01. Calculation of drug dosages Systems of Medication Measurement…htm

CALCULATION OF DRUG DOSAGES: SYSTEMS OF MEDICATION MEASUREMENT AND COMMON EQUIVALENTS, CONVERSION BETWEEN SYSTEMS

A nurse has to be able to calculate drip rates, know the metric conversion and how much oral medication to dispense. Most nursing students have to take a medication dosage calculation test (med dose) before each semester begins. A score of at least 90%-95% has to be obtained in order to move on to the next semester. That means you can only miss 1-2 questions on your math test. Most nurses are not comfortable with taking these math tests. In this day and age, the are automatic IV pumps that control drip rates and pharmacists that determine the volume of a medications based upon weight. If you conquer these few rules that this article mentions, then passing the med dose test every semester should not be a problem.

Here are a few charts that you should already have learned in grade school through high school. Metric conversions will be on the majority of the med dose tests. Nursing schools want to make sure that you have mastered this. There are three types of medication measurement systems. First is the metric system which is the most commonly used in schools and hospitals.

The health professional must be meticulous in converting those measurements into the proper amount of liquid or solid medication that a patient requires. This takes converting from or within one or more of the three systems of measurements that health professionals use.

The Apothecary system is one of the oldest system of pharmacologic measurements. It’s expressed in romaumerals and special symbols. A unit of liquid measure is a minim and a unit for weight is a grain. You may even see some roman numeric symbols written in medication orders. Last, the household system is less accurate measurement that is based upon drops, teaspoons, tablespoons, cups and glasses.

Metric Conversions

Apothecary Conversions

Other symbols that the Apothecary system uses are: ss = ½, i = one, and ounces=

Household Conversions

Medications are prescribed in a specific amount or weight per volume. For example a single tablet has 100mg of medication; the volume of that tablet is 1. A medication that comes in 80 mg per 2mL has a volume of 2. Some liquid medications are prescribed as volume alone because they are only available in one strength. Common formulas for calculating medications are ratio and proportion, “desired over have”, and dimensional analysis. If you can remember these basic conversions, you should be able to pass these quarterly tests and use this knowledge throughout your nursing career.

Making sure that you correctly calculate a dose doesn’t matter much if the medication itself is incorrect or the dosing instructions are unclear. Some abbreviations in prescriptions are unacceptable because they cause ambiguity and confusion (the enemies of patient safety and quality healthcare!). For this reason, you don’t want to see these abbreviations on any medical orders you work with.

Required Information for Every Drug Order

1.     The name of the medication.

2.     The amount of the medication to be given, with the units specified.

3.     The route of administration to be used.
Remember that this is the way the medication is given. The most common routes are by mouth (p.o. or PO), or parenterally/by injection, which are: subcultaneously (subQ), intramuscularly (IM), or intravenously (IV). To review what these words mean, reread this section of lecture 3.

4.     The frequency with which the medication is to be administered.
For example, some medications may be given only once a day, while others may be administered every 6 hours.

5.     Any other information that could vary, depending upon what drug the order is for.
For example, if the drug must be reconsituted, the order might specify the type of diluent.
Or, if the order is for insulin, the order might specify the origin of the insulin.
Some medications might have special instructions, for example, to be taken with meals, or with a full glass of water, etc.
Also, for IV medications, which are given over an extended period of time, the length of time each dose should take or the rate at which each dose should be given will also need to be included (we will discuss this more in future chapters when we learn more about IVs).

Unacceptable Abbreviations in Prescriptions

            Volume

            60 minims    =   1 dram       =  5cc  =  1tsp

            4 drams      =   0.5 ounces   =  1tbsp

            8 drams      =   1 ounce 

            16 ounces    =   1pt.

            32 ounces    =   1qt.

            Weight                                                        

            60 grains  = 1dram                           1/60 grain=1mg

            8 drams    = 1 ounce                          15 grains=1g

            12 ounces  = 1 lb. (apothecaries')             2.2 lbs.=1kg

            Household          Apothecary 

            1tsp     =         1 dram

            1tsp     =         60 gtts (drops)

            3tsp     =         0.5 ounce

            1tbsp    =         0.5 ounce

            Household                   Apothecary                   Metric

            1tsp=5cc                     1fl.dram=4cc               5cc=1tsp

            3tsp=1tbsp                   4drams=0.5oz           15cc=1tbsp

            1tbsp=0.5oz or 15cc      8drams=2tbsp(1oz)                                         30cc=2tbsp(1oz)

            2tbsp=1oz or  30cc           16minims=1cc          1cc=16minims

          1pt.=16oz or 480cc         500cc=0.5L or 1pt

          1qt=32oz or 960cc          1000cc=1L or 1qt.

