Dosage and Calculations Math Practice PDF

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Common Conversions: 1 Liter = 1000 Milliliters 1L = 1000 mL 1 Gram = 1000 Milligrams 1g = 1000 mg 1 Milligram = 1000 Micrograms 1 mg = 1000mcg 1 Kilogram = 2.2 Pounds 1 kg = 2.2 lbs

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. I.

Basic Formula: Frequently used to calculate drug dosages. D (Desired dose) H (Dose on hand) V (Vehicle-tablet or liquid) D x V = Amount to Give H 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 po TID Drug available-Dilantin 125 mg/5ml D=50 mg

H=125 mg

V=5 ml

250 50 mg x 5 mL = = 2 ml 125 mg 125

II.

Ratio & Proportion: Oldest method used in calculating dosage.

Known H : V

Desired ::

D

: X

Means Extremes III. IV. V.

Left side are known quantities Right side is desired dose and amount to give Multiply the means and the extremes HX = DV

DV H Example: Order-Keflex 1 gm po BID Drug available-Keflex 250 mg per capsule X=

VIII. IX. X.

D=1 g (note: need to convert to mg) 1 g = 1000 mg H=250 mg V=1 capsule 250mg

:

1cap XI.

XII.

XIII.

::

1000 mg

250X = 1000 1000 X= 250 X = 4 capsules

Fractional Equation H D = V X

XIV.

Cross multiply and solve for X.

:

X cap

H D = V X HX = DV

DV H Example: Order - Digoxin 0.25 mg po QD Drug Available - 0.125 mg per tablet X=

D=0.25 mg

XXII.

H=125 mg

V=1 tablet

0.125 mg 0.25 mg = X tab 1tab XX. 0.125X = 0.25 0.25 X= 0.125 XXI. X = 2 tablets Intravenous Flow Rate Calculation (two methods) Two Step Step 1 - Amount of fluid divided by hours to administer = mL/hr mL/hr x gtts/ml(IV set) Step 2 = gtts/min 60 min One Step Amount of fluid x drops/mL (IV set) Hours to administer x minutes/hour (60) Example: 1000 mL over 8 hrs IV set = 15 gtts/mL Two Step 1000 = 125 8 125 x 15 Step 2 = 31.25 (31 gtts/min) 60 One Step 1000 x 15 15,000 = = 31.25 (31gtts/min) 8 hrs x 60 480 How to Calculate Continuous Infusions Step 1 -

XXIII.

A. mg/min (For example - Lidocaine, Pronestyl) Solution mL x 60 min/hr x mg/min = mL/hr

Drug mg Drug mg x mL/hr = mg/hr Solution mL x 60 min/hr

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

Rule of Thumb NTG 100 mg/250 mL 1 mL/hr = 6.6 mcg/min NTG 50 mg/250 mL 1 mL/hr = 3.3 mcg/min G. mcg/kg/min (For example - Dopamine, Dobutamine, Nipride, etc.) 1. To calculate mL/hr (gtts/min) Solution mL x 60 min/hr x kg x mcg/kg/min = mL/hr Drug mcg Example: Dopamine 400 mg/250 cc D5W to start at 5 mcg/kg/min. Patient’s weight is 190 lbs. 250 mL x 60 min x 86.4 x 5 mcg/kg/min = 16.2 mL/hr 400,000 mcg 4. To calculate mcg/kg/min Drug mcg/ x mL/hr = mcg/kg/min Solution mL x 60 min/hr x kg Example: Nipride 100 mg/250 mL D5W was ordered to decrease the patient’s blood pressure. The patient’s weight is 143 lbs, and the IV pump is set at 25 mL/hr. How many mcg/kg/min of Nipride is the patient receiving?

