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Review of Basic Drug Calculations TOPIC Quick Conversion Reference 2 Metric Conversions 3 Methods of Solving Drug Calculations 4 Reconstitution of Powders 5 Calculating Pediatric Dosages 6 Calculating Electronically Regulated IV Flow Rates (ml/hr) 7 Calculating Manually Regulated IV Flow Rates (gtts/min) MCC PAGE 7-8 Practice #1: Conversions 9 Practice #2: Reconstitution of Powders 9 Practice #3: Pediatric Dosages 10 Practice #4: Electronically Regulated IV Flow Rates (ml/hr) 11 Practice #5: Manually Regulated IV Flow Rates (gtt/min) 11 Answers to Practice Problems 12 Page 1 QUICK CONVERSION REFERENCE CONVERSION CLOCK 60mg (gr 1) 45mg (gr 3/4) 15mg (gr ¼) 30mg ( gr ½) Weight Conversions 1 kilogram (kg) = 2.2 pounds (lb) 1 kilogram (kg) = 1000 grams (g) 1 gram (gm or g) = 1000 milligrams (mg) 1 milligram (mg) = 1000 micrograms (mcg or ug) Volume Conversions 1 milliliter (ml) = 1 cubic centimeter (cc) 1 liter (L) = 1000 milliliters (ml) 5 milliliters (ml) = 1 teaspoon (tsp) 15 milliliters (ml) = 3 teaspoons (tsp) = 1 tablespoon (T) 30 milliliters (ml) = 1 ounce (oz) = 2 tablespoons MCC Page 2 General Rounding Guidelines: Adults: round to nearest 10th for weights, drug dosages, and measurable doses Pediatrics: round to nearest 100th for weights, drug dosages, and measurable doses Metric Conversions TO CONVERT FROM A LARGER UNIT OF MEASURE TO A SMALLER UNIT OF MEASURE (for example: grams to milligrams OR milligrams to micrograms), MOVE DECIMAL TO THE RIGHT OR MULTIPLY BY 1000. TO CONVERT FROM A SMALLER UNIT OF MEASURE TO A LARGER UNIT OF MEASURE (for example: milligrams to grams OR grams to kilograms), MOVE DECIMAL TO THE LEFT OR DIVIDE BY 1000. Remember, LEFT is LARGER. EXAMPLES: To Convert Grams (large) to Milligrams (small): a) multiply by 1000 OR b) move decimal point 3 places to the right 3 g = 3000 mg 0.5 g = 500 mg 0.08 g = 80 mg To Convert Milligrams (small) to Grams (large): a) divide by 1000 OR b) move decimal point 3 places to the left 125 mg = 0.125 g 50 mg = 0.050 mg 6 mg = 0.006 g Convert Milligrams (large) to Micrograms (small): a) multiply by 1000 OR b) move decimal point three places to the right 5 mg = 5000 ug 0.8 mg = 800 ug 0.05 mg = 50 ug Convert Micrograms (small) to Milligrams (large) a) divide by 1000 OR MCC Page 3 b) move decimal point 3 places to the left 2500 ug = 2.5 mg 400 ug = 0.4 mg 10 ug = 0.01 mg See Practice Problems #1, Page 9 3 Methods of Solving Drug Calculations RATIO AND PROPORTION Dosage on Hand : Amount of Hand :: Dosage Desired : Amount Desired OR Dosage on Hand Amount on Hand = Dosage Desired Amount Desired FORMULA METHOD Desired x Amount = Have D x Amt = H DIMENTIONAL ANALYSIS Starting Factor x Converting Factors = Answer Label MCC Page 4 EXAMPLES: Order: 650mg of Tylenol PO. On hand: Tylenol tablets 325mg/1tablet. How many tablets would you administer? Ratio Proportion Method 325mg : 1 tab : : 650mg : Xtab 325X = 650 X = 2 tabs Formula Method 650mg X 1tab = 2 tabs 325mg Dimensional Analysis