Pharmacy Calculations

How to solve Weight / Weight Concentrations (Example 1)

1 g of active ingredient powder is mixed with 99 g of white petrolatum. What is the final concentration (conc. w/w)? Given: • 1g : amount of active ingredient • 99 g white petrolatum : amount of base • 100 g, total quantity = (1 g of active + 99 g of base) X = 1g (active) / 100 g (total) X = 0.01 % Conc. = 0.01 * 100 = 1% • The final w/w concentration is 1%.

Rules for interpreting Roman Numerals

1. when a smaller numeral is repeated or follows a larger numeral, the numbers are added: iii = 1 + 1 + 1 = 3 vii = 5 + 1 + 1 = 7 xvi = 10 + 5 + 1 = 16 2. if a smaller numeral precedes a larger numeral, the smaller numeral is subtracted from the larger numeral. The smaller numeral in front must not be smaller than 1/10 of the larger numeral: iv = 5 - 1 = 4 ix = 10 - 1 = 9 3. Numerals are never repeated more than 3 times. iii = 3 XXX = 30 iv = 4 (not iiii) XL = 40 (not XXXX) 4. If a smaller numeral is between two larger numeral, the smaller numeral is subtracted from the numeral FOLLOWING it: XIV = 10 + (5 - 1) = 14 XXIX = 10 + 10 + (10 - 1) = 29

Common IV drip rates

10 gtts/mL 15 gtts/mL 20 gtts/mL 60 gtts/mL The most commonly used drip rate is the microdrip, 60 gtts/mL. If a problem does not indicate a specific drip rate or drop factor, always assume 60 gtts/mL.

How to solve Volume / Volume Concentrations (Example 1)

10 mL of active ingredient is mixed with distilled water to total 200 mL. What is the final concentration (v/v)? 10 mL : amount of active ingredient 200 mL : total quantity % Conc. (v/v) = [ 10 mL (active) / 200 mL (total) ] * 100% = [ 10 ml (active) / 200 mL (total) ] * 100% = 0.05 * 100% = 5% or X = [ 10 mL (active) / 200 mL (total) ] = 0.05 % Conc. (v/v) = X * 100% % Conc. (v/v) = 0.05 * 100% = 5% The final concentration contains 5% of the active ingredient.

How to solve Weight / Volume Concentrations (Example 1)

100 g of active ingredient powder is mixed with 500 mL normal saline. What is the final concentration (w/v)? 100 g : amount of active ingredient 500 mL normal saline : amount of base 500 mL : total quantity X = 100 g (active) / 500 mL (total) X = 0.2 % Conc. = 0.2 * 100% = 20% The final w/v concentration is 20%.

How to solve Drugs per hour (Example 1)

100 mg of medication is to be administered in 500 mL of LR (Lactated Ringer's) over 2 hours. How much drug will be administered per hour? (Total mg / Total hrs) = (X / 1 hr) 100 mg / 2 hrs = X mg / 1 hr → 2hr * X = 100 mg * 1 hr → 2X = 100 mg → X = 100 mg / 2 → X = 50 mg The infusion will provide 50 mg of the medication per hour.

How to solve Weight / Weight Concentrations (Example 2)

12 g of active ingredient powder is in a 120 g compounded cream. What is the concentration (conc.) (w/w)? 12 g : amount of active ingredient not given : the amount of the base 120 g : total quantity (already contains 12 g) X = 12 g (active) / 120 g (total) = 0.1 % Conc (w/w) = 0.1 * 100 = 10% The final w/w concentration of the compounded cream contains 10% of the active ingredient.

How to solve Volume / Volume Concentrations (Example 2)

180 mL of active ingredient is added to 820 mL of an alcohol-based solution. What is the final strength (v/v)? 180 mL : amount of active ingredient 820 mL : amount of base 1000 mL : total quantity % Conc. (v/v) = [ 180 mL (active) / 1000 mL (total) ] * 100% = [ 180 ml (active) / 1000 mL (total) ] * 100% = 0.18 * 100% = 18% The final v/v strength is 18%. 18% of the final solution is the active ingredient.

How to convert a ratio to a percent

1• Divide the first number by the second number. 2• Multiply by 100. 3• Add the % sign. Example: • 1 : 10 = 1/10 = 0.10 = 0.10 * 100 = 10 = 10%

How to convert a percent to a fraction

1• Drop the % sign. 2• Write the value of the number as the numerator. 3• Place number over a denominator of 100. 4• Reduce the fraction to its lowest terms. Example: 75% = 75 / 100 --> (both divisible by 25) = 3 / 4

How to solve multiple dosage calculations (Example 1, part 2)

2. How may total doses are to be dispensed: 30 doses (30 tsp) 3. The total amount of amoxicillin, in mg, to be dispensed: • 250 mg / 5 mL = X total / 150 mL • 5 mL * X = 250 mg * 150 mL • X = 37,500 mg / 5 • X = 7,500 mg of amoxil 4. How many days will the prescription last: 10 days.

