Dosage Calculations

Daytonite, BSN, RN · Mar 1, 2007

~JR~ said:
What's the formula for figuring out mls per drop?

I believe what you are talking about is the conversion factor: 15 drops or minims = 1 mL

Daytonite, BSN, RN · Mar 6, 2007

~jr~ said:
a post surgical patient is currently having an infusion of hartmann's solution of 6/24 rate or 56 drops/min via a macro giving set. upon returning to the ward you read the post op orders and notice an order that states when hartmann's runs through, a 5% dextrose bag is to be commenced. the current infusion had 300ml remaining how long will it take for that infusion to finish?

Assuming that what is meant by a macro set means it is delivering at the rate of 10drops/ml, you want to end up with an answer providing you with a label of "minutes" or "hours". the problem would be worked out like this:

300 ml (amount to be given)x1 minute/56 drops (rate of infusion)x10 gtts/1 ml (drip factor of iv tubing being used)=53.571428 minutes (after canceling out labels repeated in numerators and denominators and doing the mathematics)=54 minutes(rounded off)

FYI: This iv is running at 336 ml/hour. this is pretty fast for an iv, but may not be totally unusual for an immediate postop.

Daytonite, BSN, RN · May 8, 2007

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iv amniphylline 750mg in 1000ml d5w at 50 mg/hr. tircacillin 1g ivpb via heparin lock every 6h. stock available: ticarcillin 1g per 50ml d5w. administer over 30 mins - 2 hrs. aminophylline stock: 500mg/20ml (25mg/ml)[/b]
1) how many ml of aminophylline must be needed to 100ml of d5w to produce the ordered concentration?
answer: 30 ml aminophylline correct!
2) what rate (ml/hr) is needed to administer 50mg of aminophylline per hr?

50 mg/1 hour (dose desired)x1000 ml/750 mg (dose on hand)=67 ml/hour(rounded off)

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3) using minidrop tubing how many ugtts/min are needed to administer aminophylline?

67 ml/1 hour(dose desired)x60 gtts/1 ml (drop factor of iv tubing)x1 hour/60 minutes(conversion factor)=67 gtts/1 minute(drip rate)

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4) the ticarcillin piggyback contains how many cc of ivf?
answer: 50 ml
5) what is the minimum infusion time for ticarcillin?
answer 30 mins
6) what is the maximum infusion time for ticarcillin?
answer: 2 hours
the information i have on iv ticarcillin (2007 intravenous medications, 23rd edition, by betty l. gahart and adrienne r. nazareno, page 1203) is that it can be infused over 30 minutes to 2 hours, so i think your answers are correct unless your instructors are basing the correct answer on their own sources.
7) using an infusion set that delivers 15 gtts/ml, determine the gtts/min needed to administer the ticarcillin over:
a) 30 minutes = 25gtts/min
b) 1 hr = 12.5gtts/min
c) 2 hrs = 6.25 gtts/min

Round your answers off in #7. there's no such thing as 12.5 drops or 6.25 drops. so, "b" should be 13 gtts/min and "c" should be 6 gtts/min.

Daytonite, BSN, RN · May 22, 2007

Entepe said:
Help!!
Can anyone figure out how to do this problem??:
IV rate is ordered to run at 150 cc/hour. At 0600 there is 400 cc TBA. How much IV fluid will there be TBA at 1400? The answer is 200 cc TBA.
I have NO idea how to figure this one out, and would GREATLY appreciate any insights on how to do this! If I fail one more med-math, I'll have to withdraw from nursing!!!
Thanks to any med-math genuises' out there!
Entepe

There is one piece of information that you need to know to work this problem: an IV bag of fluid contains 1000cc. From 0600 hours to 1400 hours is a total of 8 hours that this IV is going to be infusing. That means that over an 8 hour period the patient is going to receive a total of 1200cc's of IV fluid. Here's the math:

1400 - 0600 = 0800

(drop the 2 zeros at the end) You can also count this off on your fingers to figure out this is 8 hours, just don't let people see you doing it!

