Medmath pharmacology

Med MathMaking Nurses’ Lives

Simple in Numbers

Dr. Cyruz P. TuppalRN, RM, RT, MSN, MASPED,

DMS, [email protected]@yahoo.com

mailto:[email protected]

mailto:[email protected]

Tips for success

Pick one method, that is easiest for YOUStudy itLearn itPractice itPractice itPractice it

Topics

Apothecary SystemWeight and Temperature ConversionsMetric SystemMed Math Administration Doses Weight Based Doses Drip Rate Calculations

Apothecary System

Phased out and replaced by metric systemBasic Units: grain (gr), dram (dr), drop (gtt), ounce, (oz), pint (pt), quart (qt)Equivalents

1dr = 1 tsp = 60 gtts3tsp = 1 Tbsp

Weight Conversion

Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in pounds

Conversion Practice

80 kilogram patient, what is weight in pounds

kilograms X 2.2 = pounds

80 X 2.2 = 176 lbs.

Conversion Practice

100 kilogram patient, what is weight in pounds

kilograms X 2.2 = pounds

100 X 2.2 = 220 lbs.

Weight Conversion

Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in poundsFact: Weight in pounds / 2.2 = weight in kilograms

Conversion Practice

245 lb patient, what is weight in kilograms

lbs / 2.2 = kilograms

245 / 2.2 = 111.36 kgs

Conversion Practice

140 lb patient, what is the weight in kilograms

lbs / 2.2 = kilograms

140 / 2.2 = 63.63 kilograms

Conversion Practice

The easy way…

Half of weight in pounds, subtract 10%

Example: 180 lbs . . . . . 9010% of 90 = 981 kilograms

Conversion Practice

180 lb patient, what is the weight in kilograms

lbs / 2.2 = kilograms180 / 2.2 = 81.82 kilograms

KNOW YOUR WEIGHT CONVERSIONS!!!!!

Temperature Conversions

Fahrenheit: Water Freezes at 32º F Water Boils at 212º F

Celsuis: Water Freezes at 0º C Water Boils at 100º C


Fahrenheit CelsiusSubtract 32 from the temperatureMultiply by 0.556 or 5/9

98.6 – 32 = 66.6

66.6 X 0.556 = 37.03 = 37º C

Practice

Convert 103º F to Celsius

103 – 32 = 71

71 X 0.556 = 39.48º C


Celsius FahrenheitMultiply by 1.8Add 32

37º X 1.8 = 66.666.6 + 32 = 96.6º F

Practice

Convert 44º C to Fahrenheit

44 X 1.8 = 79.2

79.2 + 32 = 111.2 º F

On your own

120 º F Celsius76.4 º F Celsuis

60 º C Fahrenheit24 º C Fahrenheit

Metric System

System of 10 (base 10)No fractions only decimalsEASY!

Metric System

Metric System

Deca 10Hecto 100Kilo 1000

Deci0.1Centi 0.01Mili 0.001

Metric System

Gram = gLiter = lKilogram = kgMilliliter = mLMilligram = mgCubic centimeter = ccMicrogram = g

1 L = 1000 mL1 mL = 1 cc1 g = 1000 mg1 mg = 1000 g1cc = 1 mL1 g = 0.001 mg1 mg = 0.001 g

The math

Adding – keep the decimal points in lineSubtracting – see aboveMultiplying – multiply without regard to decimals then add decimal placesDividing – make the divisor a whole number and add zeroes to the dividend

Addition

4.3795+ 5.2389---------------

9.6184

Subtraction

9.6184- 5.2389---------------

4.3795

Multiplication

34.76X 4.935-------------- 17154060

Add decimal places = 5 171.54060 = 171.5406

Division

.75 / .995 75 / 99.5 move

decimal--------------0.7537

Converting

1g = 1000mg so… g mg X1000

1mg = 1000 µg so… mg g X 1000

1g = ???? g = 1,000,000 g

Converting

500mL = 0.5L so… mL L /1000

The Bottom Line…To convert from the base to mili X

1000To convert from mili to the base /

1000To convert from mili to X

1000To convert from base to X

1000000

Standard Administration

The long formula

dose desired X volume on hand

Volume to administer = ------------------------------------

dose on hand

Example

Orders call for 0.5mg Atropine for symptomatic bradycardia. You have 1mg in 10 mL pre-filled syringe