Weight / Volume Concentrations part 2

3. Multiply the result by 100 to express the final concentration as a percentage. Add the % sign. % Concentration = X * 100% When mixing powders with liquids the liquid (base) quantity is considered the total quantity, because the powder will either dissolve or suspend within the base.

How to solve Weight / Weight Concentrations (Example 3)

30 g of a compounded ointment contains 105 mg of neomycin sulfate. What is the final concentration (w/w) 105 mg * (1 g / 1000 mg) = 0.105 g 0.105 g : amount of active ingredient not provided : amount of the base 30 g : total quantity X = 0.105 g (active) / 30 g (total) X = 0.0035 % Conc. (w/w) = 0.0035 * 100% = 0.35% The final w/w concentration is 0.35%

How to solve Volume / Volume Concentrations (Example 3)

36 mL of bezoin tincture is combined with 84 mL of an 80% alcohol solution. What is the final strength (v/v)? 36 mL : amount of active ingredient 84 mL : amount of base 120 mL : total quantity (36 mL + 84 mL) 80% base : describing the base product. % Conc. (v/v) = [ 36 mL (active) /120 mL (total) ] * 100% = [ 36 ml (active) / 120 mL (total) ] * 100% = 0.3 * 100% = 30% The final v/v strength is 30%.

How to perform alligation calculations (Example 4, part 2)

4. total number of parts necessary. 7.5 part (10%) + 2.5 part (0%) = 10 parts total 5. parts needed for each ingredient. a. 10% ointment needed: = 7.5 part / 10 parts or 7.5/10 = 500 mL * (7.5/10) = 500 mL g * 0.75 = 375 mL

How to solve Drugs per hour (Example 3)

5 million units of Penicillin G Aqueous are being delivered in 1 L of D5W over 12 hours. How much drug will be administered per hour? (Total mg / Total hrs) = (X / 1 hr) 5,000,000 units / 12 hrs = X mg / 1 hr → 12 hr * X = 5,000,000 units * 1 hr → 12X = 5,000,000 units → X = 5,000,000 units / 12 → X = 416,666.67 units The infusion will provide 416,667 units of the medication per hour.

How to solve Volume per Hour (Example 2)

500 mL of D5W containing 1 g of lidocaine hydrochloride is to be given over 250 minutes. What is the infusion rate in mL per hour? Given: 1 hr = 60 min (Total mL / Total hrs) = (X / 1 hr) 500 mL / 250 min = X / 60 min 250 * X = 500 * 60 mL 250X = 30,000 mL X = 30,000 / 250 mL X = 120 mL The infusion will be administered at 120 mL per hour (60 minutes)

How to solve Drugs per hour (Example 2)

600 mg of fluorouracil is to be administered by continuous infusion over 24 hours. How much drug will be administered per hour? (Total mg / Total hrs) = (X / 1 hr) 600 mg / 24 hrs = X mg / 1 hr → 24 hr * X = 600 mg * 1 hr → 24X = 600 mg → X = 600 mg / 24 → X = 25 mg The infusion will provide 25 mg of the medication per hour.

How to perform alligation calculations (Example 2, part 1)

How much SWFI would you need to add to 500 mL stock normal saline (0.9% NaCl) to produce a 0.45% sodium chloride solution? Saline: 0.9 | | 0.45 | 0.45 | Water: 0.0 | | 0.45 Total Parts = 0.45+0.45 = 0.90 saline needed: (0.45 / 0.90) * 500mL = 250mL water needed: (0.45 / 0.90) * 500mL = 250mL

How to solve Weight / Volume Concentrations (Example 2)

9 g of sodium chloride is diluted in 1 L of sterile water for injection (SWFI). What is the final percent strength (w/v)? 9 g : amount of active ingredient 1 L = 1,000 mL : total quantity. X = 9 g (active) / 1,000 mL (total) X = 9/1000 = 0.009 % Conc. = 0.009 * 100% = 0.9% The final percent w/v strength is 0.9%.

How to perform temperature conversions: °C → °F or °F → °C

9*C = 5*F - 160 °C = ( °F - 32) / 1.8 or °C = ( °F - 32) * (5/9) °F = 1.8 * °C + 32 or °F = (9/5)*°C + 32

How to calculate flow rate duration (Example 1)

A 1 L IV bag is being administered at a rate of 200 mL per hour. How long will this IV bag last? Use dimensional analysis to solve: 1 L = 1,000 mL 1 hr = 200 mL (rate of 200 mL per hour) 1 L = (1 L / 1) * (1,000 mL / 1 L) * (1 hr / 200 mL) 1 L = (1 * 1,000 * 1 hr) / 200 1 L = 1000 / 200 1 L = 5 hrs. The 1 L bag will last 5 hours.

