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A Technicianβs Guide to
Pharmaceutical Calculations: Dosing
and Dispensing Math and
Compounding CalculationsAllison Lardieri, PharmD, BCPPS
University of Maryland School of Pharmacy
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Learning Objectives
Describe examples of common systems of measurement
and conversions used in pharmacy calculations.
Given the necessary information, perform calculations
needed while working in a community pharmacy.
Given the necessary information, perform calculations
needed while working in an institutional pharmacy.
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Common Measurements: Some (but not
all!) of the units!
Metric System
Gram (g)
Liter (L)
Prefixes
Prefix Name Value
Kilo- Kilogram (Kg)
Kiloliter (KL)
1000 grams
1000 liters
Milli- Milligram (mg)
Milliliter (mL)
0.001 gram
0.001 liter
Micro- Microgram (mcg)
Microliter (mcL)
0.000001 gram
0.000001 liter
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Common Measurements: Some (but not
all!) of the units!
1 kg = 2.2 Lbs
1 lb = 454g
1 inch = 2.54 cm
1 tsp = 5 mL
1 tbsp. = 15 mL = 3 tsp
1 oz. = 30 mL = 2 tbsp.
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Common Measurements: Some (but not
all!) of the units!
Your Turn:
70 kg = ____lb
17 g = _____mg
536 mg = _____ g
3600 mL = ______ L
4.5 tsp = _____ mL
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Common Measurements: Some (but not
all!) of the units!
70 kg = 154 lb
17 g = 1700 mg
536 mg = 0.536 g
3600 mL = 3.6 L
4.5 tsp = 22.5 mL
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Ratio and Proportion
500ππ
1 π‘ππor
1 π‘ππ
500ππ
1 ππ πππππππ πππ
$5or
$5
1 ππ πππππππ πππ
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Ratio and Proportion
Example 1:
If one teaspoonful contains 15 mg of prednisolone, how
many mg are in 4 teaspoonfuls?
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Ratio and Proportion
15 ππ
5 ππΏ=
π₯ ππ
20 ππΏ
15 ππ Γ 20 ππΏ = π₯ ππ Γ 5 ππΏ
15ππ Γ20ππΏ
5ππΏ= π₯ ππ = 60 ππ
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Ratio and Proportion
Example 2:
You must fill an order for three 1 liter bags of D5W with 12
mmols of potassium phosphate per bag. The potassium
phosphate is available as 5 mL vials with a concentration
of 3 mmol/mL. How many 5 mL vials of potassium
phosphate will you need for this order?
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Ratio and Propotion
3 ππππ Γ12 πππππ
πππΓ
1 ππΏ
3 ππππΓ
1 π£πππ
5 ππΏ= 2.4 π£ππππ
So, will need to get 3 vials!
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Community Pharmacy Calculations
Days supply and quantity
Insulin dosing
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Days Supply and Quantity
Need to know unit of measure and abbreviation
Quantity to be dispensed may or may not be listed on the prescription
Accurate days supply is important to ensure patient receives correct amount
of medication
Prevent rejected insurance claims
Inhalers, insulin, creams, eye drops
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Name _____________
Address _______________________________________
Date __________________
DOB __________________
Refill NR 1 2 3 4 5 Void after _________
Dispense As Written May Substitute
Prescription is void if more than one controlled substance is written per blank
Clindamycin 300 mg
1 cap TID X 14 days
Anthony Davis
Prescriber (Printed) Anthony Davis______
DEA # AD1212125_________
6/25/17
12/8/73
Michael Scofield
Joannaβs Pharmacy1123 Wildcat Lane
Baltimore, Maryland 21201
410-555-8888
20 N Pine St Baltimore, MD 21201
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Days Supply and Quantity
How many tablets should be dispensed for this Rx?
