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When performing drug calculations always do the following: 1. Convert to the same units 2. Consider what dosage is reasonable 3. Calculate 4. When in doubt confirm with another resource

Fractions: convert to the lowest term & lowest denominators

 Decimals: think of the decimal point as the center that separates whole and fractional Amounts  The position of the numbers in relation to the decimal point indicates the place value of the numbers

 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 ◦ 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

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= Increase the number in tenths place by 1 if the numbers in the hundredths place was 5 or more ie:0.75= 0.8

 Adding: = ? (1.55) =?(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)

 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= units or one thousand part of ◦ Micro= units or one millionth part of

 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

 Move the decimal point 3 ways, left or right depending on the conversion KgGmgmcg (ug) ,000

500 mL= L 2 kg= g g= mg 1 g= mg 8 mg= g1mL= L 10 mg= g 23 mcg= mg 60 mg= g1.05 kg= g 300 mg= g 18 mcg= mg 0.2 mg= g 0.4 mg= mcg kg= g 1.5 L= ml 5,000mL= L 1L= mL 250mL= L

500 mL= L (0.5) 2 kg= g (2000) 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 ( mg= g (0.0002)0.4 mg= mcg (400) kg= g (2.5)1.5 L= ml(1500) 5,000mL= L (5) 1L= mL (1000) 250mL= L (0.250)

Household 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 formula 2. Dimensional analysis 3. Ratio and proportion

 Most common method of calculating meds D x Q H  D= desired dose or dose prescribed  H= have dose or drug dose available  Q= quantity or form and amount in which drug comes

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 tablets Available. Give___________ 3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tablets Give__________ 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____________

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 tablets Available. Give___________(1/2 tab) 3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tablets Give__________(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)

 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 units cross multiply & cancel

 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."

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 = The 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 = 10x = 100

Find the value of x rounded to 2 places: 0.5 = x 0.5 x = 250 x 2 x= 500/ = 750 (250 x=750; x= 750/250) 1 x 3. 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)

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 then calculate the gtt/min to obtain the necessary rate

For infusion pump: Flow Rate (ml/hr) = Total infusion (ml) Hours of infusion 1000 ml/ 8 hr= 125 ml/hr Calculating based on drop factor: X gtt/min = amount of soln (ml) X drop factor time in min

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

Calculate the flow rate you will program the IV pump for the following: 1. 1 L D5W to infuse in 10 hrs_______________ mL/hr mL NS to infuse in 15 hrs ____________mL/hr mL D5W in 24 hrs ___________________mL/hr mL NS IV piggyback in 30 min______mL/hr mL medication in 15 minutes __________mL/hr 6. 2 L NS IV in 20 hrs ______________mL/hr

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) mL NS to infuse in 15 hrs __________mL/hr(120) mL D5W in 24 hrs _________________mL/hr (83.33) mL NS IV piggyback in 30 min_______mL/hr (200) mL medication in 15 min __________mL/hr (120) 6. 2 L NS IV in 20 hrs ______________mL/hr (100)

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 mL T= total time in minutes C= drop factor gtt/mL R= rate of flow gtt/min

 Order 3000 mL D5W to run for 24 hrs drop factor 10 gtt/ml 3000/(24 x 60) x 10=20.8=21 gtts/min OR 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/mL 250/(5 x 60) x 60= 50 gtts/min OR 250/5=50 mLs/hr 50O60 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/min Drop factor

1. order 1000 mL D5W to infuse in 4 hrs drop factor 15gtt/mL order 750 mL to infuse in 6 hrs drop factor 20 gtt/m order 500mL 2/3 + 1/3 to infuse in 3 hrs drop factor 10 gtt/mL order 2 L NS IV to infuse at 60 mL/hr drop factor 60 gtt/mL (

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

Based 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?

Based 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 dose per kilogram by the weight of the child Ie: If you need to give 10 mg/kg of a med for a child weighing 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

Formula Method BSA(m2)= height (cm) x weight (kg) 3600 Multiply the height in cm by weight in kg then divide by 3600 which =? then press √ Button to arrive at m2 Round m2 to nearest hundreth Formula Method BSA(m2)= height (in) x weight (lbs) 3100 Multiply the height in inches by weight in lbs then divide by 3100 which =? then press √ Button to arrive at m2 Round 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.

 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.

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

Medication dosages can be calculated based on mg/kg/day, mg/lb/day, or sometimes mcg/kg. References often state the safe amount of the drug in mg/kg/day (24‐hour period). Once you have determined the child's weight in kilograms, you are ready to calculate the medication dosage. Calculating the dosage involves three steps: 1.Calculation of the total daily dosage 2.Division of the daily dosage by the number of dosages to be administered 3.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

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.

 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

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

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.