            Temp. Conversion

            C= F-32/1.8    

            F= 1.8*C-32         

The metric system of measurement is the most widely used system of measurement in the world.  It is the preferred system for administering medications, because it is based on a series of 10 measures or multiples of 10.  It is a simple and accurate form of measurement between health care professionals. 

Metric Weight Measures

1 kilogram (kg, Kg) = 1000 grams or 1000 g
1 gram = 1000 milligrams or 1000 mg
1 milligram (mg) = 1000 micrograms or 1000 mcg
1 microgram (mcg) =  0.001 milligrams or 0.001 mg

1 milligram = 0.001 gram or 0.001 g
1 microgram (mcg) = 0.000001 gram or 0.000001 g

Metric Volume Measures

1 milliliter (ml) = 0.001 liter or 0.001 L
1 liter = 1000 milliliters or 1000 ml
1kiloliter = 1000 liters or 1000 L

Metric Length Measures
1 millimeter (mm) =  0.001 meter
1 centimeter (cm) = 0.01 meter or 0.01 m
1 decimeter (dm) = 0.1 meter or 0.1 m
1 kilometer (km) = 1000 meters or 1000 m
1 meter (m) = 100 centimeters or 100 cm
1 meter (m) = 1000 millimeters or 1000 mm

1 centimeter (cm) = 10 millimeters or 10 mm

The apothecaries system of measurement is the oldest system of drug measurement.  In fact, it was the first system used to measure medication amounts. It is infrequently used as a drug measurement. There are a few medications that are still measured in grains (gr). To ensure administration of the correct dose of medication to a patient, it is important to know the conversion of grains to milligrams and how to convert from one system of measurement to another.

The household system of  measurement is based on the apothecary system of measures. Household measures are used to measure liquid medications.

  Parents understand one teaspoon of liquid medication more clearly than ordering 15 milliliters.  The important thing to realize with household measures is that these measures are not as exact as the metric system of measurement.  Also the comparison of metric measures to household measures are not equal.  These measures are called equivalent measures because the measurement is close enough.  A liter is very close in equal measurement to a quart.  It is not an exact measure. It is an equivalent. 

These measures should be memorized to assist with medication calculation problems.  It may be necessary to convert from one measure to another before you can begin to solve medication problem.  The learning activity utilizes flash cards to help you memorize these facts. 

Many nurses are weak with drug calculations of all sorts. This article will help to review the major concepts related to drug calculations, help walk you through a few exercises, and provide a few exercises you can perform on your own to check your skills. There are many reference books available to review basic math skills, if you find that you have difficulty with even the basic conversion exercises.

Common Conversions:

1 Liter = 1000 Milliliters

1 Gram грам = 1000 Milligrams

1 Milligram = 1000 Micrograms

1 Kilogram = 2.2 pounds

General Information

There are 3 different types of measurements you will encounter when dealing with medications: Household, Apothecary, and Metric.

Type Number Solids Liquids Household

Whole numbers and Fractions before nit.

Examples:

APOTHECARY

Whole numbers, Fractions, and Roman Numerals after unit.

Ex:

Metric

Whole numbers and decimals before unit (always put a 0 in front of the decimal).

Ex:

Note: When more than one equivalent is learned for a unit, use the most common equivalent for the measure or use the number that divides equally without a remainder.

Common Conversion Factors

Roman Numerals

Methods of Calculation

Any of the following three methods can be used to perform drug calculations. Please review all three methods and select the one that works for you. It is important to practice the method that you prefer to become proficient in calculating drug dosages.

REMEMBER:

Before doing the calculation, convert units of measurement to one system.

I.            Basic Formula: Frequently used to calculate drug dosages.

D (Desired dose)

H (Dose on hand)

V (Vehicle-tablet or liquid)

D = dose ordered or desired dose

H = dose on container label or dose on hand

V = form and amount in which drug comes (tablet, capsule, liquid)

II.            Ratio & Proportion: Oldest method used in calculating dosage.

III.            Left side are known quantities

IV.            Right side is desired dose and amount to give

V.            Multiply the means and the extremes

VI.

VII.            D=1 gm (note: need to convert to milligrams)

VIII.            1 gm = 1000 mg

IX.            H=250 mg

X.            V=1 capsule

XI.            250X = 1000

XII.            X = 4 capsules

XIII.            Fractional Equation

XIV.            Cross multiply and solve for X.

XV.

XVI.

XVII.

XVIII.

XIX.

XX.            0.125X = 0.25

XXI.            X = 2 tablets

XXII.            How to Calculate Continuous Infusions

A.   mg/min (For example – Lidocaine, Pronestyl)

B.

C.

D.   mcg/min (For example – Nitroglycerin)

E.

F.

G.   mcg/kg/min (For example – Dopamine, Dobutamine, Nipride, etc.)

1.     To calculate cc/hr (gtts/min)

2.