Calculate Pediatric Dosage using Fried's Rule Example 2

A child who is 30 months old needs erythromycin; the normal adult dose is 250 mg QID. What is the appropriate dosage for the infant? Pediatric Dose (X) = [ 30 (age in months) / 150 ] * 250 mg (adult dose) X = [ 30 / 150 ] * 250 mg X = 0.2 * 250 X = 50 mg/dose. The pediatric dose appropriate for a 30-month old using Fried's Rule is 50 mg/dose.

Multiple dosage calculations

A combination of dosage calculations.

International Units (IU)

A number of drugs, such as insulin, heparin, and penicillin, are measured in IU. Ex: twenty units = 20 units ten thousand units = 10,000 units

How to calculate flow rate duration (Example 2)

A patient is set to get a 500 mL infusion of cimetidine in lactated Ringer's 5% at 10:00 a.m. The bag is set to be administered at a rate of 125 mL per hour. At what time will the infusion be complete? 500 mL : to total volume of the IV bag. 125 mL/hr = rate of administration 10:00 a.m. : when the infusion is scheduled to start. X : at what time will the infusion finish. 500 mL = (500 mL/1) * (1 hr / 125 mL) 500 mL = (500 * 1hr) / 125 500 mL = 4 The 500 mL bag will last 4 hours. 10:00 am + 4 hours = 14:00 hours or 2:00 pm

How to solve Volume per Hour (Example 1)

A patient is to receive 750 mL infused over 3 hours. What is the rate of infusion in mL per hour? (Total mL / Total hrs) = (X / 1 hr) 750 mL / 3 hrs = X / 1 hr 3 * X = 750 * 1 3X = 750 X = 750 / 3 X = 250 mL The infusion will be administered at 250 mL per hour.

Dosage amount to calculate doses

Always use the higher dosage amount when performing dosage calculations on prescriptions that have a range for the dose. Rx (Prescription): "Ibupropfen 400 mg i - ii po q 6hr prn pain Disp. #120" Solve: • Assume the most conservative usage of 2 tablets every 6 hours and not 1 tablet every 6 hours. • (1 dose / 2 tabs) = ( X doses / 120 tabs) • 2 * X = 1 * 120 • X = 120 / 2 • 60 • A minimum of 60 doses has been prescribed.

Calculate Pediatric Dosage using Young's Rule Example

An infant, 15 months old and weighting 20 pounds, needs streptomycin sulfate, which is usually administered to adults as 1 gm (1,000 mg) in a daily IM injection. What is the appropriate dosage for the infant? 15-months = 1.25 years or 12 months (1 yr) + 3 months ( 3/12 = 1/4 = 0.25 years) Pediatric Dose = [ 1.25 (age in years) / 13.25 ( 1.25 yrs + 12 yrs) ] * 1,000 mg (adult dose) X = ( 1.25 / 13.25 ) * 1,000 X = 0.094 * 1,000 X = 94 mg. The pediatric dose appropriate for a 15-month old using Young's Rule is 94 mg.

Calculate Pediatric Dosage using Fried's Rule Example 1

An infant, 15 months old and weighting 20 pounds, needs streptomycin sulfate, which is usually administered to adults as 1 gm (1,000 mg) in a daily IM injection. What is the appropriate dosage for the infant? Pediatric Dose = [ 15 (age in months) / 150 ] * 1,000 mg (adult dose) X = 15/150 * 1,000 X = 0.1 * 1,000 X = 100 mg/dose. The pediatric dose appropriate for a 15-month old using Fried's Rule is 100 mg/dose.

Calculate Pediatric Dosage using Clark's Rule Example

An infant, 15 months old and weighting 20 pounds, needs streptomycin sulfate, which is usually administered to adults as 1 gm (1,000 mg) in a daily IM injection. What is the appropriate dosage for the infant? Pediatric Dose = [ 20 (weight in lbs.) / 150 ] * 1,000 mg (adult dose) X = (20 / 150) * 1,000 X= 0.133 * 1,000 X = 133 mg. The pediatric dose appropriate for a 15-month who weights 20 lbs. using Clark's Rule is 133 mg/dose.

How to calculate dosages using mg/kg/day (Example 1)

An infant, 15 months old and weighting 20 pounds, needs streptomycin sulfate, which is usually administered to adults as 1 gm (1,000 mg) in a daily IM injection. What is the appropriate dosage for the infant? What is the appropriate pediatric dosage if it is recommended to administer 20 mg/kg/day (maximum 1 g) of streptomycin sulfate to the infant? Weight (kg) = 20 lbs * (1 kg / 2.2 lbs) = (20 / 2.2) kg = 9.09 kg Pediatric Dose = 20 mg * 9.09 kg * 1 day = 20 * 9.09 * 1 = 181.8 mg/kg/day. The patient should be given 181.8 mg of streptomycin sulfate as a daily IM injection.