Method 650mg X 1 tab = 2 tabs 325mg RECONSTITUTION OF POWDERS Many medications come in a dry form that remains stable and can be stored for varying periods of time. The drug is in a solute form (dry powder) and must be reconstituted by adding a diluent (solvent). Once the drug is reconstituted it will only remain stable for a limited time and must be used within that time or be discarded. LEARN TO READ THE LABEL FOR THIS INFORMATION, FOR EXAMPLE: NAME OF THE DRUG EXAMPLE: TAZICEF (ceftazidime); Brand name and generic name will be given AVAILABLE DOSAGE OF THE DRUG EXAMPLE: Equivalent to 1gram ceftazidime This is the total amount of the medication available in the vial. RECOMMENDED DILUENT EXAMPLE: reconstitute with Sterile Water for injection (according to table) The three most common sterile diluents are: (1) bacteriostatic water (2) sterile water (3) sodium chloride (0.9%) If this information is not on the label it WILL be in the package insert. Bacteriostatic solvents contain preservatives that may not be compatible with a specific drug. If no information is given sterile water is the diluent of choice. QUANTITY OF DILUENT EXAMPLE: Diluent to be added = 3.0ml for Intramuscular or Intravenous Direct (bolus) Injection Some labels will offer more than one choice, dependant upon the dosage desired. EXAMPLE: Diluent to be added = 10ml for Intravenous Infusion MCC Page 5 RATIO OF SOLUTE TO SOLVENT AFTER RECONSTITUTION EXAMPLE: When reconstituted, approximate average concentration = 280mg/ml (95mg/ml for Intravenous Infusion) A ratio will be given in some form, other examples: yielding concentration is 3g/ml or resulting concentration is 100mg/ml SAMPLE RECONSTITUTION PROBLEM: Ordered: Tazicef 500mg IM Available: 1gm vial of Tazicef in powdered form Directions for reconstitution: add 3.0ml Sterile Water per gram; approximate average concentration = 280mg/ml 500mg X 1ml = 1.78 or 1.8ml 280mg OR 280mg : 1ml :: 500mg : x ml x = 1.78 or 1.8ml See Practice Problems #2, Page 9 CALCULATING PEDIATRIC DOSAGES Convert Weight from Pounds to Kilograms Example: total weight is 12 lbs 8 oz 1. Convert ounces to pounds by dividing ounces by 16 8 oz 16 oz = 0.5 lb 2. Divide total pounds (to the nearest hundreth) by 2.2 Total pounds = 12 lbs + 0.5 lbs = 12.5 lbs 12.5 2.2 = 5.681 or 5.68 kg Calculate Safe Dose Ranges (SDR) Example: SDR is 30-100mg/kg/day in four divided doses Ordered dose is 150mg q 6hr 1. low range calculation: 5.68 x 30mg = 170.4mg/day high range calculation: 5.68 x 100mg = 568mg/day SDR = 170.4-568 mg/day or 42.6-142mg/dose 2. evaluate appropriateness of ordered dose: 150mg x 4 doses/day = 600mg/day 3. decision: ordered dose exceeds SDR, hold and clarify See Practice Problems #3, Page 10 MCC Page 6 CALCULATING ELECTRONICALLY REGULATED IV FLOW RATES – ML/HR Electronically Regulated Flow Rates are calculated in ml/hr. The nurse programs the infusion device to deliver the ordered solution in milliliters per hour (ml/hr) Formula for calculating ml/hr: TV (ml) = ml/hr TT (hr) OR If < 1 hr infusion: TV (ml) X 60 (min) = ml/hr TT (min) TV = total VOLUME to be infused in ml TT = total TIME of infusion EXAMPLES *IVPBs (often < 1 hr infusion) 1. Infuse 250ml over 2 hours *3. Infuse 75ml in 30 minutes (IVPB) 75ml 30min 250ml = 125ml/hr 2hr X 60 = 150ml/hr *4. Infuse 100ml in 20 minutes (IVPB) 2. Infuse 2L over 4 hours 100ml X 60 = 300ml/hr 20min 2000ml = 500ml/hr 4hr See Practice Problems #4, Page 11 CALCULATING MANUALLY REGULATED IV FLOW RATES – DROPS/MINUTE (gtt/min) Manually Regulated Flow Rates are calculated in drops/minute. The nurse calculates the number of drops the IV should flow per minute according to the ordered infusion time. The drip rate (gtt/min) is then set by adjusting the roller clamp and timed by counting the number of drops dripping per minute into the IV drip chamber. The IV solution may be a continuous infusion or an intermittent/bolus infusion. Formula #1: Use for large volume infusions; plug in hourly rate of infusion (ml/hr = ml/60minutes) D X V = gtt/min M = D X hourly rate of infusion (ml/hr) 60 D = DROP factor of tubing (gtt/ml) M = Time of infusion per 60 MINUTES (hourly rate of infusion); 60 is a constant V = Total VOLUME to be infused in ml each hour (hourly rate of infusion) MCC Page 7 EXAMPLES 1. Order is to infuse D5NS at 125ml/hr. The drop factor is 15gtt/ml 15 X 125 = 31.25 or 31gtt/min 60 2. Order is to infuse LR at 150ml/hr. The drop factor is 10gtt/ml 10 X 150 = 25gtt/min 60 3. Infuse 1L NS over 4 hours. The drop factor is10gtt/ml 10 X 250 = 41.66 or 42gtt/min 60 4. Order is to infuse 200ml 0.9% NaCl over 2 hours. The drop factor is 20gtt/ml. 20 X 100 = 33.33 or 33gtt/min 60 Formula #2: Use for small volume infusions (IVPBs) that are often < 1 hr D X V = gtt/min M D = DROP factor of tubing (gtt/ml) M = Time of infusion in total number of MINUTES V = Total VOLUME to be infused in ml *IVPBs / Small Volume Infusions (often < 1 hr infusion) *5. Order is for Clindamycin 600mg in 100ml D5W to infuse in 30 minutes. Drop factor is 20gtt/ml 20 X 100 = 133.33 or 133gtt/min 15 *6. Order is to infuse IVPB “X” in 30 minutes. The bag contains 50ml; the drop factor is 10gtt/ml. 10 X 50 = 16.66 or 17gtt/min 30 7. Infuse Drug X 1gm in 250ml in 1 ½ hrs. The drop factor is 10gtt/ml. 10 X 250 = 27.77 or 28gtt/min 90 OR Formula #2: 10 X 167 = 27.83 or 28gtt/min 60 Practice Problems #5, Page 11 MCC Page 8 PRACTICE #1: CONVERSIONS 1. 60mg = _____gr 2. 66lbs = _____kg 3. 500mg = _____gm 4. 250mg = _______mcg 5. 4oz = _____ml 6. 1tsp = _____ml 7. 1 liter = _____ml 8. 90ml = _____oz 9. 15ml = _____tsp 10. 45kg = _____lbs PRACTICE#2: RECONSTITUTION OF POWDERS 1. Chlorothiazide 750 mg IV is ordered. The drug label states that after reconstitution with 18 ml sterile water, there are 500 mg/10 ml. How many ml should be given? ml. 2. Amobarbital 75 mg is ordered IM. When the 250 mg vial is reconstituted, each ml = 100 mg. How much should be administered? ml. 3. Give Methicillin 1 g IM q6h. When the vial is diluted with 5.7 ml of diluent, each 500 mg = 1 ml. How many should be