3.

4.     To calculate mcg/kg/min

5.

6.

A.   How to calculate mcg/kg/min if you know the rate of the infusion

B.   For example:

C.   26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

D.   NOW DO THE REST!

E.    If you have a 75 kg patient for example…

F.    How to calculate drips in cc per hour when you know the mcg/kg/min that is ordered or desired

G.   For example:

H.   400 mg Dopamine in 250 cc D₅W = 26.6 mcg/cc/min

I.       ALWAYS WORK THE EQUATION BACKWARDS AGAIN TO DOUBLE CHECK YOUR MATH!

J.      For example:

K.

L.    For example:

M. 400mg of Dopamine in 250 cc D₅W = 1600 mcg/cc 60 min/hr = 26.6 mcg/cc/min

N.   26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

O.   NOW DO THE REST!!

P.    If you have a 75 kg patient for example

DRUG DOSE CALCULATIONS

 FINDING THE ORDERED DOSE

The ordered dose is the most simple dosage calculation for the prehospital care provider. In this type of problem, the paramedic is given an order to administer to a patient.

There are five (5) components to locate in this type of problem: the desired dose, the concentration of the drug, volume on hand, is a weight conversioeeded, and what unit to administer. Let’s take a look at each of the five components and what each means.

1.     THE DESIRED DOSE

The desired dose is an order from the doctor and includes the amount of the medication and should also include the route of administration. The route of administration may be subcutaneous, intramuscular, intravenous (IV), endotracheal, sublingual, intraosseous, transdermal, oral, and rectal. Orders can be verbal or written as a standing orders in your protocol. The desired dose in the example that follows is known as a basic doctor’s order. ? (2.5 mg of medication)

2 CONCENTRATION

The second item to identify is the concentration. The paramedic is given the concentration of a vial, an ampule, a prefilled syringe, or a tablet. Concentration can be listed as common fractions, percentages solutions, or by mass (e.g., grams and milligrams). Example: 10 mg/ml

3.  VOLUME ON HAND

The volume on hand refers to the amount of liquid that the drug is in. In the example: 10 mg/ml, there is a 10 mg concentration of drug in 1 ml of liquid.

4. LB TO KG

Look at the Doctor’s basic order. Is it directly tied to the patient’s weight?

Example: Give 5 mg/kg of drug X, Patient weights 220 lb. Remember, not all drug orders are based on weight.

5. UNIT TO ADMINISTER

It is essential to look at the doctor’s order and identify the unit of measurement that will be administered to the patient. Some texts refer to the unit to administer as “what you are looking for.” Example: How many ml will you administer?

Desired Dose:

 Concentration:

Volume on Hand:

Lb to Kg:

Looking for:

EXAMPLE PROBLEM

1. Doctor orders 2.5 mg of morphine to be administered IV to a patient with substernal chest pain. You have 1 ml vial that contains 10mg of morphine (10 mg/ml). How many milliliters are you going to have to draw up into a syringe and push IV into your patient’s IV line port?

NOTE: Some problems may not ask, “How many milliliters?” You will have to deduce “milliliters” from the context of the problem.

The KEY to solving dosage calculation problems consistently and accurately, you must be ORGANIZED. Developing the habit of organization early will make drug dosage problems much-MUCH easier. So, before starting any calculations, organize all of the key components to the problem.

Desired Dose: 2.5 mg of morphine IV

Concentration: 10 mg

Volume on Hand: 1 ml

Lb to Kg: None

Looking for: ml to be given

Now that you have identified the components of the doctor’s order, you caow fill-in the formula and solve the problem. There are several books and methods used to calculate drug dosages and this is what confuses most Paramedic Student, (Multiple Methods). For the purpose of this class, we will be using the Formula Method.

TOP

Cancel any like units (g, mg) and/or (zeros): BOTTOM

Formula #1

Desired Dose X Volume on Hand = ___ml to be given

Concentration

2.5 mg X 1 ml = 2.5 ml or ( 2.5 ÷ 10 ) = 0.25 ml to be given

10 mg 10

FINDING THE UNITS PER KILOGRAM

Finding the units per kilogram adds a new dimension to the previous problem. Instead of the basic order, the doctor will order a certaiumber of units (e.g., gram, milligrams, micrograms) of the drug to be administered based on the patients weight, almost always given in kilograms. This is referred to as an order based on patient’s weight. Look at the following example.

The Doctor orders 5 mg/kg of Bretylium IV to be administered to your patient. You have premixed syringes with 500 mg/10ml. Your patient weights 176 lb. How many milliliters will you administer?

Look at the Doctor’s order again. It is directly tied to the patient’s weight

(5 mg/kg). Put another way, the order is saying, “For every kilogram of patient, give 5 mg of Bretylium.”

