Common Conversions:

1 Liter = 1000 Milliliters
1 Gram = 1000 Milligrams
1 Milligram = 1000 Micrograms
1 Kilogram = 2.2 pounds

Methods of Calculation

Any of the following three methods can be used to perform drug calculations. Please review all three methods and select the one that works for you. It is important to practice the method that you prefer to become proficient in calculating drug dosages.

Remember: Before doing the calculation, convert units of measurement to one system.

  1. Basic Formula:Frequently used to calculate drug dosages.

D (Desired dose)

H (Dose on hand)

V (Vehicle-tablet or liquid)

D
H / x V = Amount to Give

D = dose ordered or desired dose

H = dose on container label or dose on hand

V = form and amount in which drug comes (tablet, capsule, liquid)

Example: / Order-Dilantin 50 mg p.o. TID
Drug available-Dilantin 125 mg/5ml
D=50 mg / H=125 mg / V=5 ml
50
125 / x 5 = / 250
125 / = 2 ml
  1. Ratio & Proportion:Oldest method used in calculating dosage.

Known / Desired
H / : / V / :: / D / : / X
Means
Extremes
  1. Left side are known quantities
  2. Right side is desired dose and amount to give
  3. Multiply the means and the extremes

HX = DV
X = / DV
H
Example: / Order-Keflex 1 gm p.o. BID
Drug available-Keflex 250 mg per capsule
  1. D=1 gm (note: need to convert to milligrams)
    1 gm = 1000 mg
  2. H=250 mg
  3. V=1 capsule

250 / : / 1 / :: / 1000 / : / X
  1. 250X = 1000

X = / 1000
250
  1. X = 4 capsules
  2. Fractional Equation

H
V / = / D
X
  1. Cross multiply and solve for X.

H
V / = / D
X
HX = DV
X = / DV
H
Example: / Order - Digoxin 0.25 mg p.o. QD
Drug Available - 0.125 mg per tablet
D=0.25 mg / H=0.125 mg / V=1 tablet
0.125
1 / = / 0.25
X
  1. 0.125X = 0.25

X = / 0.25
0.125
  1. X = 2 tablets
  1. Intravenous Flow Rate Calculation(two methods)

Two Step

Step 1 - Amount of fluid divided by hours to administer = ml/hr

Step 2 - / ml/hr x gtts/ml(IV set)
60 min / = gtts/min

One Step

amount of fluid x drops/milliliter (IV set)
hours to administer x minutes/hour (60)
Example: / 1000 ml over 8 hrs
IV set = 15 gtts/ml

Two Step

Step 1 - / 1000
8 / = 125
Step 2 - / 125 x 15
60 / = 31.25 (31 gtts/min)

One Step

1000 x 15
8 hrs x 60 / = / 15,000
480 / = 31.25 (31gtts/min)
  1. How to Calculate Continuous Infusions
  1. mg/min (For example - Lidocaine, Pronestyl)

Solution cc x 60 min/hr x mg/min
Drug mg / = cc/hr
Drug mg x cc/hr
Solution cc x 60 min/hr / = mg/hr
Rule of Thumb
Lidocaine, Pronestyl
2 gms/250 cc D5W
1 mg = 7 cc/hr
2 mg = 15 cc/hr
3 mg = 22 cc/hr
4 mg = 30 cc/hr
  1. mcg/min (For example - Nitroglycerin)

Solution cc x 60 min/hr x mcg/min
Drug mcg / = cc/hr
Drug mcg x cc/hr
Solution cc x 60 min/hr / = mcg/hr
Rule of Thumb
NTG 100 mg/250 cc
1 cc/hr = 6.6 mcg/min
NTG 50 mg/250 cc
1 cc/hr = 3.3 mcg/min
  1. mcg/kg/min (For example - Dopamine, Dobutamine, Nipride, etc.)
  1. To calculate cc/hr (gtts/min)

