL per minute
e.
Phenobarbital sodium 120 mg IV for status epilepticus. May repeat times 3. Give 60 mg per minute
Phenobarbital sodium 120 mg per 3 mL
10 mL syringe
Dilute to 10 mL with SW
10 mL
10 mL over 2 minutes = 5 mL per minute

22. Directions: Calculate the IV medication and infusion rates. Use a calculator for safe dose range calculations, multiplication, and long division as desired. Verify results using DE-style equations where requested. If the order is unsafe, do not proceed with the math. Label answers.

RX: Lanoxin 0.25 mL direct IV

Available: Lanoxin (digoxin) 0.5 mg per 2 mL.

Dilute to 4 mL SW. Give over 5 minutes.

a. How many mL will be given?

b. How many calibrations will the mL occupy on the syringe?

c. Total minutes to administer:

d. Flow rate in seconds per calibration?

ANS:

a. 4 mL SW

b. 20 calibrations

c. 5 minutes

d.

23. How many grams of dextrose are contained in 1 L of a D5W solution?

ANS:

5 g dextrose per 100 mL × 50 g per 1000 mL

24. How many approximate calories of dextrose are contained in 1 L of a D5W solution?

ANS:

50 g dextrose × 4 cal per g = approximately 200 calories

25. What is the purpose of a TPN solution?

ANS:

The purpose of a TPN solution is to provide high-calorie IV nutrition to patients unable to ingest fluids and nutrients through the alimentary tract.

26. What are the typical contents of a TPN solution?

ANS:

The typical contents of a TPN solution are amino acids, electrolytes, glucose, vitamins and minerals. Lipid emulsions may be added to the order.