First Things First!!! Convert lb to kg and then apply kg to the basic order to obtain the Desired Dose. Now, organize the other key components in the order.

Desired Dose: 400 mg (176 lb ÷ 2.2 = 80 kg, 80 X 5 mg = 400 mg, this is the Desired Dose)

Concentration: 500 mg

Volume on Hand: 10 ml

Lbs to Kg: (Yes) 176lb = 80 kg

Looking for: ml to be given

**USE THE SAME FORMULA AS BEFORE**

TOP

Cancel any like units (g, mg) and/or (zeros): BOTTOM

Formula #1

Desired Dose X Volume on Hand = ___ml to be given

Concentration

400 mg X 10 ml = 40 ml = 8 ml to be given

500 mg                    5   

There are several ways to determine how much of a medication you are supposed to administer to a patient. No matter what method you choose to use, if performed properly, they should all come up with the same answer. Following are three methods for determining the appropriate dose based on information that you have available to you.

  Method 1

The first method is based on the following   formula:

An Example:   Medical control orders you to administer 5 mg of morphine sulfate IV to your 84-year-old female patient who has signs and symptoms of a hip fracture. The morphine in your formulary   contains 10 mg in 1 mL. How many milliliters of morphine sulfate do you need to administer to this patient in order to deliver 5 mg?

You have the following information:

  Order: 5 mg morphine sulfate IV

  On hand: 10 mg/1 mL  

  Fill in the formula:

  Cancel any common values (volumes or concentrations) that exist on the top and on the bottom, and multiply across the top.

  You need to administer 0.5 mL of morphine   sulfate to your patient.  

  Method 2

  This second method involves   ratio and proportion. The symbol for proportion is and the symbol for ratio is using the same problem as in method 1, start with the known ratio on the left side of the proportion:

Place the unknown ratio on the right side of the proportion in the same sequence as the ratio on the left side of the proportion. This ratio is usually the physician order or the dosage that you are permitted to administer based on standing orders:

  First, multiply the extremes ( the far outside   values:   10 mg and   X   mL) and place the result on the left side of the equation. Second, multiply the means (  the numbers on either side of the proportion symbol:   1 mL and 5 mg) and place this value on the right side of the expression:

Multiply:

  Divide both sides by the number in front of the  X

  You need to administer 0.5 mL of morphine   sulfate to your patient.

  Method 3

The third method is referred to as the   cross   multiplication method.   This method sets the problem up using fractions. The fi rst fraction is the concentration, and the second fraction is the physician’s order over the volume of medication being administered.

Cross multiply the fractions by multiplying numerators by the denominator on the opposite side. Express the results as an algebraic equation the same as used in the proportion method.

  You need to administer 0.5 mL of morphine   sulfate to your patient.  

Many nurses are weak with drug calculations of all sorts. This article will help to review the major concepts related to drug calculations, help walk you through a few exercises, and provide a few exercises you can perform on your own to check your skills. There are many reference books available to review basic math skills, if you find that you have difficulty with even the basic conversion exercises.

Common Conversions:

1 Liter = 1000 Milliliters

1 Gram = 1000 Milligrams

1 Milligram = 1000 Micrograms

1 Kilogram = 2.2 pounds

Methods of Calculation

Any of the following three methods can be used to perform drug calculations. Please review all three methods and select the one that works for you. It is important to practice the method that you prefer to become proficient in calculating drug dosages.

Remember: Before doing the calculation, convert units of measurement to one system.

Basic Formula:

Frequently used to calculate drug dosages.

D (Desired dose)

H (Dose on hand)

V (Vehicle-tablet or liquid)

D = dose ordered or desired dose

H = dose on container label or dose on hand

V = form and amount in which drug comes (tablet, capsule, liquid)

Ratio & Proportion:

 Oldest method used in calculating dosage.

Left side are known quantities

Right side is desired dose and amount to give

Multiply the means and the extremes

D=1 gm (note: need to convert to milligrams)

1 gm = 1000 mg

H=250 mg

V=1 capsule

250X = 1000

X = 4 capsules

FRACTIONAL EQUATION

Cross multiply and solve for X.

0.125X = 0.25

X = 2 tablets

INTRAVENOUS FLOW RATE CALCULATION (TWO METHODS)

Two Steps

Step 1 – Amount of fluid divided by hours to administer = ml/hr

One Step

Two Steps

One Step

HOW TO CALCULATE CONTINUOUS INFUSIONS

mg/min (For example – Lidocaine, Pronestyl)

mcg/min (For example – Nitroglycerin)

mcg/kg/min (For example – Dopamine, Dobutamine, Nipride, etc.)

To calculate cc/hr (gtts/min)

TO CALCULATE MCG/KG/MIN

Example:         

Nipride 100 mg/250 cc D₅W was ordered to decrease your patient’s blood pressure.
The patient’s weight is 143 lbs, and the IV pump is set at 25 cc/hr. How many mcg/kg/min of Nipride is the patient receiving?