0.5 mg X 10 mL------------------ = volume to

administer 1.0 mg

Example

mg’s cancel out0.5 X 10mL = 5mL

0.5 mg X 10 mL------------------ = 5 mL

1.0 mg

Another Example

You have 100mg Furosemide in a 10mL vial. The order is for 40mg

80 mg X 10 mL------------------ = volume to

administer 100 mg

Example

mg’s cancel out80 X 10mL = 800mL/100 = 8

80 mg X 10 mL------------------ = 8 mL

100 mg

Catching on?

Try it on your own

Benadryl – 50 mg in 2 mLOrders are for 12.5 mgShow your work

Benadryl

12.5 mg X 2 mL------------------ = volume to

administer 50 mg

12.5 X 2 = 25 / 50 = 0.5 mL

The easy way

Set up an equationCross MultiplyDivideSound like algebra?

The easy way

Order is for 45 mg BenadrylYou have 50 mg in 2 mL

50 45--- --- 2 X

The easy way

50 45--- --- 2 X

Multiply 45 X 2 = 90Divide 90 by 50 = 1.8

So… you would administer 1.8 mL = 45 mg

Another example

Order is for 3 mg ValiumYou have 10 mg in 2 mL

10 3--- -- 2 X

Another example

10 3--- -- 2 X

Multiply 3 X 2 = 6Divide 6 by 10 = 0.6


Finally, the good stuff

Order is for 145 µg of Fentanyl CitrateYou have 300 mcg in 5 mL

300 145----- ----- 5 X

The good stuff

300 145----- ----- 5 X

Multiply 145 X 5 = 725Divide 735 by 300 = 2.42 = 2.4


Weight Based Dosage

1. Convert weight to kgs.2. Calculate the dose to give3. Calculate the volume to

administer

Weight Based Dosage

1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.

1. Convert the weight to kilograms. 185 / 2.2 = 84 kgsOr 93 – 9.3 = 83.7 = 84 kgs

Weight Based Dosage


2. Calculate the dose to give 84 kgs X 1.5 mg = 126 mg

Weight Based Dosage


3. Calculate the volume to administer

126 mg is the dose we want to give 10 mL pre-filled syringe containing

100 mg

Weight Based Dosage

126 mg X 20 mL------------------ = volume to

administer 200 mg

126 X 20 = 2520 / 200 = 12.6 mL

So, one complete syringe containing 10 mL plus approx. 2.6 mLfrom a second syringe

Weight Based Dosage

Pediatric2mg/kg Benadryl for a 25 lb patient

1. Convert weight to kilograms 25 / 2.2 = 11.36 kgsOr 12.5 – 1.2 = 11.3 kgs

Weight Based Dosage


2. Calculate the dose to give 11.3 kgs X 2 mg/kg = 22.6 mg

Weight Based Dosage


3. Calculate the volume to administer

22.6 mg X 1 mL-------------------- = 0.45 mL 50 mg

Or the easy way

We know we want 2mg/kgThe child ways 11.3 or roughly 11 kgsThe dose will be 22mg

50 22--- --- 1 X

Or the easy way

50 22--- --- 1 X

22 X 1 = 22 / 50 = 0.44 mL

Drip Rate Calculations

Facts: In a 60 drop set, 60 drops = 1 mL In a 10 drop set, 10 drops = 1 mL In a 15 drop set, 15 drops = 1 mL Medications are usually given in 60 gtt sets Doesn’t mean you cannot give it in a 10 gtt

set A 60 drip set is usually called a microdrip A 10 drip set is usually called a macrodrip

Microdrips

60 gtts = 1 mLIf your dose was 1 mL / hr what would your drip rate be?

1 gtt / minute

Why?60 gtts = 1 mL (our dose)1 drop / min = 60 gtts/hr = 1 mL = 60 gtts

Easy huh?