Solution cc
Drug mcg / x 60 min/hr x kg x mcg/kg/min = cc/hr
Example: / Dopamine 400 mg/250 cc D5W to start at 5 mcg/kg/min.
Patient’s weight is 190 lbs.
250 cc
400,000 mcg / x 60 min x 86.4 x 5 mcg/kg/min = 16.2 cc/hr
  1. To calculate mcg/kg/min

Drug mcg/ x cc/hr
Solution cc x 60 min/hr x kg / = mcg/kg/min
Example: / Nipride 100 mg/250 cc D5W was ordered to decrease your patient’s blood pressure.
The patient’s weight is 143 lbs, and the IV pump is set at 25 cc/hr. How many mcg/kg/min of Nipride is the patient receiving?
100,000 mcg x 25 cc/hr
250 cc x 60 min x 65 kg / = / 2,500,000
975,000 / = 2.5 mcg/kg/min
  1. How to calculate mcg/kg/min if you know the rate of the infusion

Dosage (in mcg/cc/min) x rate on pump
Patient’s weight in kg / = mcg/kg/min
  1. For example:

400mg of Dopamine in 250 cc D5W = / 1600 mcg/cc
60 min/hr
= / 26.6 mcg/cc/min
  1. 26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!
  2. NOW DO THE REST!
  3. If you have a 75 kg patient for example...

26.6 mcg/cc/min x 10 cc on pump
Patients’s weight in kg (75 kg) / = 3.54 mcg/kg/min
= 3.5 mcg/kg/min (rounded down)
  1. How to calculate drips in cc per hour when you know the mcg/kg/min that is ordered or desired

mcg/kg/min x patient’s weight in kg
dosage concentration in mcg/cc/min / = rate on pump
  1. For example:
  2. 400 mg Dopamine in 250 cc D5W = 26.6 mcg/cc/min

3.5 mcg/kg/min x 75 kg
26.6 mcg/cc/min / = 9.86 cc
= 10 cc rounded up
  1. ALWAYS WORK THE EQUATION BACKWARDS AGAIN TO DOUBLE CHECK YOUR MATH!
  2. For example:

10 cc x 26.6 mcg/cc/min
75 Kg / = 3.5 mcg/kg/min
Dosage (in mcg/cc/min) x rate on pump
Patient’s weight in kg / = mcg/kg/min
  1. For example:
  2. 400mg of Dopamine in 250 cc D5W = 1600 mcg/cc 60 min/hr = 26.6 mcg/cc/min
  3. 26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!
  4. NOW DO THE REST!!
  5. If you have a 75 kg patient for example

26.6 mcg/cc/min x 10 cc on pump
Patients’s weight in kg (75 kg) / = 3.54 mcg/kg/min

Now do some practice exercises to check what you learned

  1. Practice Problems:
  2. 2.5 liters to milliliters
  3. 7.5 grams to milligrams
  4. 10 milligrams to micrograms
  5. 500 milligrams to grams
  6. 7500 micrograms to milligrams
  7. 2800 milliliters to liters
  8. 165 pounds to kilograms
  9. 80 kilograms to pounds
  10. Practice Problems: Use the method you have chosen to calculate the amount to give.
  11. Order-Dexamethasone 1 mg
    Drug available-Dexamethasone 0.5 mg per tablet
  12. Order-Tagamet 0.6 gm
    Drug available-Tagamet 300 mg per tablet
  13. Order-Phenobarbital 60 mg
    Drug available-Phenobarbital 15 mg per tablet
  14. Order-Ampicillin 0.5 gm
    Drug available-Ampicillin 250 mg per 5 ml
  15. Order-Dicloxacillin 125 mg
    Drug Available-Dicloxacillin 62.5 mg per 5 ml
  16. Order-Medrol 75 mg IM
    Drug Available-Medrol 125 mg per 2 ml
  17. Order-Lidocaine 1 mg per kg
    Patient’s weight is 152 pounds
  18. Order- 520 mg of a medication in a 24 hour period. The drug is ordered every 6 hours.
    How many milligrams will be given for each dose?
  19. Practice Problems:

