1. DOSAGE CALCULATIONS USED IN INTRAVENOUS THERAPY
SELF STUDY GUIDE
DOSAGE CALCULATIONS USED IN INTRAVENOUS THERAPY

2. Dosage Calculations used in IV Therapy
TASK: Be able to accurately calculate medication dosages. CONTEXT: A shocking number of patients die every year in United States hospitals as the result of medication errors, and many more are harmed. One widely cited, if questionable, estimate (Institute of Medicine, 2000) places the toll at 44,000 to 98,000 deaths, making death by medication "misadventure" greater than all highway accidents, breast cancer, or AIDS. If this estimate is in the ballpark, then nurses (and patients) beware: Medication errors are the fourth to sixth leading cause of death in America. How many medication errors are miscalculation errors? No one really knows since by some estimates as little as one in ten errors are reported (Pepper, 2002). Of reported errors one FDA study (Thomas, et. al., 2001) found that 7% were due to "miscalculation of dosage or infusion rate." Combining this estimate with the estimate for total deaths, as many as 3,000 to 6,800 deaths are caused annually by medication math errors. This would mean that in the average hospital one patient dies every year or two because someone makes a miscalculation, and one or two patients are sub-lethally harmed each month. As future nurses, then, there is a distinct possibility that we will harm, or even cause the death of, a patient over the course of our career. The time to build confidence is while you are students. I suggest that as a conscientious students you should aim for 95% or better. You should, then, carefully study, learn from, and thereby avoid repeating what mistakes you do make, so that by the time you are working in the real world you can be confident that, if you are vigilant enough, you can approach 100% proficiency. Since "to err is human," you will always be at risk of not achieving a goal of 100% proficiency, but you cannot aim for less, and knowing that you are always at risk will make you extremely careful.

3. To demonstrate that you have mastered this Self Study you must be able to:
Accurately calculate medication dosages.
Show your work.
Mastery Tests Required:
Complete all of the assignments in the self study guide.
Complete and hand in final assignment.
3. All of the above are graded on a “Pass/Fail” basis.

4. IV Dosage Calculations They are easier than you think!
IV dosage calculations are of the upmost importance if you are planning on working in the medical field.

5. IV DOSEAGE CALCULATIONS
There are 3 different ways to do dosage calculations.
1. Ratio and Proportion format.
2. Formula format.
3. Dimensional Analysis format.
No one way is correct, they all are. So find the format that works for you and stick with it.

6. 1. RATIO AND PROPORTION
A ratio is composed of two numbers that are related to each other. In health care,
medications are often expressed as a ratio. For example:
• 125 mg/ 1 tablet or 125 mg : 1 tablet, read as 125 mg per 1 tablet
• 350 mg / 5 tablets or 350 mg : 5 tablets, read as 350 mg per five tablets
• 250 mg / 10 mL or 250 mg : 10 mL, read as 250 mg per 10 mL
A proportion shows two ratios that are equal, like this:
Sample Problem Proportion is often used to calculate a dosage. Suppose a drug comes in tablets of 150mg. The dosage ordered is 375mg. How many tablets are needed? Here is the problem:

7. RATIO & PROPORTION To solve for X, we have to cross-multiply:
X = 2.5 tablets

8. NOW YOU TRY SOME…….
RATIO/PROPORTION PROBLEMS
The order is for 80 mg Amoxicillin IM. The vial of the medication is labeled 100 mg/mL. How many mL will you give?
2. You are ordered to give a patient 250 mg Keflin. The bottle says to add 9.5cc of sterile water to the vial to yield 0.5 g/cc. How many cc's will you give?
3. The order is for 100,000 Units penicillin. The penicillin on hand is labeled 250,000 Units/mL. How much of the drug will you administer?

9. 4. Order: Demerol 75 mg IM q 3-4 hours prn
4. Order: Demerol 75 mg IM q 3-4 hours prn. Available is Demerol mg/mL. What is the maximum mL's of Demerol the patient might receive during your 12 hour shift?
5. The doctor ordered Ampicillin 300mg/kg/day for your patient and has ordered the medication TID. How many mg per dose would you administer to a 59 lb. patient?
6. How much would you draw up if a 70 mEq dosage is to be added to an IV from the stock solution of 200mEq/10cc?
7. The label reads 250mcg/mL and the order is for 0.6 mg. How many mL’s will be administered?

