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The Center for Nursing Excellence
Calculations of Drug Dosages and Solutions
Directions:
This learning has been compiled to assist nurses who will be taking the Medication and
Drug Calculation Test. You will need to achieve 88% on this test prior to administering
medications at Brigham and Women’s Hospital (BWH). You will be able to use a
calculator.
Learning Objectives:
1.
Identify BWH approved abbreviations*
2. Calculate drug dosages utilizing the metric system.
3. Determine the amount of the drug needed to administer the amount of drug ordered.
4. Identify the principles of conversion and use a conversion table.
5. Calculate the infusion rate of an IV solution.
6. Identify common drug scenarios.
*All abbreviations are found online in the BWH Hospital Policy Manual.
ABBREVIATIONS of COMMONLY USED IN MEDICATION ORDERS
(See Comprehensive List online in the BWH Hospital Policy Manual)
a.c.
ad lib
gm
IM
IV
L
mcg
mL
NKA
NKDA
before meals
as desired
gram
intramuscular
intravenous
liter
micrograms
milliliter
no known allergies
no known drug allergies
N/V/D
oz
pc
p.r.
p.r.n.
stat
sc
2
nausea, vomiting, diarrhea
ounce
after meals
by rectum
whenever necessary
immediately
subcutaneous
CONVERSION EQUIVALENTS
1 kg = 2.2 pounds
To convert kg to lbs: multiply (x) kg by 2.2
60 kg x 2.2 = 132 lbs
Note: DO NOT round off these values
To convert lbs to Kg: divide (:) lbs by 2.2
155 lbs : 2.2 = 70.45 kg Note: DO NOT round off these values
30 mL = 1 oz
To convert ounces to milliliters:
To convert milliliters to ounces:
multiply(x) ounces by 30
8 oz x 30 = 240 mL
divide (:) milliliters by 30
360 mL : 30 = 12 oz
1000 mL = 1 liter
1 gm = 1000 milligrams
To convert grams to milligrams:
To convert milligrams to grams:
multiply (x) grams by 1000
0.2 (grams) x 1000 = 200 mg
divide (:) milligrams by 1000
2500 (mg) : 1000 = 2.5 grams
1 mg = 1000 micrograms
To convert milligrams to micrograms:
To convert micrograms to milligrams:
multiply (x) milligrams by 1000
750 (mg) x 1000 = 750000 micrograms
divide (:) micrograms by 1000
20000 (micrograms) : 1000 = 20 mg
TIME CONVERSION
To convert US standard to international time:
AM: omit colon and AM
example: 8:45AM = 0845
PM: omit colon and PM add 1200
example: 7:50 PM= 750+1200 = 1950
To convert international time to US standard:
AM: insert colon and AM
example: 0207=2:07AM
PM: subtract 1200, insert colon and PM
example: 2125 = 2125 – 1200 = 9:25 PM
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SOLVING DRUG DOSAGE PROBLEMS
1. Dosage problems that you encounter in the hospital may be set up in the form of a simple equation
in which you must determine the value of “x”.
‘D’ = Desired – the dosage you wish to give.
‘H’ = Have – the dosage strength available.
‘Q’ = Quantity of the preparation.
‘x’ = unknown. The amount one must give to obtain the desired dosage.
DxQ=x
H
Example:
The physician orders Digoxin® 0.125 mg.
The drug label reads ‘Digoxin® 0.25 mg.
How much would you give the patient?
D = 0.125mg x 1 tablet =
H = 0.25 mg
0.125 x
0.25
1
=
0.5 tablet
2. Problems may also be solved using the proportion method. In proportion the product of the means
equals the product of the extremes. It is very important to set up the equation properly and to
remember that the means are in the inner numbers and the extremes are the outer numbers. In the
example above the problem would be set up in this manner.
a.
Set up what you KNOW then what is UNKNOWN 0.25 mg : 1 tab :: 0.125 mg : x tab
b. Multiply means and extremes
c. Solve for x by dividing (:)
1 x 0.125 = 0.125
and
0.25 x x tab = 0.25x
0.125 : 0.25 = 0.5
d. Answer
0.5 tab
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CALCULATONS OF FRACTIONAL DOSAGE
Medications are manufactured in various forms; solid drug forms such as tablets and capsules and liquid
forms such as aqueous solutions (syrups), aqueous suspensions (mixtures and emulsions), and alcohol
solutions (elixirs, tinctures and extracts). When computing the correct dosage of a medication, one must
determine the amount of the drug form needed to administer the volume of drug ordered.
1.