Then,

8 hours x 150 cc's/hour = 1200 cc's

(total amount of IV fluid patient will receive over an 8 hour period)

You started out with a total of 400cc's of IV fluid in the IV bag. This information was given to you. At some point the bag with the 400cc's TBA in it is going to run out of fluid and need to be replaced with a fresh bag that contains 1000cc's. Here's how they got the final answer of 200cc's:

400cc's (amount of IV fluid in the first bag you started with)+1000cc's(amount of IV fluid hung when the first bag was empty) =1400cc's(the total amount of IV fluid hanging and available)

Then, if you have

1400cc's

of IV fluid hanging TBA and you gave

1200cc's

of it over 8 hours (as determined above) that leaves

200cc's

TBA in the bag that is currently hanging on the IV pole.

This is a problem that is grounded in practical, clinical practice. This problem might make more sense to you if it is presented as you will more likely find it if you work in a busy hospital ward. It might help if you close your eyes and envision this scenario. You will come onto your shift and note 400cc's in the patient's IV bag and that the IV is to infuse at 150cc's per hour. You'll realize that the bag is going to run out of fluid within a couple of hours, so you'll keep your eye on it. Around 0830 or so you'll hang a new IV bag in order to keep the IV going. At 1400 you'll be checking the IV level in order to determine your patient's IV fluid intake for your shift. The IV fluid in the bag will be at 200cc TBA. You'll be recording a total of 1200cc's IV intake (400cc's from the first bag of IV fluids and 800cc's from the current bag) on the Intake & Output record. And, if you're a thoughtful nurse you'll put the next bag of IV fluids on the IV pole so the on coming nurse won't have to go running for the next bag of IV fluids. What your instructor has done is taken that scenario and jumbled some of the facts around, kept a few of them out and made one of the items an unknown for you to find the answer to. Instructors like to do this to students to see if you are thinking.

Hope that helped explain this for you.

shellek · May 26, 2007

minnielynn said:
I am in a desperate situation. I thought I was getting my calculations correctly and today I got back my math results and i got a 70% I am so disappointed I dont know what to do. On my first exam I received an 80%.
My professor said that if i get above 95% on my final (which is next week) I may be able to average a b+ or a- , but it will all depend on the overall average, if he curves grades or not. I went and bought 2 self help books on calculations .... My question is ..... do you think it is humanly possible to ingest all this info by next week (exactly a week from today)! I am having problems with the drips and the three step conversions. Is there a website that can help me? To top it off my professor sucks, so what I have learned, I have learned on my own. I am so frustrated, so much so, that it is getting harder and harder for me to pick up a book .....sorry for venting

F Y I, I know you are going through alot, however once in the "real world of nursing" you WILL have resources, pharmacist, and calculated out spread sheats for calc's, not including IV pumps with calc's on them also! You can also carry around a "cheat sheet" for your confidence. This is school so you understand the base behind the answers!! ONLY short term. I don't know if I myself could do certain calc's however I DO know how to go about finding the answers and double checking them, I even @ times double check with other co-working R.N.'s !!!!! YOU CAN DO IT !!!!

Daytonite, BSN, RN · May 30, 2007

sc1973 said:
i am having a hard time getting started with dimensional analysis on certain problems. i hope someone can please help. here's the problem. i know its simple to calculate, which i have done and gotten an answer, but i'm unsure of how to set it up with da. help please. the problem:
dosage ordered: 10mcg/kg/day. client weight: 68kg. dosage available: 5mg/ml. what is the daily dosage?

When you are setting up problems using dimensional analysis, one of your goals is to set up the equation so that the labels that will be left and remaining with the number in the numerator and the number in the denominator of your final answer are the labels you want and are in their correct position of the final fraction. All the other labels will have cancelled out because a label in the numerator of one of the terms in the equation matches with and cancels out the same label in the denominator of one of the other terms in the equation. The equation still includes the dose you desire divided by the dose on hand. When you start by using that formula you end up with a very complex fraction which has to be broken down into simple terms by sequentially simplifying the denominator until you reach a series of fractions that contain only one term in the numerator and one term in the denominator. That is done, if you will recall from math, by multiplying the numerator and the denominator of this monster fraction that you are going get when you divide the dose desired by the dose on hand by the reciprocal of what forms the fraction at the bottom of this monster in order to end up with a denominator of "1". Remember from math that whatever you multiply the denominator by you must also multiply the numerator by as well--in effect you are multiplying by a complex fraction that itself actually reduces to the number 1. You retain the numerator of the reciprocal, which is itself a fraction with a denominator of "1", after it is mutiplied with the denominator of the monster complex fraction you are reducing. You can now just eliminate the "1" on the reciprocal that is left because it is not needed and because any numerator over a denominator of 1 is equivalent to what is in the numerator (by identity). What's left of the reciprocal now becomes a term that becomes part of an equation you are starting to build. Do not do anything with the "1" that remains in the denominator of the complex fraction you are simplifying, however, or your problem is not going to come out correct. Keep repeating this simplification process with the complex fraction only until you are left with simple fractions (one term in each numerator and one term in each denominator). Starting with dose desired divided by dose on hand results in this complex fraction (what a monster!):