10. 8. You are asked to prepare a 300 mcg dose. The medication is labeled 0.4mg/ ml How many ml will you need for the prescribed dose?
9. The patient is receiving an antibiotic IV at the rate of 50mL/hr. The IV solution contains 1.5g of the antibiotic in 1000 mL. Calculate the mg/hr given
10. The order is: 25 mcg/kg/min. The patient weighs 44 kg. How many mg of medication will the patient receive in one hour? Per day?
11. An IV medication of 235 mL is to infuse at the rate of 60 mL/hr. What is the total infusion time?
12. An IV of 550 mL infused in 638 minutes. The IV infused at ______ mL/hr.

11. RATIO/PROPORTION PROBLEM SET - ANSWERS
0.8 ml
0.5 cc
0.4 ml
6 mL (range mL)
2700 mg per dose
3.5 cc ml
0.75 mL
75 mg/hr
66 mg/hr, 1584 mg/day
3 hr 55 min
51.7 mL/hr
If you answer 2 or more incorrect, go back and re-read the previous section and re-take the test. Otherwise, proceed on to the next section.

12. Formula Format ABOUT IV FLOW RATE
You may see flow rates expressed in different ways, using different names for the basic factors, but remember this ONE basic formula!

13. Here are some of the other factor names you might see.

14. RULES FOR CALCULATIONS USING THE FLOW RATE FORMULA
1. Identify the values of the three factors in the given data. You may need to use intermediate steps to determine these. 2. Plug them into the appropriate spots in the formula 3. DO THE MATH! 4. Generally for IV drips, the flow rate should be rounded to a whole number. There are no partial drops (gtts)! Some critical care IV pumps can drip at a tenth (0.1) of a drip and syringe dosages can be rounded to a tenth (usually a tenth of a mL). However, when solving flow rate problems, round to a whole number unless you are specifically told otherwise.

15. Sample Problem #1: Solve for Flow Rate The order is to infuse 250 mL of NS in 100 minutes. The set is 15 gtts/mL. What is the flow rate?

16. Sample Problem #2: Solve for Volume
The order is for an IV of D5W to infuse at 35 gtts/min for 4 hours. If the set is 20 gtts/mL, what volume will infuse?

17. Sample Problem #3: Solving for Time
A doctor orders 2 liters of 0.9% NS to infuse at 75 mcgtts/min. How long will it take to infuse the whole 2 liters? Remember: if the flow rate is in mcgtts/minute, use a microdrop set of 60 gtt/mL.
75 x = 2000 * 60
75 x = 120,000
x = 1600 minutes
1600 minutes = hours, or 26 hrs. 40 min

18. MATH IV FLOW RATE PROBLEM SET
1. The patient is to receive heparin at 1500 Units per hour. The IV contains 25,000 Units in 250 mL of D5W. Find the rate in mL/hr. 2. The order is for 125 mg Aldomet given q 6hr IVPB. The medication is diluted in 100cc of 5% dextrose. Using 60 μgtts/mL set, find the flow rate to deliver the volume in two hours. 3. Order is for Keflex 500 mg IVPB q 6 hrs for a 19 kg child. The pharmacy sends you Keflex 500 mg in 50 mL NS. What would the flow rate be if it is delivered over 30 minutes with a microdrip set? The safe child dosage is mg/kg/da. Is the dosage you have calculated a safe dosage ? 4. If an IV ran for 7 hours and 30 minutes, how much volume was given if there was a 15 gtts/mL set and the flow rate was 80mL/hr? 5. You are to set the IV pump to deliver 300 cc over 6.5 hours. What cc/hr rate would you set? 6. The order is for Penicillin G 775,000 Units q 4 hrs for a child. The Penicillin on shelf is 250,000 Units/ml. The recommended time to infuse is 30 minutes. What mL/hr will you set the IV pump at? 7. The order is for Dobutamine 250mg/250cc. The doctor wants the medication delivered at 3.5mcg/kg/min. The patient weighs 154 lbs. Using an IV pump, determine the flow rate in mL/hr. 8. The patient's IV has Dopamine 200 mg in 250 mL D5W. The drip must run at 8 mcg/kg/min and your patient weighs 66 kg. What will the rate of mL/hr be?

