Calculations for Pharmacy Technicians CATEGORIES Conversions --- weight and volume --- Fahrenheit and Celsius Concentration --- mg/ml, percent and ratio Dosage Calculations --- retail and hospital --- flow rates (ml/hr and gtt/min) 1 kilogram = 1000 grams 1 gram = 1000 milligrams 1 kg = 1000 g 1 g = 1000 mg Kilogram: largest measure of weight used in pharmacy. Used for patient weights. Gram: Used to measure bulk quantities of drugs, e.g. bulk powders in the compounding area. A few drugs are dosed in grams. 1 milligram = 1000 micrograms Factors of 1000 1 mg = 1000 mcg 1 kg = 1000 g = 1,000,000 mg = 1,000,000,000 mcg (thousand) (million) (billion) Milligram: Used to measure most drug doses. Microgram: Used for doses of very potent drugs, e.g. levothyroxine, digoxin. 1
Practice questions: How many mg in a 1 g sucralfate tablet? 1000 mg A premature baby weighs 2.5 kg. How many grams does the baby weigh? 2500 g How many mcg of haloperidol in a 2 mg tablet? 2000 mcg 1 grain = 65 milligrams (apx) 1 gr = 65 mg (apx) Grains are still used to measure doses for a few of the oldest drugs, e.g. aspirin and phenobarbital. 1 ounce = 30 grams (apx) 1 oz = 30 g (apx) 1 kilogram = 2.2 pounds 1 kg = 2.2 lb Ounces are used to measure ointments and creams, e.g. a 1 oz tube of nystatin ointment. Patient weights are measured in kilograms. Your weight in kilograms is roughly half that of your weight in pounds. Example: 132 lb = 60 kg Conversions Weight Practice Questions: A 32.4 mg tablet of phenobarbital contains apx. how many grains of phenobarbital? ½ grain A 30 g tube of bacitracin ointment contains how many ounces of ointment? 1 ounce If a baby weighs 6.6 lb, how many kg does it weigh? 3 kg Conversions Volume 1 liter = 1000 milliliters 1 L = 1000 ml A liter is approximately the same as a quart. A milliliter is about 1/5 of a teaspoon. 5ml = 1 tsp Milliliters are used in pharmacy to measure liquids of all types. 2
Conversions - Volume 1 Ounce = 30 milliliters (apx) 1 oz = 30 ml Ounces are used to measure bulk quantities of liquids. Conversions - Volume Practice Questions: An IV bag that contains half a liter of IV fluid contains how many ml? 500 ml An 8 oz bottle of shampoo contains how many ml of shampoo? 240 ml Conversions - Review 1 kg = 1000 g 1 g = 1000 mg 1 mg = 1000 mcg 1 gr = 65 mg (apx) 1 kg = 2.2 lb 1 oz = 30 g or 30 ml (apx) 1 L = 1000 ml How many mcg in a mg? 1000 mcg How many mg in 2 g? 2000 mg How many ml in an ounce? 30 ml How many ounces in 120 ml? 4 oz How many lb in a kg? 2.2 lb How many ml in a liter? 1000 ml Conversions - Drill Conversions Drill Which is larger: a mg or a mcg? mg If patient weighs 50 kg: is it a baby or an adult? adult How many mg are in half a gram? 500 mg If an adult weighs 50kg, are they fat or thin? thin How many grams in a 2 oz tube of cream? 60 g A 64.8 mg tablet is how many grains? 1 gr Freezing: 32 degrees Fahrenheit = 0 degrees Celsius 32 F = 0 C Boiling: 212 F = 100 C Body : 98.6 F = 37 C 3
Conversions between Celsius and Fahrenheit: C = ( F 32) x 5/9 Example: It s 23 F outside. What is that in C? C = ( F 32) x 5/9 C = (23 32) x 5/9 C = -9 x 5/9 = -9 x 5 = -5 C 9 It s 30 C outside. What is that in Fahrenheit? C = ( F 32) x 5/9 30 = (F - 32) x 5/9 9 x 30 = (F 32) x 5 x 9 5 9 5 270 = (F 32) 5 54 = F - 32 F = 54 + 32 = 86 F Celsius Fahrenheit Freezer -20 to -10-4 to 14 Refrigerator 2 to 8 36 to 46 Controlled Room 20 to 25 68 to 77 These are acceptable temperature ranges as defined by the USP. Drill Water freezes at? C.? F 0 C, 32 F Water boils at? C.? F 100 C, 212 F Body temperature is? C.? F 37 C, 98.6 F Give the formula to convert between C and F. C = (F 32) x 5/9 50 C is how many F? 122 F Which is lower, 0 C or 0 F? 0 F - Drill Concentration mg/ml - 4 F is how many degrees C? - 20 C A properly working refrigerator should register between what range in C? 2 8 C A properly working refrigerator should register between what range in F? 36 46 F If the A/C is broken and the pharmacy is at 90 F, is it too hot to store drugs safely? yes If the heat is broken and the pharmacy is at 55 F, is it too cold to store room temperature drugs? yes The freezer is registering -5 C. Is it working properly? no Concentration = amount of drug per unit volume Mg/ml is the most common way that concentration is expressed 20mg/ml solution --- each milliliter contains 20mg of drug 4