Calculating the Correct Days Supply

Calculating the number of days a prescription should last or days supply, if the medication is taken as prescribed. Days Supply = Qty. dispensed / ( Dose * Frequency )

How to perform alligation calculations (Example 2, part 2)

How much SWFI would you need to add to 500 mL stock normal saline (0.9% NaCl) to produce a 0.45% sodium chloride solution? Determine the total amount of final solution that will be created: Q1*C1 = Q2*C2 (0.9%)*(500mL) = (0.45%)X X = (0.9% * 500mL) / (0.45) X = 1000 mL is the total amount that will be created water needed: (0.45 / 0.90) * 1000mL = 500 mL

Volume / Volume Concentrations

Concentrations in which a liquid active ingredient is mixed with a liquid base (e.g. an emulsion). Steps to solve: 1. Setup a proportion with the amount of active ingredient listed over the total quantity, as milliliters over milliliters (mL). X = [ active ingredient (milliliters) / total qty (milliliters) ] 2. Convert the proportion to a decimal ( divide the numerator (active ingredient) by the denominator (total qty). 3. Multiply the result by 100 to express the final concentration as a percentage. Add the % sign. % Concentration = X * 100%

Weight / Volume Concentrations part 1

Concentrations in which a solid active ingredient (e.g. powder) is mixed with a liquid base (e.g. a syrup) Steps to solve: 1. Setup a proportion with the amount of active ingredient listed over the total quantity, as grams over milliliters (mL). X = [ active ingredient (grams) / total qty (milliliters) ] 2. Convert the proportion to a decimal ( divide the numerator (active ingredient) by the denominator (total qty).

Weight / Weight Concentrations

Concentrations in which a solid active ingredient (e.g. powder) is mixed with a solid base (e.g. an ointment). Steps to solve: 1. Setup a proportion with the amount of active ingredient listed over the total quantity, as grams over grams. X = active ingredient (grams) / total qty (grams) 2. Convert the proportion to a decimal ( divide the numerator (active ingredient) by the denominator (total qty). 3. Multiply the result by 100 to express the final concentration as a percentage. • Add the % sign. % Concentration = X * 100%

How to convert between conversion systems: 180 gr (grain) to ounces

Convert 180 gr to ounces Given: 1 oz. = 480 gr (1/ 480 oz.) = (X / 180 gr) 480X = 180 X = 180/480 X = 0.375 180 gr = 0.375 ounce

Perform °C → °F temperature conversions (Example 1)

Convert 60°C to °F: °F = 1.8 x 60 + 32 °C = 108 + 32 °F = 140°

Perform °F → °C temperature conversions (Example 1)

Convert 80°F to °C: °C = (80 - 32) / 1.8 °C = 48 / 1.8 °C = 26.7°

Flow Rates

Describes a number of common pharmacy calculations used in the preparation of IV infusions.

How to perform alligation calculations (Example 3, part 2)

Determine the total amount of final solution that will be created: Q1*C1 = Q2*C2 (10%)*(500mL) = (0.9%)X X = (10% * 500mL) / (0.9) X = 5555.55 mL is the total amount that will be created water needed: (9.1 / 10) * 5555.55 mL = 5055.55 mL

How to calculate the number of doses in a prescription (Option 1)

Dose to be given = [ DD (Desired dose) / DH (dose on hand) ] * QTY (quantity) Example: How many 1 tsp doses are in a 4 oz. bottle of Prozac Liquid Solution 20 mg/5mL? Given: 120 mL = 4 oz. 1 oz = 30 mL 1 tsp = 5 mL 1. Convert oz. to mL • 1 oz. / 30 mL = 4 oz. / X mL • 1 * X = 30 * 4 • X = 120 mL 2. Solve for the number of doses • 1 dose / 5 mL = X doses / 120 mL • 5 * X = 1 * 120 • 5X = 120 • X = 120 / 5 • X = 24 doses There are 24 doses (of 5 mL each) in a 4 oz. (120 mL) bottle.

Ratios

Express the relationship of two numbers, is separated by a colon (:). Example: 1:2 is "1 to 2" or ½ or "1 over 2"

How to calculate dosages using mg/kg/day (Example 2)

For children the daily dose of Omnicef is 14 mg/kg, up to a maximum dose of 600 mg/day. What is the appropriate daily dosage for a patient who weights 98 pounds. Weight (kg) = 98 lbs * (1 kg / 2.2 lbs.) = 98 / 2.2 kg = 44.5 kg Daily dose = 14 mg * 44.5 kg * 1 day = 623 mg per day. 600 mg is the maximum daily dose that should be given to the patient.