19. ANSWER KEY IV FLOW RATE PROBLEMS 1. 15 mL/hr 2. 50 μgtts/min
gtts/min. Dose is safe. mL
5. 46 cc/hr
mL/hr
mL/hr, or 15 mL/hr if necessary to round
mL/hr, or 32 mL/hr if necessary to round

20. COMPLETE SOLUTIONS FOR THE TWO IV FLOW RATE PROBLEMS IN SET
3. Order is for Keflex 500 mg IVPB q 6 hrs for a 19 kg child. The pharmacy sends you Keflin 500 mg in 50 mL NS. What would the flow rate be if it is delivered over 30 minutes with a microdrip set? The safe child dosage is mg/kg/day.
Flow rate solution:
Is this a safe dosage?
• The safe dosage is mg/kg/day.
• For this patient's weight of 19 kg, the safe dose would be mg/day.
• The order is for 500 mg q 6 hr, which equals 2000 mg/day.
• The dose is safe.

21. COMPLETE SOLUTIONS FOR THE TWO IV FLOW RATE PROBLEMS IN SET
8. The order is for Dobutamine 250mg/250cc. The doctor wants the medication delivered at 3.5 mcg/kg/min. The patient weighs 154 lbs. Using an IV pump, determine the flow rate in mL/hr.
If the IV pump cannot be calibrated to .1 mL, the answer should be rounded to 15 mL/hr
If you answer 2 or more incorrect, go back and re-read the previous section and re-take the test. Otherwise, proceed on to the next section.

22. DIMENSIONAL ANALYSIS FORMAT
So what someone figured out is that you don't need formulas at all. For every problem you can just take the factors associated with it and arrange them so all the units you don't want cancel out. You're then left with only the units you do want (the ones in your answer). This process is fairly trivial, and with only slight attention to detail, you always get the right answer, bing-bang-boom, every time.

23. DIMENTIONAL ANALYSIS
The technique has been taught to students for longer than anyone has been able to determine and for the sole reason that students using it make fewer mistakes. You pay attention to the units of measure and if they're not canceling out right, you know that you're doing something wrong and that your answer is guaranteed to be wrong.

24. DIMENTIONAL ANALYSIS
While mistakes can still be made using any technique, dimensional analysis does the best job of minimizing them. The only fault lies in the name. Perhaps the Math-Weenie-No-Brainer technique would be more appropriate. At any rate, give dimensional analysis a try.

25. DIMENSIONAL ANALYSIS
There are, as is often noted, more than one technique for doing med-math problems. If the one you are using works for you, then don't read any further. If, however, med-math is still a bit of a struggle, consider using the technique preferred by chemists, physicists, and engineers for decades called, somewhat intimidatingly, "dimensional analysis" hereafter referred to as "DA."
Advantages include:
• One technique, not several
• Works with all problems
• No formulas to know, look up, or apply
• Problems are not solved piecemeal, but in one step
• You get to the right answer quicker—less error prone
• All calculations done at one time; no rounding errors
• You focus only on units of measure, not numbers, so math phobics can rejoice
• Stepwise approach makes solving almost all problems a virtual no-brainer

26. DIMENTIONAL ANALYSIS IV DRIP RATE USING DIMENTIONAL ANALYSIS
You are to administer lidocaine at a rate of 2 mg/min to a patient with an arrhythmia. You have a vial of Lidocaine that contains 1 g in 5 mL. You also carry a 250 mLbag of Normal Saline. Your administration set is a microdrip with a rate of 60 gtts/mL. How many drops/min will you set your IV set to drip?
Step 1:Organize the information.
Order:2 mg lidocaine/min IV
On Hand:1 g lidocaine/5 mL
Bag:250 mLNS
Admset:60 gtt/mL
Looking for:gtt/min