How to calculate mcg/kg/min if you know the rate of the infusion

For example:

26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

NOW DO THE REST!

If you have a 75 kg patient for example…

How to calculate drips in cc per hour when you know the mcg/kg/min that is ordered or desired

For example:

400 mg Dopamine in 250 cc D₅W = 26.6 mcg/cc/min

ALWAYS WORK THE EQUATION BACKWARDS AGAIN TO DOUBLE CHECK YOUR MATH!

For example:

For example:

400mg of Dopamine in 250 cc D₅W = 1600 mcg/cc 60 min/hr = 26.6 mcg/cc/min

26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

NOW DO THE REST!!

If you have a 75 kg patient for example

SUMMARY

Many nurses have difficulty with drug calculations. Mostly because they don’t enjoy or understand math. Practicing drug calculations will help nurses develop stronger and more confident math skills. Many drugs require some type of calculation prior to administration. The drug calculations range in complexity from requiring a simple conversion calculation to a more complex calculation for drugs administered by mcg/kg/min. Regardless of the drug to be administered, careful and accurate calculations are important to help prevent medication errors. Many nurses become overwhelmed when performing the drug calculations, when they require multiple steps or involve life-threatening drugs. The main principle is to remain focused on what you are doing and try to not let outside distractions cause you to make a error in calculations. It is always a good idea to have another nurse double check your calculations. Sometimes nurses have difficulty calculating dosages on drugs that are potentially life threatening. This is often because they become focused on the actual drug and the possible consequences of an error in calculation. The best way to prevent this is to remember that the drug calculations are performed the same way regardless of what the drug is. For example, whether the infusion is a big bag of vitamins or a life threatening vasoactive cardiac drug, the calculation is done exactly the same way.

Many facilities use monitors to calculate the infusion rates, by plugging the numbers in the computer or monitor with a keypad and getting the exact infusion titration chart specifically for that patient. If you use this method for beginning your infusions and titrating the infusion rates, be very careful that you have entered the correct data to obtain the chart. Many errors take place because erroneous data is first entered and not identified. The nurses then titrate the drugs or administer the drugs based on an incorrect chart. A method to help prevent errors with this type of system is to have another nurse double check the data and the chart, or to do a hand calculation for comparison. The use of computers for drug calculations also causes nurses to get “rusty” in their abilities to perform drug calculations. It is suggested that the nurse perform the hand calculations from time to time, to maintain her/his math skills.

Drugs and Dosage Formulas and Conversions

Volume

         60 minims    =   1 dram       =  5cc  =  1tsp

         4 drams      =   0.5 ounces   =  1tbsp

         8 drams      =   1 ounce

         16 ounces    =   1pt.

         32 ounces    =   1qt.

Weight                                                       

         60 grains  = 1dram                           1/60 grain=1mg

         8 drams    = 1 ounce                          15 grains=1g

         12 ounces  = 1 lb. (apothecaries’)             2.2 lbs.=1kg

         Household          Apothecary

         1tsp     =         1 dram

         1tsp     =         60 gtts (drops)

         3tsp     =         0.5 ounce

         1tbsp    =         0.5 ounce

         Household                   Apothecary                   Metric

         1tsp=5cc                     1fl.dram=4cc               5cc=1tsp

         3tsp=1tbsp              4drams=0.5oz                  15cc=1tbsp

         1tbsp=0.5oz or 15cc          8drams=2tbsp(1oz)          30cc=2tbsp(1oz)

         2tbsp=1oz or  30cc           16minims=1cc               1cc=16minims

                                      1pt.=16oz or 480cc         500cc=0.5L or 1pt.

                                        1qt=32oz or 960cc          1000cc=1L or 1qt.

         Temp. Conversion

         C= F-32/1.8   

         F= 1.8*C-32             

METHODS OF CALCULATION

Any of the following three methods can be used to perform drug calculations. Please review all three methods and select the one that works for you. It is important to practice the method that you prefer to become proficient in calculating drug dosages.

Remember: Before doing the calculation, convert units of measurement to one system.

XXIII.            Basic Formula: Frequently used to calculate drug dosages.

D (Desired dose)

H (Dose on hand)

V (Vehicle-tablet or liquid)

D = dose ordered or desired dose

H = dose on container label or dose on hand

V = form and amount in which drug comes (tablet, capsule, liquid)

XXIV.            Ratio & Proportion: Oldest method used in calculating dosage.

XXV.            Left side are known quantities

XXVI.            Right side is desired dose and amount to give

XXVII.            Multiply the means and the extremes

XXVIII.