Proportions Example

Given 1 g of active ingredient per 10 g of ointment base, create an ointment that contains 10 g of active ingredient. active : base = total active : total base • 1:10 = 10:X • 1 10 --- = --- 10 X • 1*X = 10*10 • X = 100 g of ointment will be produced

How to calculate the number of doses in a prescription (Example Option 2 - dimensional analysis)

How many 1 tsp doses are in a 4 oz. bottle Prozac Liquid Solution 20 mg/5mL? Given: 120 mL = 4 oz. 1 oz = 30 mL 1 tsp = 5 mL X = 4 oz * (30 ml / 1 oz.) * (1 tsp / 5 ml) X = (4 * 30 tsp) / 5 X = 120 tsp / 5 X = 24 tsp 24 tsp are in a 4 oz. bottle

How to calculate the correct days supply (Example 2)

How many days will the following prescription last? Rx: Kaletra 133.3 / 33.3 mg i-ii po BID - food Disp. #360 Given: 1-2 po : dose BID : the frequency, 2 times per day 360 : quantity to dispense Keletra 133.3 / 33.3 mg : drug name & strength (NOT NEEDED) Days Supply = qty. dispensed / ( dose * frequency ) X = 360 / ( 2 tabs * 2 times per day) X = 360 / 4 X = 90 The prescription will last 90 days or 3 months.

How to calculate the correct days supply (Example 1)

How many days will the following prescription last? Rx: Pamelor 75 mg i po BID Disp. #50 Given: 1 po : dose BID : the frequency, 2 times per day 50 : quantity to dispense Days Supply = qty. dispensed / ( dose * frequency ) X = 50 / ( 1 dose * 2 times per day) X = 50 / 2 X = 25 The prescription will last 25 days.

How to solve dimensional analysis (Example 1)

How many hours are there in 6 days? Given: 24 hours in 1 day = 24 hrs/day 6 days = 6 days / 1 * 24 hours / 1 days 6 days = 6 * 24 hours 6 days = 144 hours There are 144 hours in 6 days.

How to solve Volume / Volume Concentrations (Example 4)

How many mL of active ingredient must be added to distilled water to produce 60 mL of a 25% solution (v/v)? not provided : amount of the active ingredient 60 mL : total qty. 25% : final v/v strength % Conc. (v/v) = [ mL (active) / mL (total) ] * 100% 25% = ( X mL / 60 mL ) * 100 25 / 100 = ( X mL / 60 mL) * (100 / 100) X mL / 60 mL = 25 / 100 Cross multiply: 100 * X = 60 * 25 100X = 1500 X = 1500 / 100 X = 15 mL 15 mL of active ingredient is necessary to produce 60 mL of a 25% solution.

How to calculate the quantity of ingredient required (Example 1)

How many mL of stock dopamine must be added to the IV solution. Rx: Dopamine 400 mg added to 500 mL of NS Stock: Dopamine HCL Injection 80 mg/mL Given: 400 mg : dose 500 mL : quantity to dispense dopamine HCl injection 80mg/mL : drug name and strength. 1. Determine how many mL of stock dopamine to add to the normal saline (NS) IV solution bag: 80 mg / 1 mL = 400 mg / X mL 80 * X = 1 * 400 X = 400 / 80 mL X = 5 mL • Add 5 mL of the stock dopamine HCl injection to the IV solution. • Restated: 5 mL of stock solution of HCl will contain 400mg of the active ingredient. • Restated: Of the total 500 mL IV solution required: 495 mL of solution will be NS and 5 mL will be the active ingredient.

How to solve dimensional analysis (Example 2)

How many seconds are in 4 days? 4 days = (4 days / 1) * (24 hours / 1 day) * (60 minutes / 1 hour) * (60 seconds / 1 minute) 4 days = 4 * 24 * 60 * 60 seconds 4 days = 345,600 seconds There are 345,600 seconds in 4 days.

How to solve Weight / Weight Concentrations (Example 3 - % Conc. given)

How much oxiconazole nitrate powder is required to prepare the prescription: Rx: 1% Oxiconazole Nitrate ointment Disp. 45g not provided : active ingredient not provided : amount of the base 45 g : total quantity 1% : final concentration Formula: (g active / g total qty.) * 100 = Final % strength • [ X g (active) / 45 g (total) ] * 100 = 1% • = ( X g / 45 g) * (100 / 100) = 1 / 100 • = ( X g / 45 g) = 1 / 100 Cross multiply: X * 100 = 1 * 45 100X = 45 X = 45 / 100 X = 0.45 g 0.45 g or 450 mg of Oxiconazole nitrate powder is needed for a 1% concentration (w/w) order.

How to calculate dilutions (Example 1)

How much stock solution of hydrogen peroxide 12% solution is needed to make 480 mL hydrogen peroxide 3% solution? Given: Q1 : X C1 : 12% Q2 : 480 mL C2 : 3 % Q1 * C1 = Q2 * C2 X * 12 = 480 mL * 3 12X = 1440 X = 1440 / 12 X = 120 mL Would need 120 mL of the 12% solution to dilute to 480 mL of a 3 % solution.