  1. Order-1000 ml over 6 hrs
  2. Order-500 ml over 4 hrs
  3. Order-100 ml over 20 min.
/ IV set 15 gtts/ml
IV set 10 gtts/ml
IV set 15 gtts/ml
  1. Practice Problems:
  2. Dopamine 400 mg in 250 cc D5W to infuse at 5 mcg/kg/min. The patient’s weight is 200 pounds. How many cc/hour would this be on an infusion pump?
  3. A Dopamine drip (400mg in 250 cc of IV fluid) is infusing on your 80 kg patient at 20 cc/hour. How many mcg/kg/min are infusing for this patient?
  4. A Nitroglycerin drip is ordered for your patient to control his chest pain. The concentration is 100 mg in 250 cc D5W. The order is to begin the infusion at 20 mcg/min. What is the rate you would begin the infusion on the infusion pump?
  5. A Nitroglycerin drip (100mg in 250 cc D5W) is infusing on your patient at 28 cc/hour on the infusion pump. How many mcg/min is your patient receiving?
  6. A procainamide drip is ordered (2gms in 250 cc D5W) to infuse at 4 mg/min. The patient weighs 165 pounds. Calculate the drip rate in cc/hour for which the infusion pump will be set at.
  7. A Lidocaine drip is infusion on your 90 kg patient at 22 cc/hour. The Lidocaine concentration is 2 grams in 250 cc of D5W. How many mg/min is your patient receiving?

Summary

Many nurses have difficulty with drug calculations. Mostly because they don’t enjoy or understand math. Practicing drug calculations will help nurses develop stronger and more confident math skills. Many drugs require some type of calculation prior to administration. The drug calculations range in complexity from requiring a simple conversion calculation to a more complex calculation for drugs administered by mcg/kg/min. Regardless of the drug to be administered, careful and accurate calculations are important to help prevent medication errors. Many nurses become overwhelmed when performing the drug calculations, when they require multiple steps or involve life-threatening drugs. The main principle is to remain focused on what you are doing and try to not let outside distractions cause you to make a error in calculations. It is always a good idea to have another nurse double check your calculations. Sometimes nurses have difficulty calculating dosages on drugs that are potentially life threatening. This is often because they become focused on the actual drug and the possible consequences of an error in calculation. The best way to prevent this is to remember that the drug calculations are performed the same way regardless of what the drug is. For example, whether the infusion is a big bag of vitamins or a life threatening vasoactive cardiac drug, the calculation is done exactly the same way.

Many facilities use monitors to calculate the infusion rates, by plugging the numbers in the computer or monitor with a keypad and getting the exact infusion titration chart specifically for that patient. If you use this method for beginning your infusions and titrating the infusion rates, be very careful that you have entered the correct data to obtain the chart. Many errors take place because erroneous data is first entered and not identified. The nurses then titrate the drugs or administer the drugs based on an incorrect chart. A method to help prevent errors with this type of system is to have another nurse double check the data and the chart, or to do a hand calculation for comparison. The use of computers for drug calculations also causes nurses to get “rusty” in their abilities to perform drug calculations. It is suggested that the nurse perform the hand calculations from time to time, to maintain her/his math skills.

Answers to Practice Problems

  1. Practice Problems
  2. 2500 mL
  3. 7500 mg
  4. 10,000 mcg
  5. 0.5 gm
  6. 7.5 mg
  7. 2.8 L
  8. 75 kg
  9. 176 lbs
  10. Practice Problems
  11. 2 tablets
  12. 2 tablets
  13. 4 tablets
  14. 10 mL
  15. 10 mL
  16. 1.2 mL
  17. 69 kg = 69 mg
  18. 130 mg for 4 doses
  19. Practice Problems
  20. 41.6 (42)
  21. 20.8 (21)
  22. 75
  23. Practice Problems
  24. 17 cc/hr
  25. 6.65 mcg/kg/min
  26. 3 cc
  27. 186.5 mcg/min
  28. 30 cc/hr
  29. 3 mg/min