Math Calculation Principles

Copyright PRIMED 2015

When performing drug calculations always do the following:

1. Convert to the same units2. Consider what dosage is reasonable3. Calculate4. When in doubt confirm with another

resource

Principles

Fractions: convert to the lowest term & lowest

denominators

Mathematics Review

Decimals: think of thedecimal point as thecenter that separateswhole and fractionalAmounts

The position of thenumbers in relation tothe decimal pointindicates the place valueof the numbers

Decimals

For safety always write a zero to the left of the decimal point if the number has no whole number◦ .5 mg should be written as 0.5 mg to avoid the

potential for errors To avoid confusion eliminate unnecessary

zeros at the end of a decimal◦ 0.500 is the same as 0.5

Convert fractions to decimals by dividing the denominator into the numerator ¼=0.25 Line up decimals for adding & subtracting

Decimals

For many dosage calculations it is necessary to round off your calculations to the nearest thousandths (3 places) or the nearest hundredths (2 places)

Rule:1. Do not change the numbers in the tenths place if the number in the hundredths place was 4 or less ie:0.13= 0.12. Increase the number in tenths place by 1 if the numbers in the hundredths place was 5 or more ie:0.75= 0.8

Rounding Decimals

Adding: 1.5 + 0.05= ? (1.55)7.8 + 1.12=? (8.92)

Subtracting: 3.75 – 2.1= ? (1.65)5.25 – 3.6=? (1.64)

Multiplying: 1.5 x 0.5=? (0.75)1.72 x 0.9=? (1.548;

1.55) Dividing: 1/ 5 (0.2)

1/4 (0.25)

Practice

When performing calculations always convert to the same units of measurement

Metric is based on the decimal system The prefix determines the amount of

measurement:◦ Kilo= 1000 units or one thousand times◦ Centi= 0.01 units or one hundredth part of◦ Milli= 0.001 units or one thousand part of◦ Micro= 0.000001 units or one millionth part of

Metric Conversion

The prefix determines the type of measurement:◦ Milli, kilo, centi

The suffix determines what is being measured:◦ Gram = basic unit for weight (solid)◦ Liter = the basic unit for volume (liquid)◦ Meter= the basic unit for length

Metric Units

Move the decimal point 3 ways, left or right depending on the conversion

Kg G mg mcg (ug)

0.000001 0.001 1 1000

0.001 1 1000 100,000

Metric Units

500 mL= L 2 kg= g 0.015 g= mg 1 g= mg 8 mg= g 1mL= L 10 mg= g 23 mcg= mg 60 mg= g 1.05 kg= g 300 mg= g 18 mcg= mg 0.2 mg= g 0.4 mg= mcg 0.0025 kg= g 1.5 L= ml5,000mL= L 1L= mL250mL= L

Practice Converting the Following

500 mL= L (0.5) 2 kg= g (2000)0.015 g= mg (15) 1 g= mg (1000)8 mg= g (0.008) 1mL= L (1000)10 mg= g (0.01) 23 mcg= mg (0.023)60 mg= g (0.6) 1.05 kg= g (1050)300 mg= g (0.3) 18 mcg= mg (0.0180.2 mg= g (0.0002) 0.4 mg= mcg (400)0.0025 kg= g (2.5) 1.5 L= ml (1500)

5,000mL= L (5) 1L= mL (1000)250mL= L (0.250)

Answers

Household Systems of MeasurementHousehold Unit

1 teaspoon (tsp or t)1 tablespoon (Tbsp or T)1 fluid ounce (oz)1 cup (C)1 quart (qt)

SI Unit

5 milliliters (mL)15 milliliters (mL)30 milliliters mL)250 milliters (mL)1 Liter (L)

Drug calculations are completed by 3 methods:

1. Use of a formula2. Dimensional analysis3. Ratio and proportion

Calculation of Drug Dosages

Most common method of calculating medsD x QH

D= desired dose or dose prescribed H= have dose or drug dose available Q= quantity or form and amount in which

drug comes

Formula Method

1. Doctor orders metformin 500 mg PO OD. The drug container reads metformin 100 mg tablets. Give_______________

2. Hydrochlorothizide 12.5 mg PO TID ordered; 25 mg tabletsAvailable. Give___________3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tabletsGive__________4. Ibuprofen 600 mg PO BID. Available Ibuprofen 300 mg

tablets. Give_______________5. Available: Cefazolin 1 g per 10 ml. Dose to be given is

Cefazolin 500mg. Give___________6. Levothyroxine 50 mcg tablets available. Dose ordered

Levothyroxine 0.05 mg PO OD. Give______________7. Propanolol 15 mg PO TID. Dose available Propanolol 10 mg.