XXIX.            D=1 gm (note: need to convert to milligrams)

XXX.            1 gm = 1000 mg

XXXI.            H=250 mg

XXXII.            V=1 capsule

                                                                                                                           XXXIII.            250X = 1000

                                                                                                                       XXXIV.            X = 4 capsules

XXXV.            Fractional Equation

XXXVI.            Cross multiply and solve for X.

XXXVII.

XXXVIII.

XXXIX.

XL.

XLI.

                                                                                                                                  XLII.            0.125X = 0.25

                                                                                                                                 XLIII.            X = 2 tablets

XLIV.            How to Calculate Continuous Infusions

H.  mg/min (For example – Lidocaine, Pronestyl)

I.

J.

K.   mcg/min (For example – Nitroglycerin)

L.

M.

N.   mcg/kg/min (For example – Dopamine, Dobutamine, Nipride, etc.)

7.     To calculate cc/hr (gtts/min)

8.

9.

10.                       To calculate mcg/kg/min

11.

12.

Q.  How to calculate mcg/kg/min if you know the rate of the infusion

R.   For example:

S.    26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

T.   NOW DO THE REST!

U.   If you have a 75 kg patient for example…

V.   How to calculate drips in cc per hour when you know the mcg/kg/min that is ordered or desired

W.For example:

X.   400 mg Dopamine in 250 cc D₅W = 26.6 mcg/cc/min

Y.   ALWAYS WORK THE EQUATION BACKWARDS AGAIN TO DOUBLE CHECK YOUR MATH!

Z.    For example:

AA.

BB.                    For example:

CC.                   400mg of Dopamine in 250 cc D₅W = 1600 mcg/cc 60 min/hr = 26.6 mcg/cc/min

DD.                   26.6 is the dosage concentration for Dopamine in mcg/cc/min based on having 400 mg in 250 cc of IV fluid. You need this to calculate this dosage concentration first for all drug calculations. Once you do this step, you can do anything!

EE.                    NOW DO THE REST!!

FF.                      If you have a 75 kg patient for example

CALCULATING IV DRUG DOSES

Principles

1. For drugs already in solution, check the amount of drug in each ml and the total amount of drug in the container.

2.Make sure you are clear about the dose units used.Most commonly prescribed are milligrams (mg) or micrograms.

3. Beware of drugs such as insulin and heparin, for which doses are prescribed in international units (which is sometimes, but should never be abbreviated to i.u. which can be misread as 10).

4. Check the dose on the prescription and that it is expressed in the same units as on the medicine label.

5. If the prescription and the medicines label use different units of strength, refer to the conversion table and calculation examples on page 4 and 5.

6. Once you are sure that the units are the same, divide the required dose by the amount of the drug in the ampoule and multiply by the volume of solution in the vial or ampoule.

7. The answer is the volume needed for each dose.

CALCULATING DRIP RATES FOR GRAVITY FLOW INFUSIONS

PRINCIPLES

1.     Without a flow control device such as a pump, infusion rates depend entirely on gravity. Rate of flow is measured by counting drops per minute.

2.     Administration sets deliver controlled amounts of fluid at a predetermined fixed rate, measured in drops per minute.

3.     It is also important to check the number of drops per ml delivered by the administration set (which is printed on the outer packaging). This may vary between sets, between manufacturers and between different infusion fluids or drug solutions.

4.     A (drug) solution administration set will usually deliver 20 drops per ml of clear infusion fluid such as 0.9% sodium chloride injection.

5.     A blood administration set will deliver 15 drops per ml of blood.

6.     A burette administration set will usually deliver 60 drops per ml of infusion fluid or drug solution.

CALCULATING INFUSION RATES FOR INFUSION DEVICES

1.     All infusions require rate control. This can be achieved using a roller clamp (gravity flow), an infusion pump, a syringe driver, a syringe pump or a disposable device.

2.     When using any sort of rate control device, check at least the following parameters at regular intervals in accordance with local policy:

3.     • Volume given

4.     • Volume remaining

5.     • Administration rate

6.     • Condition of the patient including the administration site.

7.     Before and after transfer of care between units or teams, make sure you repeat the above checks.

8.     You should always check the manufacturer’s instructions or refer to local policy to ensure you use the correct administration set for the device and that the device is programmed correctly.

9.     An administration device should only be used by practitioners who have been trained and are competent in the use of the particular device.

10.           The rate may be prescribed in terms of:

11.           Volume: For example ml per hour or ml per min OR amount of drug:

For example mg per min or international units per hour.

CALCULATING RATES FOR SYRINGE DRIVERS

A syringe driver pushes the plunger of a syringe forward at an accurately controlled rate.

• For most syringe pumps the rate is set according to the volume of solution injected per hour i.e. in ml per hour.

• For some syringe drivers the rate is set according to the distance travelled by the plunger in mm per hour or mm per 24 hour.