1 cap TID = 3 caps per day
3 ππππ
1 πππ¦Γ 14 πππ¦π = 42 ππππ πππ π‘ππ‘ππ πππ’ππ π
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Name _____________
Address _______________________________________
Date __________________
DOB __________________
Refill NR 1 2 3 4 5 Void after _________
Dispense As Written May Substitute
Prescription is void if more than one controlled substance is written per blank
Albuterol HFA
2 puffs QID
Anthony Davis
Prescriber (Printed) Anthony Davis______
DEA # AD1212125_________
6/25/17
12/8/73
Michael Scofield
Joannaβs Pharmacy1123 Wildcat Lane
Baltimore, Maryland 21201
410-555-8888
20 N Pine St Baltimore, MD 21201
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Days Supply and Quantity
What is the days supply for this Rx?
Need to know how many puffs are in the inhaler?
Usually on the box or outer wrapping of the inhaler
Also in package insert
Albuterol has 200 metered inhalations
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Days Supply and Quantity
2 puffs QID = 8 puffs per day
1 πππ¦
8 ππ’πππ =
π₯ πππ¦π
200 ππ’πππ
π₯ πππ¦π = 200 ππ’πππ Γ· 8 ππ’πππ πππ πππ¦ = 25 πππ¦π
OR
200 puffs total / 8 puffs per day = 25 days
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Name _____________
Address _______________________________________
Date __________________
DOB __________________
Refill NR 1 2 3 4 5 Void after _________
Dispense As Written May Substitute
Prescription is void if more than one controlled substance is written per blank
Lantus Insulin vial
12 units
subcutaneously once
daily
Anthony Davis
Prescriber (Printed) Anthony Davis______
DEA # AD1212125_________
6/25/17
12/8/73
Michael Scofield
Joannaβs Pharmacy1123 Wildcat Lane
Baltimore, Maryland 21201
410-555-8888
20 N Pine St Baltimore, MD 21201
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Days supply and Quantity
What is the days supply for this Rx?
Need to know how many units are in one vial
Usually, 1000 units/vial
Each vial is 10 mL and the concentration is 100 units/mL
100 units/mL X 10 mL = 1000 units
Exception U-500 insulin: 5000 units/vial
Each vial is still 10 mL, but the concentration is 500 units/mL
500 units/mL X 10 mL = 5000 units
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Days Supply and Quantity
12 π’πππ‘π
1 πππ¦=
1000 π’πππ‘π
π₯ πππ¦π
π₯ = 83.33 πππ¦π
Lantus vial only good for 28 days, so will default to 28 days for days supply
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Name _____________
Address _______________________________________
Date __________________
DOB __________________
Refill NR 1 2 3 4 5 Void after _________
Dispense As Written May Substitute
Prescription is void if more than one controlled substance is written per blank
Lantus Insulin pen
50 units
subcutaneously once
daily
Dispense: 1 box
Anthony Davis
Prescriber (Printed) Anthony Davis______
DEA # AD1212125_________
6/25/17
12/8/73
Michael Scofield
Joannaβs Pharmacy1123 Wildcat Lane
Baltimore, Maryland 21201
410-555-8888
20 N Pine St Baltimore, MD 21201
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Days Supply and Quantity
Insulin pen
Still has 100 units/mL
Total volume of pen is 3 mL
Often, come as 5 pens per box
How many units of insulin in entire box?
5 ππππ Γ3 ππΏ
1 πππΓ
100 π’πππ‘π
1 ππΏ= 1500 π’πππ‘π
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Days Supply and Quantity
What is the days supply for the prescription?
1500 units total Γ· 50 π’πππ‘π πππ πππ¦ = 30 πππ¦π
Or
1500 π’πππ‘π Γ1 πππ¦
50 π’πππ‘π = 30 πππ¦π
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Hospital Pharmacy Calculation
Weight based dosing
Drip rate calculations
BSA based dosing
Dilutions
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Pediatric Dosage Determination
Weight expressed in kg, not lbs
1 kg = 2.2 lbs
Medication doses expressed in mg/kg/day or mg/kg/dose
Adolescents should be dosed based on pediatric data until the calculated dose
per weight is equal to or exceeds the adult dose. Then, the adult dose is
used.
Ceftriaxone 75 mg/kg/dose once daily
Child weighs 32 kg
Dose: 75 x 32 = 2400 mg
Cap dose at 2000 mg (adult max dose)
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Your turn!