27. DIMENSIONAL ANALYSIS

28. DIMENSIONAL ANALYSIS Here is another step-by-step example of DA
The patient weighs 73 kg. The MD orders dopamine at 3 mcg/kg/min. The dopamine is mixed as 400 mg in 250 mL of solution. What is the infusion rate in mL/hr?
First you focus on what units of measure you want in the answer. In this problem we are kindly given "mL/hr." We are also given that there are 400 mg dopamine in 250 mL (or 400 mg/250 mL), but also that in 250 mL there are 400 mg dopamine (or 250 mL/ 400 mg). It is important to realize that factors can be turned over or inverted as needed.
The other important bit to realize in order to do DA is that 3 mcg/kg/min can also be written as 3 mcg/(kg x min). This may seem a little weird, but if asked to divide 1/4 by 2 you have 1/4/2. But dividing is the same as inverting and multiplying, so inverting 2 to get 1/2 and multiplying you have 1/4 x 1/2, or 1/(4 x 2), or 1/8. Another example is acceleration, which is measured in ft/sec/sec. This can be written as ft/(sec x sec) or, more familiarly, as ft/sec2.
Since you want "mL" on top in your answer you won't go wrong starting with 250 mL/400 mg as a logical starting factor.
250 Ml
400 mg

29. You are now ready to play a game called "plug in other factors to cancel out the units you don't want until you end up with the units you do want." Here goes:
The horizontal bar means "divide," as usual, and the vertical bars mean "multiply." If the units cancel out properly, then your set up is correct and you can be quite sure the answer will be correct if you just manage to punch the right keys on your calculator. The most twisted of med-math problems devised by the most fiendish minds can be solved, bing-bang-boom, in this manner.

30. DIMENSIONAL ANALYSIS QUESTIONS
The patient is receiving nitroprusside at 23 mL/hr. The bag has 50 mg of nitroprusside in 250 mL of solution. The patient weighs 67 kg. What dosage of nitroprusside in mcg/kg/min is the patient receiving?
Your patient receives an order for procainamide at 3 mg/min. She weighs 58 kg. The pharmacy has mixed 2 g of procainamide in 500 mL of solution. What is the infusion rate in mL/hr?
The patient weighs 117 pounds. Dopamine is running at 30 mL/hr. There is 400 mg of dopamine in 500 mL of solution. How much dopamine is the patient receiving in mcg/kg/min?
You need to start a continuous drip of amiodarone at 1 mg per minute (by pump). The standard IV mixture is 450 mg in 250 mL.

31. ANSWER KEY FOR DIMENSIONAL ANALYSIS QUESTIONS1. 2. 3.
Since you want kg, a unit of weight (mass) on the bottom, starting with pounds on the bottom makes sense. 4.
First, think what units will be in the answer. Since you're using a pump, it's mL/hr.
If you get any answers wrong, re-read the previous section and re-take the test. Otherwise, continue on.

32. PEDIATRIC DOSEAGE CALCULATIONS
Order: Ceclor (cefaclor) 100 mg p.o. q8h is ordered for a child weighing 32 lb. The recommended dosage is 20 to 40 mg/kg/day divided q8h. (a.) What is the child's weight in kilograms? _____ (b.) What is the safe 24-hour dosage range for this child? _____ (c.) Is the dosage ordered safe? (Prove mathematically.) _______________ Explain your action:
step #1
Determine child's weight in kg (if given in pounds) lb/ 2.2 = 14.5 kg ALWAYS ROUND KILOGRAM WEIGHT TO THE NEAREST TENTH, NOT WHOLE NUMBER

33. PEDIATRIC DOSEAGE CALCULATIONS
step #2
Determine the safe 24-hour dosage range As stated in the problem "The recommended dosage is 20 to 40 mg/kg/day divided q8h." multiply low range (stated in problem) by weight in kg: Low range = 20 so 20 x 14.5= multiply high range (stated in problem) by weight in kg: High range = 40 so 40 x 14.5= Therefore- The safe doseage range for this child is mg PER DAY

