1. By: Mary Jacobs, RNC, MSN-ED
Calculating Dosages
By: Mary Jacobs, RNC, MSN-ED

2. Dosage Calculation in Nursing
Determining what the question is asking. Look at the following scenario: What is the question asking you to calculate:
Provider orders Dopamine 5 mcg/kg/day to be infused over 8 hours for a client weighing 115 kg. How much Dopamine will the client receive in 8 hours? How much Dopamine will the client receive per hour?
To determine what the question is asking we must determine key terms within the question.

3. Key Terms
Provider orders Dopamine 2 mcg/kg/day to be infused over 8 hours for a client weighing 5 kg. How much Dopamine will the client receive in 8 hours? How much Dopamine will the client receive per hour?
The first part of the problem asks us how much Dopamine the client will receive in 8 hours, since the provider order reads for the total dopamine dose to infuse over 8 hours we simply need to multiply to determine the dose the client will receive
5kg/pt x 2 mcg/kg/day = 5 x 2 mcg/day = 10 mcg/day dose infused in 8 hours

4. Provider orders Dopamine 2 mcg/kg/day to be infused over 8 hours for a client weighing 5 kg. How much Dopamine will the client receive in 8 hours? How much Dopamine will the client receive per hour?
We determine the answer to the second part of the question once we have answered the first part. Now that we know the patient will receive 10 mcg/day infused over 8 hours, we can then divide the total dose by the total infusion time
Total dose/total infusion = 10 mcg/8 hours = 1.25 mcg/hr
So that was pretty simple, right? Let’s take a look at another scenario.

5. Calculating ml/hr from units/hr
A provider orders Heparin 10 units/kg/hr for a client weighing 185 lbs. Heparin is supplied premixed 25,000 units in 250 ml 5% Dextrose solution. Calculate the ml/hr flow rate to the nearest 10th of an ml.
First off we need to determine what we need to calculate in this case we need to know how fast to set our IV pump in ml/hr. The following calculation can assist us in determining the correct flow rate.
ml/hr = 250 ml/25,000 units x 10 units/kg/hr x 1 kg/2.2 lbs x 185 lbs/1pt
We then multiply 250x10x1x185(all the top row) and divide by 25,000x2.2x1 (all the bottom row multiplied together)
462,500/55,000 = (repeating) rounding to the nearest 10th of an ml we should set our pump to 8.4 ml’s/hr to provide the client with the prescribed dose of 10 units/kg/hr.

6. Understanding drop factors
Provider orders IV hydration Normal Saline to run at 125 ml/hr for a client weighing 98 kg. Unfortunately there is no IV pump available. The drip factor on the available tubing is 10 gtts/ml. Calculate the infusion rate in gtts/min.
Now in this scenario, there is a lot of unnecessary information. So how do we pick out the most important or key terms?

7. Provider orders IV hydration Normal Saline to run at 125 ml/hr for a client weighing 98 kg. Unfortunately there is no IV pump available. The drip factor on the available tubing is 10 gtts/ml. Calculate the infusion rate in gtts/min.
As we can see we are being asked to convert the hourly rate from ml’s/hr to gtts/min.
gtt/min = drop factor x hourly rate x 1 hour/60 min
10 gtts/ml x 125 ml/hr x 1 hr/60 min = 1250/60 = since we cannot measure partial drops we then round and the answer would equal 21 gtts/min (rounding if number >5 round up <5 round down)

8. Calculating Doses for single administration
A provider orders a Heparin bolus dose of 50 units/kg to a client weighing 48 kg to be given IV push. Heparin is supplied in 5000 units/1 ml in a 10 ml vial. How many ml’s should the nurse administer? Round to the nearest 10th of an ml.
In this question we need to determine an IV push dose of Heparin. It’s crucial that we verify our calculations and give the correct dose as an overdose could be detrimental to the client. To set up the problem we will use the following calculation.
ml to administer = 1 ml/5000 units x 80 units/kg x 48 kg/1 pt

9. ml to administer = 1 ml/5000 units x 80 units/1kg x 48 kg/1 pt
We then multiply 1x80x48 (all the top row) and divide by 5000x1x1 (all the bottom row)
3840/5000= since we need to round to the nearest 10th of an ml we look at the number in the hundreds place. That number is a 6 which is >/= to 5 meaning we round up.
The nurse will administer 0.8 ml’s of IV push heparin
Prior to administering, it is important to verify the calculation and amount drawn with a second nurse. This two step process is in place to help keep clients safe from medication errors.