given to the patient? ml. 4. Give Nafcillian 500mg IM q6h. When 3.4 ml diluent is added to the 1 g vial, 250mg/1ml is the result. What volume should be given. ml. MCC Page 9 PRACTICE #3: PEDIATRIC DOSAGES Convert the following weights from pounds to kilograms: 1. _____ 8lb 3. _____ 4lb, 6oz 2. _____ 5lb, 8oz 4. _____ 18lb, 9oz 5. Child with nausea post-operatively Order: phenergan 20mg IM q6h Child’s weight: 99lbs Drug reference: 0.25-0.5mg/kg/dose, repeat q 4-6h Drug available: phenergan 25mg/ml a. What is the SDR for this child? b. How much will the nurse draw up to administer a single dose? 6. 9 day old infant with R/O sepsis; IV access lost – order to give last dose IM Order: Gentamicin 10mg IM now (original order for 10mg Gentamicin IV q 8hrs) Child’s weight: 8lbs 13oz Drug reference: > 7 days old: 5-7.5mg/kg/day in 3 divided doses Drug available: gentamicin 40mg/2ml a. What is the safe dose range for this child (include SDR per day and per dose)? b. How much will the nurse draw up to administer a single dose? 7. Child receiving pre-operative medication Order: atropine 0.2mg IM Child’s weight: 12kg Drug reference: 0.2mg/24-40 lbs Drug available: atropine 0.4mg/ml a. Is this a safe dose for this child (include supporting information)? b. How much will the nurse draw up to administer the ordered dose? MCC Page 10 PRACTICE #4: ELECTRONICALLY REGULATED FLOW RATES (ml/hr) *IVPBs (often < 1 hr infusion) Calculate the IV flow rate in ml/hr for each of the following problems: 1. Infuse 1.5 liters of NS over 3 hours *2. Unasyn 0.5gm in 75ml D5W IVPB to infuse over 20 minutes *3. Zantac 50mg in 100ml NS to infuse over 30 minutes 4. Infuse 500ml LR over 2 hours *5. Ancef 1gm in 100ml D5W IVPB to infuse in 45 minutes PRACTICE #5: MANUALLY REGULATED FLOW RATES (gtts/min) *IVPBs (often < 1 hr infusion) Calculate the IV flow rate in gtt/min for each of the following problems: 1. Infuse 1L NS bolus IV over 2 hours. Drop factor of tubing is 20gtt/ml. 2 Infuse 1000ml of lactated ringers IV in 6 hours with a 10gtt/ml administration set. *3. Order is for Ancef 2gm IVPB diluted in 100ml D5W to infuse in 45 minutes. Drop factor of the tubing is 15gtt/cc *4. Order is for Zosyn 3gm in 100ml D5W to be infused in 40 minutes. Drop factor is 10gtt/ml. How many drops/minutes do you infuse the IVPB? *5. Order is for carbenicillin disodium 2gm IVPB diluted in 50ml D5W to infuse in 30 minutes. Drop factor is 60gtt/ml. MCC Page 11 ANSWERS Practice #1 Conversions 1. 1gr 2. 30kg 3. 0.5gm 4. 250,000mcg 5. 120ml 6. 5ml 7. 1000ml 8. 3oz 9. 3tsp 10. 99lbs Practice #2 Reconstitution 1. 15 ml 2. 0.75 ml 3. 2 ml 4. 2ml Practice #3 Pediatric Dosages 1. 2. 3. 4. 3.64kg 2.5kg 1.99kg 8.44kg 5a. 11.25-22.5mg /dose 5b. 0.8ml 6a. 20-30mg /day OR 6.67-10mg/dose 6b. 0.5ml 7a. yes, 26.4lbs falls w/in safe dose/kg 7b. 0.5ml MCC Practice #4 IV Flow Rates (ml/hr) 1. 500ml/hr 2. 225ml/hr 3. 200ml/hr 4. 250ml/hr 5. 133ml/hr Practice #5 IV Flow Rates (gtts/min) 1. 167gtts/min 2. 28gtts/min 3. 33gtt/min 4. 25gtts/min 5. 100gtts/min Page 12