How to convert Wight from Pounds to Kilograms

If an infant weights 20 pounds, what is her weight in kg? Given: 2.2 lbs. = 1 kg X = 20 lbs * (1 kg / 2.2 lbs) X = (20 / 2.2) kg X = 9.09 kg The infant weights 9.09 kg.

How to calculate dilutions (Example 3)

If you dilute 90 mL of an 8% benzocaine lotion to 6%, how much could you produce? Given: Q1 : 90 mL C1 : 8% Q2 : X mL C2 : 6% Q1 * C1 = Q2 * C2 90 * 8 = X * 6 720 = 6X 720 / 6 = X 120 = X You would be able to produce 120 mL of the diluted 6% solution.

Diluent in a dilution

In a dilution, the diluent is the larger volume that is mixed with the stock solution.

Dosages using mg/kg/day

Is the most precise and preferred method of calculating pediatric dosages.

Alligation Method for Calculations

Is used to determine how many parts of the SAME product, with different strengths will be needed to create the final strength desired/requested. It may be used to calculate exactly how many milliliters or grams you need for each constituent (beginning) product.

Clark's Rule for Pediatric Dosage

Mnemonic: CCWp (Clark's Child's Weight pounds) • May be used for newborns and young infants. Clark's Child's Dosage = (Child's weight in pounds / 150) * Adult Dosage

Fried's Rule for Pediatric Dosage

Mnemonic: FM/150 • May be used for toddlers. Fried's Child's Dosage = (Age in months / 150) * Adult Dosage

Young's Rule for Pediatric Dosage

Mnemonic: YY or Young Years • May be used for older children. Young's Child's Dosage = (Age of child in years / (Age of child in years + 12) ) * Adult Dosage

Normal Saline

Normal saline is 0.9% NaCl (sodium chloride)

Drugs per hour

Or mg/hr. Refers to the dosage or amount of medication in milligrams that will be administered per hour of infusion. (Total mg / Total hrs) = (X / 1 hr)

Calculate percent by setting up a proportion

Parts of the whole ÷ Whole = Percent (%) ÷ 100 To solve: 1. Two of the three variables need to be present: parts of the whole, the whole, or the percent. 2. Identify each term as part of the whole, the whole, or a percent. 3. Place values in the equation. 4. Cross multiply across the equal sign. 5. Divide to find the missing term.

Calculating Pediatric Dosage

Pediatric patients include both infants and children

Drop factor

Refers to a specific drip rate. Is a simpler way of stating a drip rate. When preparing sterile products, personnel may be responsible for calculating the rate of IV administration, expressed as drops per minutes (gtts/min). The drip rate will determine how the IV pump is calibrated and the volume of medication to be administered each minute.

Flow rate duration

Refers to the length of time over which an IV will be administered or how long an IV bag will last before it must be changed.

How to solve Weight / Volume Concentrations (Example 3)

Rogaine Extra Strength is a 5% solution of minoxidil in alcohol. How much active ingredient is in a 2 ounce bottle? 2 oz * ( 30 mL / 1 oz) = 2 * 30 mL = 60 mL not provided : amount of active ingredient 60 mL : total quantity 5% : final strength (g active / mL total qty ) * 100 = Final % strength → [ X g (active) / 60 mL (total) ] * 100 = 5% → [ X g / 60 mL ] * (100 / 100) = ( 5 / 100) → X g / 60 mL = 5 / 100 → 100 * X g = 60 * 5 → X = 300 / 100 g → X = 3 g A 60 mL bottle of 5% Rogaine Extra Strength contains 3 g of minoxidil powder.

Roman Numerals

Roman Numerals ss = one-half, 1/2 I or i = 1 II or ii = 2 III or iii = 3 IV or iv = 4 V or v = 5 X or X = 10 L or l = 50 C or c = 100 D or d = 500 M or M = 1000

How to perform alligation calculations (Example 1, part 2)

Rx: Prepare 120 g of a 2% hydrocortisone ointment using a 1% ointment and a 2.5% ointment. 3. Calculate the numbers that does into the top right and bottom right boxes: → Done by working diagonally and taking the different between the two numbers already in place. Only positive numbers can go into the grid. a. 2.5 - 2 = 0.5 Higher: 2.5 | | Desired: | 2 | Lower: 1 | | 0.5 b. 1 - 2 = - 1 Change -1 to 1 Higher: 2.5 | | 1 Desired: | 2 | Lower: 1 | | 0.5

How to perform alligation calculations (Example 1, part 3)

Rx: Prepare 120 g of a 2% hydrocortisone ointment using a 1% ointment and a 2.5% ointment. 4. Add the numbers in the 3rd column of the grid, to determine the total number of parts necessary. 1 part (2.5%) + 0.5 part (1%) = 1.5 parts total

How to perform alligation calculations (Example 1, part 4)

Rx: Prepare 120 g of a 2% hydrocortisone ointment using a 1% ointment and a 2.5% ointment. 5. Determine the number of parts needed for each ingredient. % product X = (Parts needed / Total parts) a. 2.5% ointment needed: = 1 part / 1.5 parts or 1 / 1.5 = 120 g * (1 / 1.5) = 120 g * 0.667 = 80 g b 1% ointment needed: = 0.5 part / 1.5 parts = 0.5 / 1.5 = 120 g * (0.5 / 1.5) = 120g * 0.33 = 39.96 g = 40 g Would need to combine 80 g of the 2.5% ointment and 40 g of the 1% ointment to produce 120 g of a 2% ointment.

