MathNursing_03.htm
0302 Essential Mathematics for Nursing

Liquid Dosage Calculations

 

 

The concentration of medication in a liquid solution or suspension is expressed in mass/volume (such as milligrams per milliliter) . Orders for liquid medication, however, are expressed in mass (milligrams, for example). Suppose the dosage ordered is 500 mg and the available concentration is 2.50 mg/ml.  Our usual set-up for dosage calculations would be:

The problem that the dosage on hand is expressed as a concentration mg/ml.  But we need to flip over the expression. That is why the boxes above show instead of .

So the procedure is correctly expressed with the Dosage on Hand term flipped over. And now the mg labels cancel out perfectly:

500

x

1 ml = 200 ml
1 2.5

200 ml is required.

Note

The previous example shows how proper dimension-analysis procedures can tell you when you are making a set-up error. This feature helps prevent math errors. It can save your reputation ... and even a life.

 

Example

Ordered:  750 mg of xyz
On Hand:  35 mg / ml
 
Set up the ratios:
750 mg

x

1 ml  
1 35 mg
Cancel the labels:
750

x

1 ml  
1 35
Complete the math:
750

x

1 ml = 21.43 ml
1 35
Result: 21.4 ml  

 

Note

Round P.O. liquids to the nearest tenth place.

 

Ordered:  800 mcg of xyz
On Hand:  10 mg / ml
 
Make sure units are identical
Convert mcg to mg:
800 mcg = 0.8 mg
Set up the ratios:
0.8

x

1 ml  
1 10
Cancel the labels:
0.8

x

1 ml  
1 10
Complete the math:
0.8

x

1 ml = 0.08 ml
1 10
Result: 0.08 ml or 80 mcg  

Here is how you would actually work such problems for exams or on the job.

Dosage Ordered: 400 mg
Stock Available: 500 mg/L

400

x

1 L = 0.8 x 1 L = 0.8 L
1 500

Answer: 0.8 L or 800 ml

Liquid Dosage Drill

Work with this drill routine until you can consistently answer the questions correctly. You should have no need for a calculator.

[ ** Interactive 020301 here **]

 

Real-World Examples

1. You are to give the patient Ampicillin 250 mg PO q 6h. The suspension on hand contains 125 mg per 5 ml. How many ml will the patient receive per dose? ______

250

x

5 ml =10 ml
1 125

Ans: 10 ml

2. The order is to give Dilantin 100 mg PO t.i.d. The available suspension contains 30 mg per 5 ml. How many ml. will you give? ______

100

x

5 ml =16.67 ml
1 30

Ans: 16.7 ml

3. The physician has ordered Tetracycline syrup 500 mg q 6h PO The available medication contains 125 mg per 5 ml. How many ml will you give? ______

500

x

5 ml =20 ml
1 125

Ans: 20 ml

4. The doctor has ordered 65 mg of Garamycin IM for your patient. You have available a multidose vial of Garamycin labeled 40 mg/ml. How much of the medication will the patient receive? ______

65

x

1 ml = 1.63 ml
1 40

Ans: 1.6 ml

5. The doctor has ordered an injection of Atropine 0.3 mg IM for your patient. You have available a multi-dose vial labeled Atropine 1 mg/ml. You will administer _____ ml to your patient.

0.3

x

1 ml = 0.3 ml
1 1

Ans: 0.3 ml or 300 mcL

Liquid Dosage Word Problems

Work with this drill routine until you can consistently answer the questions correctly.  You should have no need for a calculator.

[ ** Interactive 020302 here **]

0303

Special  Parenteral Medication Dosages

Some medications become unstable in solution over time. You may see these medications manufactured as dry powders. Prior to administration of these medications, an appropriate diluent (sterile water, normal saline, and so forth) must be added. The term used to describe the process of adding the diluent to the medication is reconstitution.

Usually the volume of the diluent is expanded somewhat when added to the dry powder. For example, when 2 ml of diluent is added to a dry vial of 1 gram of Mefoxin, the resulting withdrawable volume is 2.5 ml.

The directions for reconstitution of a medication may list a number of different amounts of diluent, each resulting in a different concentration. If that is the case, choose a concentration, which would provide an appropriate volume for the injection. When selecting a concentration, keep in mind that no more than 3-4 ml should be injected into one IM site. However, it may be necessary to divide the dose and inject it into two different sites.

 

Example

The order is to give 300,000 units of Penicillin G Potassium IM. A concentration of 200,000 units/ml should be used. The medication on hand is in a 1,000,000 unit vial. How many ml will you give?

Here are typical instructions for reconstitution of medication
supplied in a 1,000,000 unit vial
Concentration Diluent to be Added
100,000 units/ml
200,000 units/ml
250,000 units/ml
9.6 ml
4.6 ml
3.6 ml

According to these instructions, you should add 4.6 ml of dilutent to the stock penicillin.