If the rate is to be set in mm, the volume to be adminstered by a syringe driver depends on the diameter of the syringe barrel as well as on the rate setting. Different makes of syringe may have different barrel sizes. It is essential that the brand of syringe to be used is specified and the stroke length is measured.

Serious errors have occurred when settings in mm per hour and ml per hour have been confused.

1. Prepare prescribed infusion.

2. Prime the extension set with fluid.

3. If using a syringe driver, measure the stroke length (the distance the plunger has to travel) in mm.

4. Check carefully the units of time in which the syringe driver operates:

Is the rate set in mm per hour or mm per day (24 hours)?

See diagram for example.

CALCULATING IV DRUG DOSES FOR CHILDREN AND NEONATES

1. Remember that many injections are made for adults. For children’s doses, you may need as little as one tenth (1/10) or even one hundredth (1/100) of the contents of one ampoule or vial.

2.When calculating infusions, consider the child’s total daily fluid allowance.More concentrated individual infusions may be required. Discuss with the pharmacist or prescriber.

3. Ensure the prescribed infusion fluid/diluent is appropriate for the child e.g. the sodium content of an infusion contributes to the child’s total daily sodium requirement.

4. Displacement Values.

For many injections presented as powders for reconstitution, the powder adds to the volume of the final solution after the diluent has been added. This ‘displacement value’ must be taken into account when the dose needed is less than the full contents of the vial or ampoule.

The displacement value can be found on the package insert. It may vary with brands, so it is crucial to check the package insert for the product you are actually using.

5. For the above reasons, the calculations involved in preparing and administering infusions for children are often particularly complex. It is most important that these calculations are independently checked

 DRUGS CALCULATION.

There are several ways to determine how much of a medication you are supposed to administer to a patient. No matter what method you choose to use, if performed properly, they should all come up with the same answer. Following are three methods for determining the appropriate dose based on information that you have available to you.

  Method 1

The first method is based on the following   formula:

An Example:   Medical control orders you to administer 5 mg of morphine sulfate IV to your 84-year-old female patient who has signs and symptoms of a hip fracture. The morphine in your formulary   contains 10 mg in 1 mL. How many milliliters of morphine sulfate do you need to administer to this patient in order to deliver 5 mg?

You have the following information:

  Order: 5 mg morphine sulfate IV

  On hand: 10 mg/1 mL  

  Fill in the formula:

  Cancel any common values (volumes or concentrations) that exist on the top and on the bottom, and multiply across the top.

  You need to administer 0.5 mL of morphine   sulfate to your patient.  

  Method 2

  This second method involves   ratio and proportion. The symbol for proportion is and the symbol for ratio is using the same problem as in method 1, start with the known ratio on the left side of the proportion:

Place the unknown ratio on the right side of the proportion in the same sequence as the ratio on the left side of the proportion. This ratio is usually the physician order or the dosage that you are permitted to administer based on standing orders:

  First, multiply the extremes ( the far outside   values:   10 mg and   X   mL) and place the result on the left side of the equation. Second, multiply the means (  the numbers on either side of the proportion symbol:   1 mL and 5 mg) and place this value on the right side of the expression:

Multiply:

  Divide both sides by the number in front of the  X

  You need to administer 0.5 mL of morphine   sulfate to your patient.

  Method 3

The third method is referred to as the   cross   multiplication method.   This method sets the problem up using fractions. The fi rst fraction is the concentration, and the second fraction is the physician’s order over the volume of medication being administered.

Cross multiply the fractions by multiplying numerators by the denominator on the opposite side. Express the results as an algebraic equation the same as used in the proportion method.

  You need to administer 0.5 mL of morphine   sulfate to your patient.  

Many nurses are weak with drug calculations of all sorts. This article will help to review the major concepts related to drug calculations, help walk you through a few exercises, and provide a few exercises you can perform on your own to check your skills. There are many reference books available to review basic math skills, if you find that you have difficulty with even the basic conversion exercises.

TOP CALCULATION TIPS

Drugs are formulated into medicines in such a way that most adult doses are easily calculated and predictable, e.g.1 or 2 tablets, 1 or 2 capsules, 1 vial or ampoule of an injectable medicine, 1 suppository.

Before doing a calculation, it is sensible to estimate the dose you are likely to require so that you know whether your calculated answer seems reasonable i.e. roughly what you expected.

To check doses use a reliable reference source, such as the BNF or BNF for Children.

For recommended administration methods, see local drug policies or national guides such as The IV Guide.

Dose volumes of oral liquid medicines are typically 5-20mls for adults and 5mls or less for children.

Crushing tablets should be avoided wherever possible. Some tablets, such as ‘modified release’ products should never be crushed.Always ask your pharmacists’ advice before crushing tablets. If itmust be done, a pestle and mortar or tablet crusher should be used and the tablet ground to as fine a powder as possible.