Colace® is available in 100 mg capsules. The basic vehicle for Colace® is one capsule, each of
which carries 100 mg of the drug. The amount of drug is usually obvious when the solid forms of
capsules or tablets are the vehicles. However, some people have difficulty perceiving that the
liquid vehicle measure of ‘mL’ should be treated in the same fashion as the solid drug vehicles.
Example: Morphine is available in 30 mL vials, with each mL of volume containing 1 mg of
morphine. If a physician orders 2 mg to be administered, the correct amount to be given is 2 mLs
(SEE SOLVING DRUG DOSAGE PROBLEMS page 4).
2. In multiple-dose vials, the powder to be dissolved often adds to the final total volume of the liquid
in the vial. When this is the case, the label indicates the amount of solution to use to dissolve the
powder volume factor. Example: If a vial contains 1 gm of Cefazolin® powder and you are to
give 500 mg IM, you must first dissolve the powder in sterile water. This label states “Dissolve
powder in 2.5 mL. Total volume will equal 3 mL”. This vial should then contain 1000mg/3L.
You will need to administer 1.5 mL.
MEDICATIONS REVIEW
The test includes but is not limited to the following drugs. You are encouraged to review them.
•
Dilantin®
•
Insulin
•
Coumadin®
•
Heparin
•
Digoxin®
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CALCULATION OF INTRAVENOUS FLOW RATE
When electronic device is not used
1. The eye of the dropper greatly influences the actual number of drops required to move 1 mL
of fluid into the drip chamber. The label on the tubing box will indicate the dropper capacity
of the specific tubing used. The calibration of IV tubing in gtt/mls is known as the drop factor.
Common macrodrop factors are 10 gtt/mL, 15gtt/mL, 20gtt/mL and the common microdrop
factor is 60gtt/mL.
2. Determine drip capacity by choosing the microdrop chamber or macrodrip chamber. If you
are infusing under 60 mL/hr, then choose a micro or mini drip set which delivers 60gtt/mL.
3. To calculate the gtt of IV solution that should be administered per minute, you need to
calculate the amount of fluid to be delivered per hour, the number of drops to be administered
per hour and then the drops per minute. To calculate the mL that should be delivered in 1hour, divide the total fluid volume ordered by the number of hours over which the fluid is to be
infused.
Formula states: gtt/min = amount of solution (mL) multiply by drop factor then divide by
infusion time in minutes
You are to administer 1000 mL NS in 5 hours using a 10 gtt/mL drop factor.
How many mL/hr are needed? 1000mL : 5hrs = 200mL/hr
How many gtt/minute?
200 mL/hr x 10 gtt/mL = 2000 drops/hr
2000drops/hr : 60 min = 33.333333 drops/min
•
If decimal answer is <0.50: Round DOWN
•
If decimal answer is >0.51: Round UP
•
Otherwise it will be incorrect. You CANNOT measure or count one third of a drop!
You are to administer 2000 mL D5W in 10 hours using a 15 gtt/min drop factor.
How many mL/hr are needed? 2000mL : 10 hrs
How many drops per minute are needed?
2000 mL : 10 hr = 200 mL/hr
200 mL/hr x 15 gtt/mL
=
3000 drops/hr : 60 min
=
3000 drops/hr
50 drops/min
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COMMON DRUG SITUATIONS
1.
Drugs are also ordered for patients based on dose per kg. per minute. These drugs include
Nipride®, Dopamine® and Dubutamine®, among others. Example: Dr. orders Dopamine®
2 mcg/kg/min. The solution available is 400 mg in 250 mL D5W. The patient weights 150 lbs.
How many micrograms do you administer per minute?
a) Convert the patient’s weight to kg. 150 lbs : by 2.2 = 68.18 kg
b) Determine dose per minute. 2 mcg x 68.16 kg = 136.36 mcg/min
2.
The common heparin drip mix at Brigham and Women’s Hospital is 25000 units in
250 mL D5W. Therefore, 100 units are equal to 1 mL.
Example: Dr. orders 1400 units per hour IV. How many mL’s are administered?
a) Set up known and unknown:
25000 units : 250 mL :: 1400 units : x mL
b) Multiply means and extremes:
250 x 1400 = 350000
c) Solve for X:
350000 : 25000 = 14
d) Answer:
and 25000 x x mL = 25000x
14 mLs
3. When administering a mixture of short acting (Regular) and long acting insulin, the short acting
(clear) insulin is always withdrawn from the vial first. Remember “Clear then Cloudy”. Only
Regular insulin may be administered IV. Insulin drips expire in 24 hours. Verify ALL insulin
doses with a 2nd nurse.