Concentration - Ratio Concentration can also be expressed as a ratio The ratio is defined as grams per ml 1:1000 = 1 g / 1000 ml 1:100 = 1 g / 100 ml 1:10 = 1 g / 10 ml 1:200,000 = 1 g / 200,000 ml Epinephrine is one of the few drugs still expressed in ratio concentrations. Concentration Ratio Converting ratio concentrations to mg/ml 1:1000 = 1 g / 1000 ml = 1000 mg/1000 ml = 1 mg/ml 1:100 = 10 mg/ml 1:10 = 100 mg/ml Shortcut: Multiply numerator (top number) by 1000 and divide to get mg/ml Concentration - Percent Concentrations can also be expressed as percents, or parts per 100. Percent concentration is defined as g / 100ml. 1 % = 1g/100ml = 1000mg/100ml = 10mg/ml 10%=10g/100ml=10000mg/100ml=100mg/ml Shortcut: To convert a % concn. to mg/ml, multiply by 10. Concentration Percent (g/100ml) Ratio (g/ml) Mg/ml 0.01% 1:10000 0.1 mg/ml 0.1% 1:1000 1 mg/ml 1% 1:100 10 mg/ml 10% 1:10 100 mg/ml 50% 1:2 500 mg/ml Concentration Most drugs are expressed as mg/ml Some drugs use other measures of weight Heparin and insulin are measured in units/ml Electrolytes are often measured in meq/ml (e.g sodium bicarbonate) or mmoles/ml (e. g. potassium phosphate) Concentration - Drill D5 is what percentage strength of dextrose? How many mg/ml is this? 5 %, 50 mg/ml 20% is how many mg/ml? 200 mg/ml A 5 % tube of ointment has how many mg of drug in each mg of ointment? 50 mg 1:100 is the same as how many mg/ml? What percent? 10 mg/ml, 1% What is 10% written as a ratio concentration? 1:10 What is 0.1% written as a ratio concentration? 1:1000 5
Concentration - Drill Dosage Calculations A vial label says 40 meq in 20ml. How many meq in 1 ml? 2 meq 900mg/6ml is equivalent to how many mg/ml? What percent concentration? 150 mg/ml, 15% A solution that is 5% strength has how many mg/ml? 50 mg/ml Which is more concentrated: 1:100 or 1:1000? 1:100 Which is more concentrated: 1:1000 or 1mg/ml? they re the same Normal saline is what percentage strength of sodium chloride? How many mg/ml is this? 0.9%, 9 mg/ml Set what you have or already know EQUAL TO what you want or need. HAVE = WANT Make sure units on both sides are the same. If not, convert. Use cross multiplication to solve the equation. Example # 1 : Retail pharmacy Dosage Calculations You have a bottle of diphenydramine oral solution that is labeled 12.5 mg / 5ml. The Rx reads Take 50 mg bid po for 5 d. (take 50mg twice daily by mouth for 5 days) What is the patient s dose in ml? How many ml total are needed to fill the Rx? HAVE = WANT 12.5 mg = 50 mg 5 ml x ml Units on both sides match. Cross multiply. 12.5 (x) = 5 (50) 12.5 (x) = 250 x = 20 ml is the patient s dose. To fill the Rx: 20 ml x 2 doses/day x 5 days = 200 ml Dosage Calculations Example # 2: Hospital pharmacy You have a vial of calcium gluconate labeled 10%. Your IV label says to prepare an IV with 2 g calcium gluconate in 100ml NS. How much calcium gluconate do you need to draw up? HAVE = WANT 10 % = 2 g x Change 10 % to mg/ml. Change 2 g to mg. 100 mg = 2000 mg ml x 100 (x) = 2000 (1) x = 20 ml Example # 3: Dosing by weight Dosage Calculations A baby weighs 8.8 lb. The baby has an order for furosemide 20mg/kg/day, to be given every 6 hours. What is the baby s daily dose? How much will it get every 6 hrs? HAVE = WANT 20 mg = x kg 8.8 lb Units are not the same. Convert lb to kg. ( 1 kg = 2.2 lb) 20 mg = x kg 4 kg 20 (4) = x (1) x = 80mg daily Every 6 hours = 4 times daily 80mg/4 = 20 mg every 6 hours Dosage Calculations - Drill You have a 2 mg/ml solution of Drug X. Patient needs 4 mg. How many ml is this? 2 ml Now the patient needs a 5 mg dose. How many ml? 2.5 ml Now the patient needs a 1 mg dose. How many ml? 0.5 ml An IV needs 100 mg of Drug X added to it. How many ml to add? 50 ml A prescription states Take 2 tabs bid. How many tablets for a 30 day supply? 120 tablets A prescription states Take 3 tabs qhs. How many tablets for a 90 day supply? 270 tablets 6