10 mcg/1 kg/1 day(dose desired)/5 mg/1 ml (dose on hand)begin simplifying:10 mcg/1 kg/1 day/5 mg/1 ml x1 ml/5 mg/1 ml/5 mg (the reciprocal)results in:10 mcg/1 kg/1 day/1 x1 ml/5 mgsimplify again:10 mcg/1 kg/1 day/1 x1/1 day/1/1 day (the reciprocal)

results in:10 mcg/1 kg x1/1 day

Simplified, that complex monster becomes an equation of 3 simple fractions (i highlighted them in blue). If you study the resulting equation closely you will see how the mathematical manipulation of multiplying with reciprocals has resulted in a flipping around of what is in the numerators and denominators of the various fractions. Work this out on paper if you have to in order to see how the magic happens. Now you have this resulting equation:

10 mcg/1 kg x 1/1 day x 1 ml/5 mg

(i've highlighted the terms you want in the final answer in red. you want ml in the numerator and day in the denominator of your answer)

To complete the calculation of the problem, you need to include the patient's weight and a conversion factor that changes the mcg to mg in order to clear those labels from the equation. Keep in mind that conversion factors are actually a manipulation of the use of the number 1 (if the numbers in the numerator are equal to the numbers in the denominator the fraction reduces to the number 1 and any number multiplied by 1 is equal to itself). You perform the math with the numbers that are remaining:

10 mcg/1 kg x 1/1 day (these two fractions are the dose desired)x 1 ml/5 mg(dose on hand)x 68 kg/1 (patient's weight)x 1 mg/1000 mcg (conversion factor)= 680 ml/5000 day (notice that the labelsmcg, kgandmg have all cancelled each other out which is what you wanted)= 0.136 ml/1 day(simplified)

It is generally best to work out da in a step-by-step way on a piece of paper so nothing gets left out or forgotten. Some of these da equations can get long depending on how many conversion factors you have to use. If the patient's weight had been given to you in pounds instead of kg, you would have had to apply another conversion factor to the da equation and sequence the terms in the numerator and denominator positions so that other labels in the da equation would cancel out.

Daytonite, BSN, RN · Jun 17, 2007

aadsmom said:
hello, can anyone help me figure out a problem?
500 mg dopamine in 250ml what rate would equal 5mcg/kg/min. pt wt 106 kg.

this problem has to be worked by dimensional analysis. there are lots of examples of problems solved by dimensional analysis on this thread for you to also view. you want to end up with the labels of ml/minute with ml in the numerator and minutes in the denominator. this is how this problem is set up and worked:

5 mcg/1 kg x1/1 minute (these first two terms are the dose desired)x106 kg/1(patient's weight)x 250 ml/500 mg(dose on hand)x1 mg/1000 mcg (conversion factor)=0.265 ml/minute.

For all practical purposes, however, you would be using an iv pump. most pumps can only be programmed for ml/hour, so this would need to be converted to an hourly rate:

0.265 ml/1 minute(infusion rate per minute)x60 minutes/1 hour(conversion factor)=15.9 ml/1 hour =16 ml/hour(infusion rate on an iv pump rounded off)

Salamandrina · Aug 8, 2007

Bigbear71 said:
I am stuck on 2 questions. Still very new to drug calculations. Reading everything I can get my hands on. I'm starting my last semester in an ASN program and we have hardly touched dosage calculations. Basically trying to teach myself. Anyhow, would someone please explain how to do these 2 problems? Thank you very much..
1. The Dr. has ordered Cordarone IV 900mg to be added to 500 ml D5W and run iv at a rate of 1mg/min for 6 hours. The manufacturer's directions agree with the Dr order. The available 3ml vials of Cordarone contain 50mg per 1 ml. Drop rate is 60 per 1 ml.

To begin, lets look at what we are asked to infuse TOTAL. So we got 1 mg per minute for 6 hours. Thats 1 (mg) x 60 (minutes) x 6 (hours) or 360 mg. We don't need this now, but it will help us check our math later. Watch...