How to perform alligation calculations (Example 1, part 1)

Rx: Prepare 120 g of a 2% hydrocortisone ointment using a 1% ointment and a 2.5% ointment. Given: 2.5% : higher strength 1% : lower strength 2 % : desired/final strength 120 g : desired/final quantity 1. Draw the alligation grid, a 3x3 tic-tac-toe board. 2. Fill the alligation grid: → The higher strength goes in the top left box. → The lower strength goes in the bottom left box. → The desired strength goes in the center box. Higher: 2.5 | | Desired: | 2 | Lower: 1 | |

How to perform alligation calculations (Example 4, part 1)

Rx: Prepare 500 mL of a 7.5% dextrose solution using SWFI and D10W. Given: D10W = 10% dextrose : higher strength SWFI = 0% : lower strength 7.5% : desired strength 500 mL : desired quantity D10W is dextrose 10% in water, this is a 10% strength solution. SWFI are 0% strength, they contain no active ingredient. Higher: 10 | | Desired: | 7.5 | Lower: 0 | | a. 10 - 7.5 = 2.5 b. 0 - 7.5 = - 7.5 = 7.5 Higher: 10 | | 7.5 Desired: | 7.5 | Lower: 0 | | 2.5

How to solve multiple dosage calculations (Example 2, part 2)

Rx: Xanax 0.25 mg i-ii TID prn x 14d 3. What is the maximum amount of alprazolam, in mg to be taken daily: X = 0.25 mg / 1 tab * 6 tabs / day X = 0.25 mg * 6/day = X = 1.5 mg/day 4. How many days will the prescription last if 60 tablets are dispensed. quantity to dispense = dose x frequency x duration 60 tabs = 2 tabs * 3 times * X day X = 60 / 6 X= 10 days 60 tablets will last 10 days.

How to solve multiple dosage calculations (Example 2, part 1

Rx: Xanax 0.25 mg i-ii TID prn x 14d Given: Xanax 0.25 mg : drug name & strength i-ii tabs : dose TID : frequency, 3 times per day. 14d : days duration 1. What is the maximum quantity to dispense: X = 2 (doses) * 3 (frequency) * 14 (days) X = 2 * 3 * 14 X = 84 2. What is the maximum number of doses if 60 tablets are dispensed: Disp. Qty = Dose * Duration 60 = 2 * X X = 60 / 2 X = 30 doses

How to solve multiple dosage calculations (Example 1, part 1)

Rx: amoxil 250 mg / 5 mL i tsp. TID x 10d Given: • i tsp = 5 mL : dose • TID : frequency, 3 times per day • 10d : days supply • amoxil 250 mg / 5 mL : drug name & strength 1. Quantity to dispense: 150 mL Quantity to dispense = dose x frequency x duration • = 1 tsp. (dose) * 3 (frequency) * 10 (days duration) • = 1 tsp * 3 * 10 • = 30 tsp • 30 tsp * ( 5 mL / 1 tsp) = 150 mL

How to determine the quantity to dispense - for a 3-month supply

Rx: furosemide 20 mg i po qod • Take 1 tablet of furosemide 20 mg every other day by mouth. Solve: • Every other day = 30 days/ 2 = 15 days • 15 days * 3 month supply = 45 tablets

How to perform alligation calculations (Example 3, part 1)

Rx: normal saline. How many milliliters of water must you add to 500mL of a 10% stock solution of sodium chloride to make a batch of normal saline (sodium chloride 0.9% solution) 10% Saline: 10 | | 0.9 | 0.9 | Water: 0.0 | | 9.1 Total Parts = 0.9 + 9.1 = 10 10% saline needed: (0.9 / 10) * 500mL = 45 mL water needed: (9.1 / 10) * 500mL = 455 mL

Dilutions

Stock solutions are strong (very concentrated) solutions that can be diluted to the strength ordered or desired. Formula: Q1 * C1 = Q2 * C2 As a ratio and proportion: Q1 / Q2 = C2 / C1 Q1 : initial quantity or volume (milliliters or grams). Q2 : final or desired quantity or volume (milliliters or grams). C1 : initial concentration, expressed as a percentage (stock solution) C2 : final or desired concentration expressed as a percentage ( final solution)

Drops per minute (gtts/min)

The volume of medication to be administered each minute. • IV administration sets release specific drops per milliliter. • Microdrip sets are calibrated to deliver 60 drops per mL. Macrodrip sets may be calibrated to deliver ∼The larger the number of drops per milliliter, the smaller the drops will be.