A 4 year old female patient weighs 33 lbs. How much does she weigh in kg?
A 6 month old male patient weights 17 lbs. How much does he weight in kg?
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Answer
A 4 year old female patient weighs 33 lbs. How much does she weigh in kg?
33lb / 2.2 = 15 kg
A 6 month old male patient weights 17 lbs. How much does he weight in kg?
7.7 kg
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Pediatric Dosing: Example #1
A 2 year old girl who is 12 kg is ordered Ibuprofen 10 mg/kg PO Q6 hours
What dose should be administered every 6 hours?
10 mg/kg X 12 kg = 120 mg
What is the total dose per day?
120 mg X 4 times in one day = 480 mg
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Pediatric Dosing: Example #1
Ibuprofen oral suspension is available in 100mg/5mL
How many mLs should be drawn up for each dose for this patient?
120 mg X 5mL/100 mg = 6 mL per dose
How much should be dispensed for a 7 day supply?
6 mL per dose X 4 doses in one day X 7 days
= 168 mL total
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Your Turn!
A 4 year old boy who weighs 15 kg is ordered for clindamycin 10 mg/kg PO Q8
hours. The oral solution is available in 75 mg/5 mL.
β’ How many mLs per dose should be drawn up?
β’ How many mLs per day will this child need?
β’ For a 10 day supply, how many mLs should be dispensed?
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Review
10 mg/kg X 15 kg = 150 mg per dose
150 mg X 5 mL/75 mg = 10 mL per dose
10 mL per dose X 3 times per day = 30 mL per day
30 mL per day X 10 days = 300 mLs for course
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Your Turn!
A 4 year old boy who is 16 kg is ordered cefazolin 25 mg/kg IV Q8 hours
β’ What dose should administered every 6 hours?
25 mg/kg X 16 kg = 400 mg
β’ What is the total dose per day?
400 mg X 3 times per day = 1200 mg
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Your Turn!
Cefazolin IV is available in a concentration of 100 mg/mL at your hospital
How many mLs should be drawn up for each dose for this patient?
400 mg X 1mL/100mg = 4 mL per dose
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Your Turn!
A 13 day old girl who is 4.5 kg is ordered for ampicillin 400 mg/kg/day divided
every 6 hours
What dose should be administered every 6 hours?
400 mg/kg/day divided by 4 times per day = 100 mg/kg/dose
100 mg/kg/dose X 4.5 kg = 450 mg per dose
Ampicillin is available in a concentration of 250 mg/mL in your hospital. How
many mLs should be drawn up for each dose?
450 mg X 1 mL/250 mg = 1.8 mL
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Definitions
IV Infusion- administration of a drug directly into the vein over a period of
time
Rate of Flow- volume of drug solution to be delivered per a unit of time, can
be expressed as mL/min, drops/min, or amount of drug(mcg, mg, g) /unit of
time
Reminder!
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Useful Conversions
60sec = 1min
60min = 1 hour
1000mcg = 1mg
1000mg = 1g
1000mL = 1L
Reminder!
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Drip Rate Calculations
Used for medications given via IV route
Expressed in dose per hour (mg/hour or mg/min) or weight based dose per
hour (mg/kg/hr or mg/kg/min)
Need to determine:
How much volume to be administered
How long it will take to deliver a volume at a certain rate
When the next bag needs to be prepared
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Drip Rate Calculations: Example #1
A 5 kg baby is receiving a fentanyl drip at 4 mcg/kg/hr. Fentanyl is available in
100 mL bag, with a concentration of 15 mcg/mL.
What rate in mL/hr should be ordered?
How long will the 15 mcg/mL drip last for this patient?
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Drip Rate Calculations: Example #1
What rate in mL/hr should be ordered?
5 ππ Γ4 πππ
ππ= 20 πππ πππ βππ’π
20 πππ Γ1 ππΏ
15 πππ= 1.33 ππΏ πππ βππ’π
How long will the 15 mcg/mL drip last for this patient?