Give____________

Practice

1. Doctor orders metformin 500 mg PO OD. The drug container reads metformin 100 mg tablets. Give_______________(1 tab)

2. Hydrochlorothizide 12.5 mg PO TID ordered; 25 mg tabletsAvailable. Give___________(1/2 tab)3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tabletsGive__________(1/2 tab)4. Ibuprofen 600 mg PO BID. Available Ibuprofen 300 mg

tablets. Give_______________(2 tabs)5. Available: Cefazolin 1 g per 10 ml. Dose to be given is

Cefazolin 500mg. Give___________(5 mLs)6. Levothyroxine 50 mcg tablets available. Dose ordered

Levothyroxine 0.05 mg PO OD. Give______________(1 tab)7. Propanolol 15 mg PO TID. Dose available Propanololl 10

mg. Give____________(1.5 tabs)

Practice

Useful when meds are ordered in different units

For example: the available dose is 750 mg in 2.5 mL which

you must prepare a 600 mg dose. How many mL is this?

mL= 2.5 mL x 600 mg = (2.5 x 600)/750= 2mLs

750mg 1 unitscross multiply & cancel

Dimensional Analysis

We use ratios to make comparisons between two things. When we express ratios in words, we use

the word "to"‐‐we say "the ratio of something to something else." Ratios can be written in several different ways: as a fraction, using the word "to", or with a colon A proportion is simply a statement that two ratios

are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty five as four is to five."

Ratio and Proportion

To solve equations using this method it is necessary to express the numbers as ratios or as fraction and cross multiply:5: 10 = 10:20 is the same as 5 = 10

10 20The 2 outer numbers are called the extremes and the

2 inner numbers are called the means.

In this method the extremes are multiplied and the means are multiplied or cross multiplied.

5x20= 100 & 10x10=100 5x20 = 10x10100 = 100

Ratio and Proportion

Find the value of x rounded to 2 places:0.5 = 250

2 x0.5 x = 250 x 2 x= 500/0.5

2. 250 = 750 (250 x=750; x= 750/250)

1 x3. How much salt would you add to 500 mL of

water to make a solution that contains 5 mL of salt for every 250 mL?

5mL/250mL=xmL/750mL: (5mL /250 x 750mL/1 =15mL)

Practice

Medical CalculationsIV Therapy

Calculating IV Rates & Drip Rates

•Drips rates need to be calculated to ensure safe delivery of IV fluids

•Many are administered via a pump

•To calculate manually you need to determine the hourly rate and thencalculate the gtt/min to obtain the necessary rate

For infusion pump:Flow Rate (ml/hr) = Total infusion (ml)

Hours of infusion1000 ml/ 8 hr= 125 ml/hr

Calculating based on drop factor:

X gtt/min = amount of soln (ml) X drop factortime in min

IV Calculations

Macrodrip: drip factor 10‐20 gtt/ml Microdrip: drip factor is 60 gtts/ml Drip factor is on IV tube packaging

Drop Factors

Calculate the flow rate you will program the IV pump for the following:

1. 1 L D5W to infuse in 10 hrs_______________ mL/hr 2. 1800 mL NS to infuse in 15 hrs ____________mL/hr3. 2000mL D5W in 24 hrs ___________________mL/hr4. 100 mL NS IV piggyback in 30 min______mL/hr5. 30 mL medication in 15 minutes __________mL/hr6. 2 L NS IV in 20 hrs ______________mL/hr

Practice

Calculate the flow rate you will program the IV pump for the following:

1. 1 L D5W to infuse in 10 hrs_______________ mL/hr (100)2. 1800 mL NS to infuse in 15 hrs __________mL/hr(120)3. 2000mL D5W in 24 hrs _________________mL/hr (83.33)4. 100 mL NS IV piggyback in 30 min_______mL/hr (200)5. 30 mL medication in 15 min __________mL/hr (120)6. 2 L NS IV in 20 hrs ______________mL/hr (100)

Practice

Calculate the IV flow rate in drops per minute (gtt/min) using the formula method

V/T x C= R

V= total volume to be infused in mLT= total time in minutesC= drop factor gtt/mLR= rate of flow gtt/min

Formula Method

Order 3000 mL D5W to run for 24 hrs drop factor 10 gtt/ml3000/(24 x 60) x 10=20.8=21 gtts/minOR 3000/24=125 ; 125/60 x 10=20.8=21 gtts/min

Order 250 mL RL to infuse in 5 hrs drop factor 60 gtt/mL250/(5 x 60) x 60= 50 gtts/minOR250/5=50 mLs/hr50O60 x 60= 50 gtts/min

Order 100 mL NS medication to infuse in 40 min dropfactor 20 gtt/mL

100/40 min x 20 = 50 gtts/min

NS to run at 25 mL/hr drop factor 60 gtt/ mL

25/60 x 60=25 gtts/min

For each drop factor there is a constant as follows:

10 gtt/mL= 6 15 gtt/mL= 4 20 gtt/ml= 3 60 gtt/ml= 1

Calculate the IV flow rates in drops per minute(gtt/min) by using the short cut method:

mL/h = gtt/minDrop factor

Shortcut Method

1. order 1000 mL D5W to infuse in 4 hrs drop factor 15gtt/mL

2. 2. order 750 mL to infuse in 6 hrs drop factor 20 gtt/m

3. 3. order 500mL 2/3 + 1/3 to infuse in 3 hrs drop factor 10 gtt/mL

4. 4. order 2 L NS IV to infuse at 60 mL/hr drop factor 60 gtt/mL (

Practice

1. order 1000 mL D5W to infuse in 4 hrs drop factor 15gtt/mL (1000/4)/4(constant)= 250/4= 62.5=63 gtts/min

2. order 750 mL to infuse in 6 hrs drop factor 20 gtt/m (750/6)/3= 125/3=41.67=42gtts/min

3. order 500mL 2/3 + 1/3 to infuse in 3 hrs drop factor 10 gtt/mL (500/3)/5= 166/67/5= 33.3=33 gtts/min

4. order 2 L NS IV to infuse at 60 mL/hr drop factor 60 gtt/mL (60/1=60 gtts/min

Practice

Reconstitution of Meds

Reconstitution QuestionBased on this label you need to know: What is the total dosage strength of Ceftriaxone

in this vial? For what routes of administration is the

medication indicated? How much diluent must be added to the vial to

prepare the medication for IV use? What kind of diluent is recommended for IV

reconstitution? What is the final concentration of the prepared

solution for IV use? 1 g IV q12h is ordered. How many milliliters will

you give?

AnswersBased on this label you need to know: What is the total dosage strength of Ceftriaxone

in this vial? (1g or 1000 mg) For what routes of administration is the

medication indicated? (IM or IV) How much diluent must be added to the vial to

prepare the medication for IV use? (9.6) What kind of diluent is recommended for IV reconstitution? (sterile water) What is the final concentration of the prepared

solution for IV use? (100 mg/mL) 1 g IV q12h is ordered. How many milliliters will

you give? (10mL)

Pediatrics clients less then 45 kg are given medications based on either their weight or their Body Surface Area (BSA)

To calculate by weight you need to multiply the doseper kilogram by the weight of the child

Ie: If you need to give 10 mg/kg of a med for a childweighing 10 kg then: 10 mg: 1 kg = x mg: 10 kg multiply the extremes then the means 10 mg x 10 kg= 100 mg/kg 1kg x= 100 mg/ 1kg= 100 mg

Pediatric Calculations

BSAFormula MethodBSA(m2)= height (cm) x weight (kg)

3600Multiply the height in cm byweight in kg then divide by3600 which =? then press √Button to arrive at m2Round m2 to nearest hundreth

Formula MethodBSA(m2)=

height (in) x weight (lbs)3100

Multiply the height in inches by

weight in lbs then divide by3100 which =? then press √Button to arrive at m2Round m2 to nearest hundreth

Calculation of pediatric dosages, as with adult dosages, involves the use of ratio and proportion, the formula method, or dimensional analysis to determine the amount of medication to administer. Pediatric dosages are much smaller than those for an adult.