Always check childrens’ and babies’ weights carefully.Make sure they are weighed in kg and that their weight is recorded in kg.

If a calculation using weight or surface area gives an answer equivalent to or greater than the normal adult dose, reconfirm that it is what is really required.

If you are in any doubt about a calculation, stop, and contact the ward pharmacist, an on-call pharmacist or the prescriber.

Principles

The way the strength of a drug in a solution is described will affect the way a dose calculation is carried out

Doses may be expressed in a number of different ways:

1.Mass (weight) per volume of solution e.g. mg in 10ml, mMol/L.

2. Units of activity per volume of solution e.g. units per ml.

3. Percentage This is the weight of the drug in grams that is contained in each 100ml of the solution. Common examples are 0.9% sodium chloride; 5% glucose

If you know the number of grams in 1000ml, divide by 10 to convert to % strength.

If you know the % strength, multiply by 10 to give the number of grams of drug in 1000ml.

If you know the % strength, divide by 100 to calculate the amount of drug in 1ml.

4. Ratios Strengths of some drugs such as adrenaline (epinephrine) are commonly expressed in ratios

CALCULATING ORAL DOSES IN TABLETS

Principles

1. Check the strength of (amount of drug in) each tablet or capsule.

2.Make sure you are clear about the dose units used, most commonly prescribed are milligrams or micrograms.

3. Check the dose on the prescription and that it is expressed in the same units as on the medicine label.

4. If the prescription and the medicines label use different units of strength, refer to the conversion table and calculation examples on page 4 and 5.

5. Once you are sure that the units are the same, divide the required dose by the strength of the tablet or capsule.

6. The answer is the number of tablets/capsules needed for each dose.

Extra safety tip

If your first calculation gives a dose of more than two tablets, double check the calculation and confirm thatthe dose doesn’t exceed the manufacturer’s recommended maximum. If it does, or if you are still unsure that the dose is correct, check with the prescriber or pharmacist.

CALCULATING ORAL DOSES FOR CHILDREN AND NEONATES

Principles

1. Always use the smallest oral syringe that will hold the volume you need to measure.

2. If the dose prescribed means that less than a whole tablet or capsule is required, check with the pharmacy that it is appropriate to break a tablet or split a capsule before doing so.

3. If it is essential, dissolve or disperse the powder/crushed tablet in an accurately measured amount of water (e.g. 5ml). Stir and draw up the required volume immediately

4. If the result cannot be accurately measured e.g. 0.33ml, it is generally acceptable to round the dose up or down. However, the actual dose given must be within 10% of the calculated dose. If this cannot be achieved, discuss with the prescriber and pharmacist.

CALCULATE AN IV DRIP INFUSION

In many cases, patients require medication to be infused on a continual base. Paramedics will receive orders to administer a certaiumber of units (usually milligrams or micrograms) of a medication per minute to a patient through an IV. Known as an infusion, it is also referred to as an IV drip because it involves calculating the number of drops that “drip” and are delivered intravenously each minute to deliver the amount of drug the doctor is ordering. Even though most of these IV infusions are commercially available already premixed, paramedics will be tested on mixing the medication and starting the infusion correctly without the medication being premixed.

Formula #2 The Doctor orders 2 mg/min of Lidocaine to be infused to a patient who is experiencing an arrhythmia. Your ambulance carries only 250 ml bags of D5W. You have a 60 gtt/mL microdrip setup. How many drops per minute will you adjust your administration set to drip?

Before starting any drug calculation, organize the key information just as you’ve been doing, but, there will be a couple of new categories in this formula and set up a little differently.

Desired Dose: 2 mg Lidocaine IV

Concentration: 1 g Lidocaine

IV Bag in ml: 250 ml D5W

Lbs to Kg: None

Admin. Setup: 60 gtt/ml

Looking for: gtt/min

IV bag volume (ml) Desired Dose Admin. Setup (gtt)

———————- X ————— X ———————- = gtt/min

Concentration of Drug 1 min 1ml

250 ml 2 mg 60 gtt

——- X ——– X ———- = gtt/min

1 g 1 min 1 ml

Note: Convert the grams you mixed in the bag to match the milligrams in the Doctor’s order:

250 ml 2 mg 60 gtt 25 2 6 gtt

——- X ——– X ———- = —- X —- X —- = 300 ÷ 10 = 30 gtt/min

1000 mg 1 min 1 ml 10 1 min 1

MILLILITERS PER HOUR for IV Fluids

Often, doctor’s order or protocols state that you are to run an IV in milliliters per hour of over a specific period of time. To set an IV’s administration set, the mL must be converted to drops per minute. This section shows how to convert that type of order. This may sound confusing but a simple conversion formula is all that is needed.

EXAMPLE PROBLEM