10. Calculating TPN doses
The provider has ordered a TPN infusion for a client of 25 cal/kg/day with protein of 0.8 g/kg/day for a client weighing 70 kg. Determine the total number of calories per day and the total protein per day that the TPN should include for the client.
Wait what? You might ask, doesn’t pharmacy calculate this for us? They should, but remember pharmacy is not infallible and if an order is taken over the phone, the nurse needs to know how to calculate and input the order correctly.
First let’s determine what our question is asking us for. We need to calculate the needed calories and grams of protein per day for our client.

11. Let’s start by calculating the calories per day
Cal/day = ordered dose x kg/pt
Protein/day = ordered dose x kg/pt
Let’s start by calculating the calories per day
Cal/day = 25cal/kg/day x 70 kg/pt
25x70 = 1750 cal/day
Now we need to calculate the grams of protein per day
grams protein/day = 0.8 g/kg/day x 70 kg/pt
0.8x70 = 56 grams of protein per day
When verifying we have received the correct dosages from pharmacy we can calculate the total per bag x # bags in 24 hrs to see that we have the correct numbers. Remember TPN must be infused via a central line as it is hard on the veins.

12. TPN for Malnutrition
A provider orders TPN to run over 24 hours containing the following: 70 grams of Amino Acids (protein) per 24 hours, Dextrose 150 grams per 24 hours, and Lipids 75 grams per 24 hours. Calculate the total Kcal in provider order for the 24 hour period. Calculate the total number Kcal/day based on a 52 yr old male client 6’4” weighing 54 kg on admission. Based on typical needs for malnutrition is the provider order sufficient, too much, or too little for client weight.
First of all there is some missing information that we need to answer these questions. The number of kcal(cal) ger gram of substance and the nutritional needs for malnutrition
[amino acids 4kcal/gram, lipids 9kcal/gram, dextrose 3.4kcal/gram]
[malnutrition should receive approx kcal/kg/day]

13. Let’s start by calculating the caloric total for 24 hours in the order.
Amino Acids kcal = 70 g x 4 kcal = 280 kcal
Dextrose kcal = 150 g x 3.4 kcal = 510 kcal
Lipids kcal = 75 g x 9 kcal = 675 kcal
Know that we know the kcal supplied by each portion of the TPN we can add them together to get the total kcal in the provider order per 24 hours.
= 1,465 kcal/24 hours ordered.
The next part of the question asks us to determine the nutritional needs of a malnourished client which is approximately kcal/kg/day.
30 kcal/kg/day x 54 kg = 1,620 kcal/day
35 kcal/kg/day x 54 kg = 1,890 kcal/day

14. Now that we’ve determined the total daily calories ordered in the TPN and the needs of the client based on his diagnosis of malnutrition and admission kg we can answer the third part of the question.
1,465 kcal/24 hours ordered
30 kcal/kg/day x 54 kg = 1,620 kcal/day
35 kcal/kg/day x 54 kg = 1,890 kcal/day
In examining the third portion of the question, the nurse would need to question the provider as to the ordered dosages. Remember TPN patients are usually not eating so assuming the client is going to get another kcal per day from eating is a stretch. The nurse should point out that the order is too low based on the caloric needs of a malnourished client.

15. Calculating a single dose based on 24 hr order
A client is to receive Ampicillin 60 mg/kg/24 hours divided into 8 hour doses. The client weighs 100 kg. How much Ampicillin will the nurse administer per dose?
First the question is giving us a 24 hr/kg total dosing that we must calculate and then divide into 8 hour doses. We can simplify this a little by recognizing that the client will receive 3 doses per 24 hours.
60 mg/kg/24 hr x 100 kg/pt = 6,000 mg/24 hrs. since 24/8 = 3 we can perform the following to find out the single dose amount
6,000 mg/3 doses = 2,000 mg/1 dose
The nurse will administer 2,000 mg of Ampicillin per 8 hour dose.

