Med Math

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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 . . . . . 90

10% 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

Temperature Conversions

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

Temperature Conversions

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

Deca10Hecto 100Kilo 1000

Deci 0.1Centi 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

So… you would administer 0.6 mL = 3 mg

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

So… you would administer 2.4 mL = 145 mg

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

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

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

Weight Based Dosage

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

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

Pediatric2mg/kg Benadryl for a 25 lb patient

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

Weight Based Dosage

Pediatric2mg/kg Benadryl for a 25 lb patient

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