Dosage Calculations - Drill A prescription states Take 1 cap q 6hr. How many caps for a 10 day supply? 40 capsules A prescription states Take 3 ml po ac for 10 days. How many ml to dispense? 90 ml A patient weighs 100 kg. Their dose is 3mg/kg/day. How many mg will they get in a day? 300 mg If this drug is to be given 3 times a day, how many mg will be in each dose? 100 mg A baby weighs 4.4 lb. It needs Drug Z dosed at 15mg/kg/day. How much drug will baby receive daily? 30 mg If Drug Z is to be given q 4 hr, how many mg in one dose? 5 mg FLOW RATE = VOLUME / TIME Examples of IV flow rates: 60 ml / hr 1 ml / min The flow rate tells how rapidly the IV is being administered. Finding the flow rate Use FLOW RATE = VOLUME / TIME Example: an IV is 500ml and is given over 2 hours. What is the flow rate in ml / min? flow rate = volume / time Flow rate = 500 ml / 2 hours Convert hours to min (1 hour = 60 min) Flow rate = 500 ml / 120 min Flow rate = 4.2 ml / min Finding the duration of an IV (how long will it run?) Use FLOW RATE = VOLUME / TIME Example #1: A Protonix drip is running at 25 ml/hr. It is a 250ml IV bag. How long will it run? FLOW RATE = VOLUME / TIME 25 ml = 250 ml 1 hr x hr Units are the same. 25 (x) = 250 (1) x = 10 hours Example # 2: An IV is running at 10ml/min. Total volume is 1000 ml. How long will it run in hours? FLOW RATE = VOL/TIME 10 ml = 1000 ml 1 min x min Units are the same. 10 (x) = 1000 (1) x = 100 min. Convert min to hours (1 hour = 60 min) HAVE = WANT 1 hour = x 60 min 100 min 1 (100) = x (60) 100 / 60 = x = 1.67 hours IV sets are calibrated in gtt/ml (drops/ml). Typical sets are 10, 15, 20 or 60 gtt/ml. Pharmacy uses a flow rate of ml/hr or ml/min But nurses use flow rates of gtt/min. Steps: 1. using FLOW RATE = VOLUME / TIME, find the flow rate for the IV in ml / min 2. Multiply flow rate (ml / min) by the set calibration ( gtt / ml). Answer will be flow rate for IV in gtt / min. ml x gtt = gtt min ml min 7
Example: A nurse has an IV of 150ml that needs to be infused in 1 hour using a set that is calibrated at 15 gtt/ml. What should she set the drip rate at (in gtt/min)? FLOW RATE = VOL / TIME 150ml / 1 hour = 150 ml / 60 min = 2.5 ml / min 2.5 ml x 15 gtt = 37.5 gtt / min min ml Another example: Nurse has an IV of 150ml of NS to administer over 3 hours. She is using a set calibrated at 60 gtt/ml. What flow rate in gtt/min should the nurse use? Flow rate = volume / time 150 ml / 180 min = 0.83 ml / min 0.833 ml x 60 gtt = 50 gtt/min min ml - Drill Give the basic formula used in all IV calculations. FLOW RATE = VOLUME / TIME What is the flow rate in ml/hr for an IV of 600 ml to be given over 10 hours? 60 ml/hr What is the flow rate in ml/min for this IV? 1 ml/min How long will it take for a 1000ml IV running at 200ml/hr to run out? 5 hours How long will it take for a 100 ml IV running at 2 ml/min to run out? 50 min The doctor told the nurse to infuse 500ml of D5 at 50ml/hr. The bag has been hanging for 2 hours and has run out. Is there a problem? yes - Drill Pharmacy IV labels typically have flow rates in? ml/hr If a nurse is manually setting the flow rate, she will typically use a flow rate in? gtt/min If an IV is to run at 1 ml/min and the nurse has a set calibrated at 10gtt/ml, she should set the flow rate at? 10 gtt/min A flow rate of 90 ml/hr is how many ml/min? 1.5 ml/min If an IV is to run at 90 ml/hr with a set calibrated at 30 gtt/ml, what will be the flow rate in gtt/min? 45 gtt/min Questions? 8