The reconstitution process.

Then set up the dimensional analysis so that "units" cancel and ml is left for the answer:

300,000 

x

1 ml = 1.5 ml
1 200,000

Ans: 1.5 ml

Example

The physician has ordered 0.5 gm of Mefoxin IM b.i.d. You have a 1 gm vial available. Directions for reconstitution are:

Concentration Amount of Diluent Withdrawable Volume
400 mg/ml
95 mg/ml
2 ml for IM use
10 ml for IV use
2.5 ml
10.5 ml

Before setting up the dimensional analysis, you need to determine the concentration that is needed. This is for IM use, and the table states the appropriate concentration is 400 mg/ml. That is the value to be used in the dimensional analysis. Also convert the prescribed amount from 0.5 gm to 500 mg.

500  mg

x

1 ml = 1.25 ml
1 400 mg

Ans: 1.25 ml or round to  1.3 mll

Since the recommended dilution of 2 ml creates 2.5 ml of medication, you will have a sufficient amount for the prescribed dose of 1.3 ml.

 

Heparin Calculations

Heparin is supplied in various concentrations, labeled in units per ml. It is administered subcutaneously or intravenously, usually with a tuberculin syringe.

Tuberculin syringe.

Note

Heparin calculations should be rounded to the hundredth place. This is consistent with the markings on the TB syringe.

 

Example

The physician has ordered heparin 5,000 units SC q 8h. Using a vial labeled 40,000 units per ml, calculate the amount of heparin to give.

5000 

x

1 ml = 0.125 ml
1 40,000

Rounding 0.125 ml to the nearest 100th, the answer is: 0.13 ml.

 

Insulin Calculations

Insulin is supplied in 10 ml vials labeled in the number of units per ml. U-100 insulin is the most commonly used concentration.

U-100 insulin.

The simplest and most accurate way to measure insulin is with an insulin syringe. An insulin syringe is calibrated in units and the ordered dose is read directly on the syringe. Therefore, to measure 16 units of U-100 insulin, you would simply measure to the 16 unit mark on the U-100 insulin syringe.

Measuring insulin in an insulin syringe.

When measuring U-100 insulin (100 units per ml) in a 1 ml tuberculin syringe, the number of units ordered will always equal an equivalent number of hundredths of a milliliter. Therefore, to measure 16 units of U-100 insulin, measure to the 0.16 ml mark on the tuberculin syringe. Be sure to use the cc scale on the syringe.

Measuring insulin in a tuberculin syringe.

Note

Calculations for insulin dosages are carried out in the same manner as for other parenteral medications. However, as with heparin, all insulin calculations should be rounded to the hundredth place.

Examples

  1. The order is to give 20 units of Regular Insulin. You are using U-100 insulin and a tuberculin syringe. What is the required dose?
20

x

1 ml = 0.2 ml
1 100

Ans: 0.2 ml

 

  1. The order is to give 35 units of NPH insulin SC. Available is a 10 ml vial labeled U-100 NPH insulin. Calculate the amount of insulin to give.
35

x

1 ml = 0.35 ml
1 100

Ans: 0.35 ml

 

0304

IV  Rate Calculations

INFORMATION REQUIRED ON AN ORDER FOR IV FLUIDS

  1. Type of fluid to be infused.
  2. Volume of the fluid to be infused.
  3. Time period over which the fluid is to be infused.

IV Administration Set Calibrations

IV flow rates are regulated in drops per minute (gtts/min). The size of the drop (drop factor) varies from large to small, and depending on the manufacturer and type of set used, it will require 10, 15, or 20 gtts to equal 1 ml in standard macrodrip sets, and 60 gtts to equal 1 ml in micro- or minidrip sets.

 

IV Drop Rate for

 

Note

For IV's, round off to the nearest whole number.

 

Example 1

The order is for D5 NS 1000 ml to be infused over eight hours. Calculate the infusion rate using an IV set calibrated to deliver 20 gtts/ml.

1000

x

20 gtts = 41.67 or 42 gtts/min
8 x 60 min 1

 

Example 2

The patient is to receive 1000 ml of 0.45% sodium chloride over the next 10 hours. The drop factor of the tubing is 15 gtts/ml. Determine the rate in gtts/min.

1000

x

15 gtts = 25 gtts/min
10 x 60 min 1

 

 

IV Drop Rate Calculations for Continuous Infusion

With continuous I.V. infusions of medications, the physician will order a medication dosage and not fluid volume. For example, the order may specify mg/hr or units/hr.

 

Example 1

The order is to administer a continuous I.V. Heparin drip at a rate of 1200 units per hour. The pharmacy sends up a 250 ml bag of Normal Saline with 25,000 units of Heparin added. Using a drop factor of 60 gtts/ml, determine the infusion rate to deliver the ordered amount of medication.

 

1000

x

15 gtts = 25 gtts/min
10 x 60 min 1