16. Weight based doses
A provider order reads rifampin 5 mg/kg to be administered to a client weighing 60 kg. On hand the nurse has rifampin 25 mg/1 ml vials. How much rifampin will the nurse administer in mg? How much will the nurse administer in ml’s to the nearest 10th of an ml?
To answer this question we must look at both the ordered dose and what is on hand.
The first calculation will determine the dose needed in mg
5mg/kg x 60kg/pt = 300 mg/dose

17. We now need to calculate the ml’s to draw up
ml’s = amt on hand x total dose
1 ml/25 mg x 300 mg = 300/25 = 12 ml’s per dose.
Although this question was laid out in such a way that the student can easily see that they need to calculate both to get the answer, you may only be asked how many ml’s do you need to administer per dose given an on hand amount and a dose per kg. Keep in mind you will need to find your total dose amount prior to being able to determine how much you need to draw up to administer.

18. Reconstituting Medications for Injection
A nurse is to administer ceftriaxone 1 gram IM to a client. On hand the nurse has ceftriaxone powder form and a 10 ml vial of normal saline. How many ml’s will the nurse draw up to administer the ceftriaxone IM?
First off we need to remember that when administering an IM injection the age and size of the client matters. We want to limit IM injections to 1 or 2 ml’s per injection at most. Ceftriaxone is a very thick antibiotic and does burn a little but the nurse should only draw up 1 ml to reconstitute the medication as they will administer it IM.

19. Oral medications
When determining medications doses in pill or oral liquid form, it’s important to look at the dose ordered and the amount provided per tablet or per ml. For example oxycontin comes in 5 mg tablets if the provider orders 7.5 mg the nurse will need to cut a tablet in half and waste 2.5 mg while administering 1.5 tablets to the client.
Liquid acetaminophen comes in 5mg/1 ml if the provider orders 17.5 mg’s the nurse will need to draw up 3.5 mg’s in an oral syringe.

20. Calculating Temperatures
A client temperature was written in Fahrenheit 100.4 degrees. The nurse must calculate it to Celsius to chart the temperature. What is the correct temperature in Celsius? _______
In calculating temperatures we need to keep in mind that if we are going from Fahrenheit to Celsius we need to subtract 32 and then times by 5/9.
For this problem you would set it up as follows
( ) x 5/9 = 68.4 x 5/9 = 38

21. Convert the following client temperature to Celsius. 102.6
Let’s try a few more:
Convert the following client temperature to Celsius
(102.6 – 32) x 5/9 = 70.6 x 5/9 = (39.2)
Convert the following client temperature to Celsius 97.6
(97.6 – 32) x 5/9 = 65.6 x 5/9 = 36.4
Convert the following client temperature to Celsius 98.5
(98.5 – 32) x 5/9 = 66.5 x 5/9 = (36.9)
Convert the following client temperature to Celsius 99.1
(99.1 – 32) x 5/9 = 67.1 x 5/9 = (37.3)
Convert the following client temperature to Celsius100.0
(100.0 – 32) x 5/9 = 68.0 x 5/9 = (37.8)

22. Let’s try calculating Celsius to Fahrenheit
A client temperature was charted in Celsius 37.9 degrees. The nurse needs to know what that translates to in Fahrenheit to know if the client needs treatment. What is the correct temperature in Fahrenheit? _______
In calculating temperatures we need to keep in mind that if we are going from Celsius to Fahrenheit we need to multiply the degrees in Celsius by 9/5 then add 32.
For this problem you would set it up as follows
(37.9 x 9/5) + 32 = = (100.2)

23. Convert the following temperature into Fahrenheit 36.8
Let’s try a few more:
Convert the following temperature into Fahrenheit 36.8
(36.8 x 9/5) + 32 = = (98.2)
Convert the following temperature into Fahrenheit 39.8
(39.8 x 9/5) + 32 = = (103.6)
Convert the following temperature into Fahrenheit 41.2
(41.2 x 9/5) + 32 = = (106.2)
Convert the following temperature into Fahrenheit 36.2
(36.2 x 9/5) + 32 = = (97.2)
Convert the following temperature into Fahrenheit 37.5
(37.5 x 9/5) + 32 = = 99.5

24. Additional practice
Utilize the scenarios within the presentation changing the numbers and practice the calculations. I have uploaded a practice math exam for you to utilize on canvas as well.