Given a specific total quantity, determine how much of each ingredient is needed to prepare a different total quantity

To calculate the amount or quantity of active ingredient required, usually for compounding. [ Total qty of form (specified) / Qty of ingredient (specified) ] = [ Total desired qty / Qty Desired qty ]

How to convert a decimal to percent

To convert a decimal to percent: 1. Multiply the number by 100. 2. Add a percent (%) sign. Examples: • 0.45 * 100 = 45% • 1.00 * 100 = 100% • 1.25 * 100 = 125%

How to convert a percent to decimal

To convert a percent to decimal: 1. Remove the % sign. 2. Divide by 100. Examples: • 95% / 100 = 0.95 • 50% / 100 = 0.50 • 0.25% / 100 = .0025 • 105% / 100 = 1.05

Proportions

Two or more equivalent ratios or fractions that both represent the same value. The double colon translates to "equals" or "is equal to". The = sign is sometimes used in place of the double colon Ex: 2:10 :: X:30 2/10 = X/30 → 2*30 = 10*X → 60 = 10X → X = 60/10 → X = 6 2:10 :: 6:30

How to convert between conversion systems

Units that you have * (Number of units that you want / Units that you have) 1. 5 tsp. to millimeters = 5 tsp * (5 mL / 1 tsp) = 25 mL 2. 3 Tbsp to millimeters = 3 Tbsp. x (15 mL / 1 Tbsp) = 45 mL

Volume per Hour

Volume/hour or mL/hr. Refers to the amount of fluid or solution that will be administered to the patient intravenously per hour. (Total mL / Total hrs) = (X / 1 hr)

How to calculate dilutions (Example 2)

You had 60g of a 20% coal tar solution, which you diluted to produce 100 g. What is the strength of the final product Given: Q1 : 60 g C1 : 20% Q2 : 100 g C2 : X Q1 * C1 = Q2 * C2 60 * 20 = 100 * X 1200 = 100X 1200 / 100 = X 12 = X The final product is a 12% coal tar solution.

How to calculate the quantity of ingredient required (Example 2)

Z-pak contains 6 tablets of azithromycin 250 mg, which are taken over the course of 5 days. How may total mg of active ingredient are contained in a Z-pak? X = 250 mg * 6 tabs X = 1500 mg of active ingredient

Milliequivalents (mEq)

the number of grams of a drug in 1 mL of a normal solution. Potassium chloride is expressed in mEq. Ex: fifty milliequivalents = 50 mEq fifteen milliequivalents = 15 mEq

IV infusions

are compounded solutions that provide fluids, specific medications, nutrients, electrolytes, and minerals to a patient

How to perform alligation calculations (Example 4, part 3)

b 0% ointment needed: = 2.5 part / 10 parts or 2.5/10 = 500 mL * (2.5/10) = 500 mL g * 0.25 = 125 mL Would need to combine 375 mL of D10W and 125 mL of the SWFI to prepare 500 mL of a 7.5% dextrose solution.

How to determine the quantity to dispense (Example)

quantity to dispense = dose x frequency x duration How many Biaxin 250 mg tablets should be dispensed for the following prescription: Rx: "Biaxin 250 mg i po BID x 10d " Solve: • X (qty to dispense) = 1 (dose) * 2 (frequency, 2x/day) * 10 (duration, days) • X = 1 * 2 * 10 • X = 20 doses • 20 doses/tablets of Biaxin 250 mg should be dispensed.

Percentages and medication strength

• Percent means "parts per 100". • Can calculate using ratios, fractions, or decimals.

How to convert a fraction to a ratio

• Place the numerator first. • Followed by a colon. • Place the denominator next. Example: • 1/2 is "1 over 2" • 1 : 2 is "1 to 2"

Alligation Calculations - Things to Know (part 1)

• Solvents and diluents, such as water, vanishing cream base, and white petrolatum, are considered to be a percent strength of zero (0). • Liquids, including solutions, syrups, elixirs, and lotions, are expressed in MILLILITERS (Ml). • Solids, including powders, creams, and ointments are expressed in GRAMS (g).

Alligation Calculations - Things to Know (part 2)

• The alligation formula requires that you express the strength as a percentage when setting up the problem. You must convert any ration strength in the initial question to a percent strength. • When writing percent or using decimals, always use a leading zero (e.g. 0.25%). • 1 fl. oz. = 29.57 mL. This is commonly rounded to 30 mL. • 1 avoirdupois oz. = 28.35 g. The measurement is commonly used for solids and it is rounded to 30 g.

Concentration/Dilution - preventing erros

• initial strength must be larger than final strength. • initial volume must be less thanfinal volume. • final volume minus initial volume equals amount of diluent (inert substance) to be added to make final volume