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How many ml of Cordarone IV should the nurse add to the 500ml D5W?

There are 3 mls per vial and 50 mg per ml therefore there are 150 mg per vial. For a total of 900 mg to be added, you need to add 18 ml (or 6 vials)

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How many mg of drug are present in 1 ml of the Cordarone IV 900 mg in 500ml D5W?

Once you add the meds there are 1.7 mg per ml. Here's the math, you have a total of 900 mg in a solution of 518 mls (this is of course after you add the meds, you are adding 18 mls to the 500 ml solution). 900 mg per 518 ml reduces to 1.7 mg per 1 ml.

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How many ml per minute must infuse to deliver the prescribed amount of drug?

To run at 1 mg per minute, that is 60 mg per hour. If there are 1.7 mg per ml, then you have to figure out how much it will take to get 60 mg in an hour. Take 60 mg / 1.7 mg per ml and you get 35.3 mls per hour. But you are asking about how much per minute, so you have to devide by 60 and you get ~0.6 mls per minute.

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How mant ml per hour should the IV be set to deliver?

See above. It is 35.3 mls per hour.

Checking the math:

35.3 (mls per hour) x 6 (hours) x 1.7 (mg per ml) = 360.06 mg. Looking back at the top, that is was we were asked to infuse. Bingo!

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2. The Dr has ordered Dobutrex 250 mg to be added to 500ml of D5W to run IV at a rate of 5mcg/kg/min. The manufacturer directions agree with the Dr. The available 20 ml vials of Dobutrex contain 250 mg. The IV set delivers 60 drops per 1 ml. The pt. weighs 65kg.

Start off with a conversion 1000 mcg = 1 mg. So this pt can tolerate 325 mcg per minute. (65 (kg) x 5 (mcg)). Hourly that would be 19,500 mcg (325 mcg x 60 minutes) or 19.5 mg per hour.

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How many ml of Dobutrex should the nurse add to the 500 ml D5W?

There are 250 mg in a 20 ml vial. The math is done for you. You add 20 mls.

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Based on weight, how many ug/min of Dobutrex should the pt. receive?

325 mcg per minute (see above)

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How many mg of drug present in ml of the Dobutrex 250mg in 500ml D5W?

250 mgs in a 520 mls solutin (500 D5W + 20 mls of Dobutrex). 250 mg /520 mls = 0.5 mg per ml.

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How many ml per minute must infuse to deliver prescribed amount?

Pt can tolerate 325 mcg per minute. That is equivalent to 0.325 mg. There are 0.5 mgs in each ml. 0.325 mg / 0.5 mg per ml is a run rate of 0.65 mls per minute.

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How many ml per hour should the IV set to deliver?

Going back to the top with the maximum of 19.5 mg per hour and a total of 0.5 mg per ml, the MAXIMUM run rate would be 39 mls per hour. (19.5 / 0.5 = 39)

Daytonite, BSN, RN · Aug 10, 2007

smurfy said:
a pregnant woman is scheduled for labor induction w/pitocin. available is 20 units pitocin in 1000cc lr. the md has ordered the infusion to 3mu/min. how many cc's are ordered per hour?

First off, you need to know that 20 units of pitocin in 1000cc of lactated ringers gives you 20 mu (milliunits) of pitocin per ml of lactated ringers. you must know this information to get the correct answer to this question. You would find this is a drug reference book. i happened to find it in 2007 intravenous medications, 23rd edition, by betty l. gahart and adrienne r. nazareno on pages 958-960. Then, to get the answer in cc/hour:

3 mu/1 minute

(dose desired)

x 1 ml/20 mu

(dose on hand)

x 1 cc/1 ml

(conversion factor)

x 60 minutes/1 hour

(conversion factor)

=

9 cc/1 hour

(dose to give)

abebe12525 · Sep 20, 2007

lpnlpn said:
i am having trouble converting between systems of measurement, i am trying to teach myself the conversion factor method as well as the ratio proportion method but this problem is giving me a bit of a problem the problem is ---3g=gr_____ help!

this is how i would solve it

1g=gr15

therefore3g = 15 x 3 = 45

3g = gr45

i hope this helps you

abebe12525 · Sep 20, 2007

gr means grain

abebe12525 · Sep 20, 2007

this is how i would solve this problem

d (desired )/h (have) x q (quantity)

300,000/200,000 x 5 = 7.5

round it up to 8