34. PEDIATRIC DOSEAGE CALCULATIONS
Determine the safe 24-hour dosage range As stated in the problem "The recommended dosage is 20 to 40 mg/kg/day divided q8h." multiply low range (stated in problem) by weight in kg: Low range = 20 so 20 x 14.5= 290 multiply high range (stated in problem) by weight in kg: High range = 40 so 40 x 14.5= 580 Therefore- The safe doseage range for this child is mg PER DAY
step #3
So, is the doseage ordered safe? Per the problem, the MD has ordered 100 mg q 8 hr = 300 mg per day (q 8 hr= 3 times a day 100mg x 3 = 300mg PER DAY) You determined the safe range to be mg per day in the previous step mg is within this range so, YES, the ordered dose is safe for this child
So, is the doseage ordered safe? Per the problem, the MD has ordered 100 mg q 8 hr = 300 mg per day (q 8 hr= 3 times a day 100mg x 3 = 300mg PER DAY) You determined the safe range to be mg per day in the previous step 300 mg is within this range so, YES, the ordered dose is safe for this child
step #4
Explain your action: You would administer the dose as ordered because it has been determined to be safe

35. PEDIATRIC DOSEAGE QUESTIONS
1. A two year old toddler who weighs 30 pounds is diagnosed with otitis media (middle ear infection.) The physician ordered the antibiotic amoxicillin 20 mg/kg PO q8h. The label reads 125 mg in 5 mL. How many milliliters will you administer?
a. 20 mL
b. 5 mL
c mL
10.9 mL
2. Claforan (cefotaxime) 50 mg/kg/d q8h via IVSS is ordered for a child who weighs 12 kg. The label reads 50 mg/mL. How many milliliters would you withdraw from the Claforan vial to add to the IVSS?
a. 1 mL
b. 4 mL
c. 6 mL
d. 12 mL

36. PEDIATRIC DOSEAGE QUESTIONS
3. Prescriber's order: Lanoxin (digoxin) 0.1 mg IM daily. The label reads 0.1 mg/mL injection. What is the dose in micrograms? a. 0.1 mcg b. 10 mcg c mcg d. 100 mcg 4. A child who weighs 100 pounds is admitted to the hospital for a repair of an inguinal hernia. The pre-op order is: Versed (midazolam HCl) 0.08 mg/kg IM, 30 minutes before surgery. The label reads 5 mg/mL. How many milliliters will you administer? a. 0.8 mL b mL c. 8 mL d. 1.7 mL

37. ANSWER KEY (d) 10.9 ml (b) 4 ml (d) 100 mcg (b) 0.73 ml
If any answers were incorrect, go back and re-read the previous section and re-take the test. Otherwise, proceed on to the next section.

38. Now perform these calculations using the format that is easiest for you to follow
Show all work and submit to instructor for grading. This project will have a “Pass/Fail” grade. It is imperative that you answer all questions correctly.
A client is ordered 35 milligrams of Codeine phosphate by subcutaneous injection. 50 milligrams in 1 mL of liquid for SC Injection is available. How many mL will you administer?_____
A client is ordered 30 milligrams of Furosemide intravenously. 10 mg in 1 mL of liquid for IV Injection is available. How many mLs will you administer?______
A client is ordered 50 mg of Aminophylline intravenously. 250 mg in 10 mL of liquid for IV Injection is available. How many mLs will you administer?_____
Calculate the drip rate for 100 mls of IV Fluids to be given over a half hour via an administration set which delivers 10 drops/ml._____
One litre of Normal Saline is ordered over 9 hours. The drop factor is 15. Calculate the number of drops per minute._____
Three litres of Lactated Ringer's is ordered over 12 hours. The drop factor is 15. The IV has been running for 9 hours. 800 mls remain. How many drops per minute are needed so that the IV finishes in the required time?______

39. Teacher Answer Key for Final Test.
mls 2. 3 mls 3. 2 mls gtts/min gtts/min gtts/min