100,000 mcg x 25 mL/hr 2,500,000 = = 2.5 mcg/kg/min 250 mL x 60 min x 65 kg 975,000 A. How to calculate mcg/kg/min if the rate of the infusion is known Dosage (in mcg/mL/min) x rate on pump = mcg/kg/min Patient’s weight in kg B. For example: 1600 mcg/mL 400mg of Dopamine in 250 mL D5W = 60 min/hr = 26.6 mcg/mL/min C. 26.6 is the dosage concentration for Dopamine in mcg/mL/min based on having 400 mg in 250 mL of IV fluid. This is necessary to calculate this dosage concentration first for all drug calculations. Once this step is done, you can do anything! D. NOW DO THE REST! E. If you have a 75 kg patient for example... 26.6 mcg/mL/min x 10 mL on pump = 3.54 mcg/kg/min Patients’s weight in kg (75 kg) = 3.5 mcg/kg/min (rounded down) F. How to calculate drips in mL/hr when it is known what mcg/kg/min is ordered or desired mcg/kg/min x patient’s weight in kg = rate on pump dosage concentration in mcg/mL/min G. For example: H. 400 mg Dopamine in 250 mL D5W = 26.6 mcg/mL/min 3.5 mcg/kg/min x 75 kg = 9.86 mL 26.6 mcg/mL/min = 10 mL(rounded up) I. ALWAYS WORK THE EQUATION BACKWARDS AGAIN TO DOUBLE CHECK YOUR MATH! J. For example: 10 mL x 26.6 mcg/mL/min = 3.5 mcg/kg/min 75 Kg Dosage (in mcg/mL/min) x rate on pump = mcg/kg/min Patient’s weight in kg L. For example: M. 400mg of Dopamine in 250 mL D5W = 1600 mcg/mL 60 min/hr = 26.6 mcg/mL/min N. 26.6 is the dosage concentration for Dopamine in mcg/mL/min based on having 400 mg in 250 mLof IV fluid. It is necessary to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything! O. NOW DO THE REST!! P. If you have a 75 kg patient for example

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

A. Practice Problems: 1. 2.5 L to mL 2. 7.5 g to mg 3. 10 mg to mcg 4. 500 mg to g 5. 7500 mcg to mg 6. 2800 milliliters to liters 7. 165 lbs to kg 8. 80 kg to lbs B. Practice Problems: Use the method you have chosen to calculate the amount to give. 1. Order-Dexamethasone 1 mg Drug available-Dexamethasone 0.5 mg per tablet 2. Order-Tagamet 0.6 gm Drug available-Tagamet 300 mg per tablet 3. Order-Phenobarbital 60 mg Drug available-Phenobarbital 15 mg per tablet 4. Order-Ampicillin 0.5 gm Drug available-Ampicillin 250 mg/5 mL 5. Order-Dicloxacillin 125 mg Drug Available-Dicloxacillin 62.5 mg/5 mL 6. Order-Medrol 75 mg IM Drug Available-Medrol 125 mg/2 mL 7. Order-Lidocaine 1 mg/kg Patient’s weight is 152 pounds 8. Order- 520 mg of a medication in a 24 hour period. The drug is ordered every 6 hours. How many mg will be given for each dose? C. Practice Problems: IV set 15 gtts/mL Order-1000 mL over 6 hrs 1. 2. Order-500 mL over 4 hrs IV set 10 gtts/mL 3.

Order-100 mL over 20 min.

IV set 15 gtts/mL D. Practice Problems: 1. Dopamine 400 mg in 250 mL D5W to infuse at 5 mcg/kg/min. The patient’s weight is 200 pounds. How many mL/hour should the nurse set the infusion pump?

2. A Dopamine drip (400mg/250 mL of IV fluid) is infusing on an 80 kg patient at 20 mL/hour. How many mcg/kg/min should infuse for this patient? 3. A Nitroglycerin drip is ordered for a patient to control chest pain. The concentration is 100 mg/250 mL D5W. The order is to begin the infusion at 20 mcg/min. At what rate should the nurse begin the infusion on the infusion pump? 4. A Nitroglycerin drip (100mg/250 mL D5W) is infusing on a patient at 28 mL/hour on the infusion pump. How many mcg/min should the patient receive? 5. A procainamide drip is ordered (2g/250 mLD5W) to infuse at 4 mg/min. The patient weighs 165 pounds. Calculate the drip rate in mL/hour for which the infusion pump should be set. 6. A Lidocaine drip is infusion on a 90 kg patient at 22 mL/hour. The Lidocaine concentration is 2 g/250 mL of D5W. How many mg/min should the patient receive?

Summary Many nurses have difficulty with drug calculations. Mostly it is 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 an 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. Remember: if you give it, you are responsible!

Answers to Practice Problems A. Practice Problems 1. 2500 mL 2. 7500 mg 3. 10,000 mcg 4. 0.5 g 5. 7.5 mg 6. 2.8 L 7. 75 kg 8. 176 lbs B. Practice Problems 1. 2 tablets 2. 2 tablets 3. 4 tablets 4. 10 mL 5. 10 mL 6. 1.2 mL 7. 69.1 kg = 69.1 mg 8. 130 mg for 4 doses C. Practice Problems 1. 41.6 (42) 2. 20.8 (21) 3. 75 D. Practice Problems 1. 17 mL/hr 2. 6.65 mcg/kg/min 3. 3 mL 4. 186.5 mcg/min 5. 30 mL/hr 6. 3 mg/min

Reference: Dosage Calculations Made Incredibly Easy! by Springhouse Corporation, 1998...