Drip is running at 1.33 mL per hour, and bag is 100 mL total volume
100 ππΏ Γ· 1.33 ππΏ πππ βππ’π = ~ 75 βππ’ππ
Or1 βπ
1.33 ππΏΓ 100 ππΏ = ~75 βππ’ππ
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Drip Rate Calculations: Example #2
A 55 year old patient with septic shock in on Norepinephrine at 0.2
mcg/kg/minute. The patient weighs 95 kg and the drip concentration is 8 mg
in 250 mL.
What rate in mL/hour should be ordered?
How many hours will this drip last for this patient?
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Drip Rate Calculations: Example #2
What rate in mL/hr should be ordered?
95 ππ Γ0.2 πππ/ππ
πππΓ
60 πππ
1 βπ= 1140 πππ πππ βππ’π
1140πππ
βπΓ
1 ππ
1000 πππ= 1.14 ππ πππ βππ’π
1.14ππ
βπΓ
250 ππΏ
8 ππ= 35.6 ππΏ πππ βππ’π
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Drip Rate Calculations: Example #2
How long will this drip last for this patient?
Drip running at 35.6 mL per hour, and bag is 250 mL total volume
250 ππΏ Γ· 35.6ππΏ
βππ’π= ~ 7 βππ’ππ
Or
1 βπ
35.6 ππΏΓ 250 ππΏ = ~ 7 βππ’ππ
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BSA based dosing
Often used for chemotherapy and oncology medications
Most accurate form of dosing calculation
If weight based and BSA are both available, use BSA based dose
BSA equation based on height and weight
BSA (m2) = (βπππβπ‘ π₯ π€πππβπ‘) Γ· 3600
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BSA Based Dosing: Example
You receive a prescription for dexamethasone 10mg/ m2/ day x 1 week. The
patient is 5 ft 2 in tall and weighs 108 lbs. How many 5 mg tablets should be
dispensed to the patient for the entire treatment course?
Convert height to cm and weight to kg
Use BSA equation to determine total dose in mg for 1 week
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BSA Based Dosing: Example
5 ft 2 inches: 5 ππ‘ Γ12 πππβππ
1 ππππ‘= 60 πππβππ + 2 πππβππ = 62 inches
62 πππβππ Γ2.54 ππ
1 πππβ= 157.48 ππ
108 lbs Γ1 ππ
2.2 ππ= 49.09 kg
BSA equation:
157.8ππ Γ 49.09ππ Γ· 3600 = 1.47 m2
Dose: 10 mg/m2 X 1.47 m2 = 14.7 mg/day
14.7 ππ Γ1 π‘πππππ‘
5 ππ= 3 π‘πππ πππ πππ¦ π 7 πππ¦π = 21 π‘πππππ‘π
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Pediatric Dilutions
Commercially available products may be too concentrated
Need to give a small dose
Cannot measure accurately
Syringe accurate to half of a marking
Ex. if marked to 0.1 mL, accurate to measure in 0.05 mL increments
How will we measure 0.037 mL?
Institutions may have standard dilutions
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Pediatric Dilutions
Gentamicin available in 40 mg/mL vial for injection butβ¦
We need Gentamicin 10 mg/mL concentration
How do we make this dilution?
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Pediatric Diltuions
Use 40 mg/mL
Withdraw 10 mL =
10 ππΏ Γ40ππ
1ππΏ= 400 ππ
Add NS 30 mL for a total of 40 mL
Final concentration is 400 mg/ 40 mL = 10 mg/mL
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Pediatric Dilutions
Insulin aspart is available in 100 units/mL vials
Dose for a 1 year old may be 0.5 units
0.5 units X 1 mL/100 units = 0.005 mL
Not Measurable!
Diluted Insulin aspart
10 units/mL
50 units/mL
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Pediatric Dilutions
Need Insulin aspart 10 units/mL concentration
Use 100 units/mL
Withdraw 1 mL =
1 ππΏ Γ100 π’πππ‘π
1 ππΏ= 100 π’πππ‘π
Add 9 mL of diluent
Final concentration = 100 units/10 mL = 10 units/mL
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Questions?