4. Amphotericin® IV, a systemic antifungal, is only compatible in D5W. premedication with
acetaminophen and diphenhydramine is common. An infusion may produce ‘rigors’, shaking
chills, which can be controlled with meperidine IVB. Blood should not be administered
concurrently.
5. Dilantin® must be administered only in Normal Saline through a 0.22 micron filter.
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6. Amiorodone®, used for ventricular and supraventricular dysrrhythmias, must be given diluted and
in a glass bottle, through a dedicated central line.
7. Maximum acetaminophen dose per day 4000 mg. Watch combination drugs such as Percocet®,
which contains oxycodone® with acetaminophen.
8. Intravenous Gamma Globulin is not compatible with ANY other drug. It is recommended that it
NOT be administered within 2 hours after receiving a blood product. Patient’s weight must be
known in kilograms. Patient should receive premedications of acetaminophen and
diphenhydramine 30 minutes prior to infusion. Use appropriate filter with corresponding brand of
Immune Globulin. Frequent vital signs are required.
FOLLOW DRUG ADMINISTRATION GUIDELINES CLOSELY!
IMPORTANT NOTE: All medication policies can be accessed in the Clinical Practice Manual and the
Drug Administration Guidelines (DAG).
Calculating Percentages in Relationship to Time
Example: How long will it take 925 mL to infuse if it is running at 75 mL/hr?
Divide 925 by 75 = 12.33
Caution: that is NOT the final answer. It is incorrect to leave it at that.
You must calculate what percentage .33 is of one hour.
Multiply .33 (the percentage) by 60 (minutes) .33 x 60 = 19.8
then divide by 100
19.8 : 100 = 0.198 or 20 minutes
So, final answer is 12 hours and 20 minutes.
8
PRACTICE PROBLEMS
Follow directions in each section below. You may answer problems directly in space provided you may
use a calculator. Double check all of your work.
1. Identify the following abbreviations.
a) IM ____________________
d) mL___________________
b) IV_____________________
e) a.c.___________________
c) stat ___________________
f) mg.___________________
2. Complete the following equivalents.
a) 10 cc = ___________mL d) 500 mg = __________ gm
b) 0.2 gm = _________ mg e) 1 kg. = _____________lbs
c) 30 mL = __________oz
f) 0.5 liter = __________ mL
3. Order states: Pentobarbital® 150 mg IM X 1 now. Drug available is Pentobarbital® 150 mg per 1
mL. How many milliliters would you give?
4. Order states: Tetracycline® 0.5 gm p.o. twice a day. Drug available is 250 mg per tablet.
How many tablets would you give in 24 hours?
5. Order states: Morphine Sulfate 5 mg IVB q2h. Drug is available in 15 mg/mL multi-dose vial.
How many milliliters would you give per dose?
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6. Order states: NS IV @ 50 mL / hr x 24 hours. No infusion pumps are available. Using a
microdrip chamber (60 drops per mL), how many drops per minute will the patient receive? How
many milliliters in 12 hours?
7. Order states: Heparin 2500 units subcutaneous daily. Drug is available in 10,000 Units per mL.
How many milliliters would you give? What needle gauge would you use?
8. Order states: Regular insulin U-100 18 Units subcutaneous and NPH U-100
40 Units subcutaneous each morning.
How many total Units do you administer?
Which do you withdraw first?
Which syringe is better suited for this patient?
A.
B.
9. Order states: NS IV 3 liters over 24 hours. How much will the patient have received in 11 hours?
What would a pump be set at?
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10. Order states: Dopamine® 400 mg in 250 mL D5W administer 5 mcg/kg/min IV.
How many mL/hr will you administer?
11. Order above unable to compute without patient’s weight. You weight the patient and find she is
192 lbs. How many mcg/hr will you administer?
12. Order states: Half strength Jevity® at 60 cc/hr via NG tube. How many mL’s of Jevity® will you
need for the next 4 hours?
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ANSWERS TO PRACTICE QUESTIONS
1. Abbreviations
a) Intra-muscular
d) milliliters
b) Intra-venous
e) before meals
c) Immediately
f) milligrams
2. Equivalents
a) 10 mL
d) 0.5 grams
b) 200 mg
e) 2.2 lbs
c) 1 oz
f) 500 mL
3. 1 mL
4. 4 tablets
5. 0.33 mLs
6. 50 drops per minute. 600 mLs in 12 hours
7. 0.25 mLs. 25G needle
8. 58 units. Regular Insulin, clear. B) 100 units syringe
9. 1375 mL in 11 hours. 125 mL
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10. Insufficient information
11. Patient’s wt 87.27 kg. 436.35/min. 26181 mcg/hr.
12. 120 mL Jevity® and 120 mL of water
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