Let’s try another

Using a 60 drop set, the dose is 30 mL/hr60 gtts = 1 mL30 mL = 1800 gtts1800 gtts/60 min = 30 gtts/min

And another

Using a 60 drop set, the dose is 45 mL/hr60 gtts = 1 mL 45 mL = 2700 gtts2700 gtts / 60 min = 45 gtts / hr

Dose not in mL/hror

mL/min?

No sweat…

Understanding Concentration of drug in fluid

A liter bag of fluid = 1000 cc or 1000 mLIf you add 800 mg of a drug to 1000 mL of fluid, what would ur ratio of drug to fluid be?

800 mg X mg---------- --------1000 mL 1 mL

Drug in fluid

800 mg X mg---------- --------1000 mL 1 mL

800 X 1 = 800 / 1000 = 0.8 mg/mL

Drug in fluid

400 mg X mg---------- --------250 mL 1 mL

400 X 1 = 400 / 250 = 1.6 mg / mLConvert mg mcg Dopamine1.6 X 1000 = 1600 mcg / mL

You do it

You add 1 gram of Lidocaine to 250 mL NSThe answer should be in mg/mL

Survey Says….

1 gm = 1000 mg

1000 mg in 250 mL = 4mg/mL

Not mL/hr but mg/min

Lidocaine 2mg/minMixed 1gm/250ml

1000mg = 1gm1000mg/250ml = 4mg/ml

Drip rate = 30gtts/min

Why?

4mg/mlThe dose is 2mg/minUsing a microdrip (60) 60gtts=1ml4mg/min = 602mg/min = 301mg/min = 15

The Math

Drug order (mg/min) X IV Drip rate (gtts/ml)

-------------------------------------------Drug concentration (mg/ml) X 1min

2mg/min X 60 gtts/ml--------------------------

4mg/ml X 1min

2mg/min X 60 gtts/ml--------------------------

4mg/ml X 1min

2 X 60 120-------- = ---4 X 1 4

30 gtts

Putting it ALL together

Dopamine

Weight BasedOver time (mcg/kg/min)

Weight based over time

Order is for 7mcg/kg/minDrug on hand is 800 mgDrip Set is 60gtts/mlPt weight is 220 lbsIV solution 500mL NS

1. Convert Weight from lbs to kgs2. Convert measurements (mgs

µg)3. Determine µg/mL4. Formula

Step 1: Convert Weight

220 lbs kgs220 / 2.2 = 100 kgs

Step 2: Convert Measurements

800 mg µgMg µg = X 1000800,000 µg

Step 3: Determine µg/mL

800,000 µg / 500 mL1600 µ / mL

Step 4: Formula

Drug order (µg/kg) X weight (kgs) X drip rate

---------------------------------------------------Concentration on hand (µg/ml) X

time (min)

Step 4: Formula

7 µg/kg X 100 kgs X 60 gtts/mL---------------------------------------

1600 µg/mL X 1 min

7 X 100 = 700 X 60 = 4200

4200 / 1600 = 26.25 = 26 gtts/min

Another

Order is for 5 µg/kg/minDrug on hand is 800 mg = 800,000 µg60 Drop setPt weighs 175 lbsIV solution 500 mL NS

Step 1: Convert Weight

175 lbs / 2.2 = 79.5 ~ 79 kgs87.5 – 8.7 = 78.8 ~ 79 kgs

Step 2: Convert Measurements

800 mg µg800,000 µg

Step 3: Determine µg/mL

800,000 mcg / 500 mL1600 mcg / mL

Step 4: Formula

Drug order X weight X drip rate---------------------------------------

Conc on hand X time

5 mcg/kg X 79 kgs X 60-----------------------------1600 mcg/mL X 1 min

Step 4: Formula

5 X 79 X 60 = 2370023700 / 1600 = 14.81 ~ 15 gtts/min

An easy check to your work

For 5 µg / kg / minTake weight in pounds (175)Drop the last digit (17)Subtract 1 (16) in the ballpark, not completely accurate

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