Micrograms are used a great deal. The tuberculin syringe (1‐mL capacity) is used to administer very small dosages.

Intramuscular (IM) dosages are usually not more than 1 mL for small children and older infants; however, this can vary with the size of the child. The recommended IM dosage for small infants is not more than 0.5 mL.

Pediatric Principles

The recommended subcutaneous dosage for children is not more than 0.5 mL. Dosages that are less than 1 mL may be

measured in tenths of a milliliter, or with a tuberculin syringe in hundredths of a milliliter.

Medications in pediatrics generally are not rounded off to the nearest tenth but may be administered with a tuberculin syringe

(measured in hundredths) to ensure accuracy. All syringes must be labeled.

Pediatric Dosage

Step 1: convert pounds to kilograms and ounces to parts of a pound:

To convert from kilograms to pounds, use the conversion1 kg = 2.2 lb.

To convert from kilograms to pounds multiply by 2.2, and express your weight to the nearest tenth.

For Ounces convert to partial pounds: 16 oz = 1 lb 4 oz=0.25 lb

You may have to convert grams to kilograms

Conversion

Medication dosages can be calculated based on mg/kg/day,mg/lb/day, or sometimes mcg/kg. References often statethe safe amount of the drug in mg/kg/day (24‐hourperiod). Once you have determined the child's weight inkilograms, you are ready to calculate the medicationdosage. Calculating the dosage involves three steps:

1.Calculation of the total daily dosage2.Division of the daily dosage by the number of dosages to be

administered3.Use ratio and proportion, the formula method, or dimensional analysis to calculate the number of tablets or capsules or the volume to give to administer the ordered

dosage

Safe Dosage

Example

Order: Dilantin 30 mg PO q8h.Child weighs 18 kg. Is the dosage safe? Recommended dosage: 5 mg/kg/day in 2 or 3 equally

divided dosages. (Notice the information written sideways on the left of the Dilantin label.)

Now that we have the dosage information and the child’s weight, we can calculate the safe total daily dosage for the child.

Note: The child's weight is in kilograms (18 kg), and the average dose range is 5 mg/kg/day. No conversion of weight is required.

Example

Start by calculating the safe total daily dosage for this child. Multiply the recommended dosage in milligrams by the child's weight in kilograms.

The safe dosage for this child (total) is 90 mg/day. Now determine the amount of each dosage. The dosage is to

be given in three equally divided dosages. Therefore: 90/3 = 30 mg per dose After calculating the safe dosage for a child, you can assess

whether what the prescriber ordered is a safe dosage. The order is 30 mg Q8H=

Q8H= 24/8= 3doses, 30 mg x 3= 90 mg= Safe Dose

Calculating Safe Dose

This Is a quick way to calculate titrations 1. Look at the units of measures in the order ( this is usually

stated that you will give X units of measure/ min or hr) and the units of measure on medication in the IV bag ( this will say X units of measure in X mL of solution). Convert these so that they are the same. Make sure you have the correct number of decimal point!!!!

2. Look at the order or rate you are to infuse the medication. If the dose is dependent on the patient’s weight, figure out the number of units of medication the patient will get for their weight. This may mean converting lbs to kg. This will now give you the measurement of medication you must give. It may be /min or it may be/hr

How to Calculate Titrations

3. If it is units of measure/min, you must then multiply this by 60 min. This is now your rate/hr and is your DD (Desired dose).

4. Take your DD from step 3 , divide it by the converted units of measure from step 1 that is in the IV solution (this is you DH, dose on hand) and multiply by the volume (which is the number of mL in the IV bag supplied.

How to Calculate Titrations