A Technician’s Guide to

Pharmaceutical Calculations: Dosing

and Dispensing Math and

Compounding CalculationsAllison Lardieri, PharmD, BCPPS

University of Maryland School of Pharmacy

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.

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

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.

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

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

Ratio and Proportion

500𝑚𝑔

1 𝑡𝑎𝑏or

1 𝑡𝑎𝑏

500𝑚𝑔

1 𝑘𝑔 𝑝𝑟𝑒𝑑𝑛𝑖𝑠𝑜𝑛𝑒

$5or

$5

1 𝑘𝑔 𝑝𝑟𝑒𝑑𝑛𝑖𝑠𝑜𝑛𝑒

Ratio and Proportion

Example 1:

If one teaspoonful contains 15 mg of prednisolone, how

many mg are in 4 teaspoonfuls?

Ratio and Proportion

15 𝑚𝑔

5 𝑚𝐿=

𝑥 𝑚𝑔

20 𝑚𝐿

15 𝑚𝑔 × 20 𝑚𝐿 = 𝑥 𝑚𝑔 × 5 𝑚𝐿

15𝑚𝑔 ×20𝑚𝐿

5𝑚𝐿= 𝑥 𝑚𝑔 = 60 𝑚𝑔

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?

Ratio and Propotion

3 𝑏𝑎𝑔𝑠 ×12 𝑚𝑚𝑜𝑙𝑠

𝑏𝑎𝑔×

1 𝑚𝐿

3 𝑚𝑚𝑜𝑙×

1 𝑣𝑖𝑎𝑙

5 𝑚𝐿= 2.4 𝑣𝑖𝑎𝑙𝑠

So, will need to get 3 vials!

Community Pharmacy Calculations

Days supply and quantity

Insulin dosing

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

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

Joanna’s Pharmacy1123 Wildcat Lane

Baltimore, Maryland 21201

410-555-8888

20 N Pine St Baltimore, MD 21201

Days Supply and Quantity

How many tablets should be dispensed for this Rx?

1 cap TID = 3 caps per day

3 𝑐𝑎𝑝𝑠

1 𝑑𝑎𝑦× 14 𝑑𝑎𝑦𝑠 = 42 𝑐𝑎𝑝𝑠 𝑓𝑜𝑟 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑢𝑟𝑠𝑒

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

Joanna’s Pharmacy1123 Wildcat Lane

Baltimore, Maryland 21201

410-555-8888

20 N Pine St Baltimore, MD 21201

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

Days Supply and Quantity

2 puffs QID = 8 puffs per day

1 𝑑𝑎𝑦

8 𝑝𝑢𝑓𝑓𝑠=

𝑥 𝑑𝑎𝑦𝑠

200 𝑝𝑢𝑓𝑓𝑠

𝑥 𝑑𝑎𝑦𝑠 = 200 𝑝𝑢𝑓𝑓𝑠 ÷ 8 𝑝𝑢𝑓𝑓𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 = 25 𝑑𝑎𝑦𝑠

OR

200 puffs total / 8 puffs per day = 25 days

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

Joanna’s Pharmacy1123 Wildcat Lane

Baltimore, Maryland 21201

410-555-8888

20 N Pine St Baltimore, MD 21201

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

Days Supply and Quantity

12 𝑢𝑛𝑖𝑡𝑠

1 𝑑𝑎𝑦=

1000 𝑢𝑛𝑖𝑡𝑠

𝑥 𝑑𝑎𝑦𝑠

𝑥 = 83.33 𝑑𝑎𝑦𝑠

Lantus vial only good for 28 days, so will default to 28 days for days supply

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

Joanna’s Pharmacy1123 Wildcat Lane

Baltimore, Maryland 21201

410-555-8888

20 N Pine St Baltimore, MD 21201

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 𝑝𝑒𝑛𝑠 ×3 𝑚𝐿

1 𝑝𝑒𝑛×

100 𝑢𝑛𝑖𝑡𝑠

1 𝑚𝐿= 1500 𝑢𝑛𝑖𝑡𝑠

Days Supply and Quantity

What is the days supply for the prescription?

1500 units total ÷ 50 𝑢𝑛𝑖𝑡𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 = 30 𝑑𝑎𝑦𝑠

Or

1500 𝑢𝑛𝑖𝑡𝑠 ×1 𝑑𝑎𝑦

50 𝑢𝑛𝑖𝑡𝑠= 30 𝑑𝑎𝑦𝑠

Hospital Pharmacy Calculation

Weight based dosing

Drip rate calculations

BSA based dosing

Dilutions

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)

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?

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

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

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

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.

• How many mLs per dose should be drawn up?

• How many mLs per day will this child need?

• For a 10 day supply, how many mLs should be dispensed?

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

Your Turn!

A 4 year old boy who is 16 kg is ordered cefazolin 25 mg/kg IV Q8 hours

• What dose should administered every 6 hours?

25 mg/kg X 16 kg = 400 mg

• What is the total dose per day?

400 mg X 3 times per day = 1200 mg

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

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

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!

Useful Conversions

60sec = 1min

60min = 1 hour

1000mcg = 1mg

1000mg = 1g

1000mL = 1L

Reminder!

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

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?

Drip Rate Calculations: Example #1

What rate in mL/hr should be ordered?

5 𝑘𝑔 ×4 𝑚𝑐𝑔

𝑘𝑔= 20 𝑚𝑐𝑔 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

20 𝑚𝑐𝑔 ×1 𝑚𝐿

15 𝑚𝑐𝑔= 1.33 𝑚𝐿 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

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 𝑚𝐿 ÷ 1.33 𝑚𝐿 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 = ~ 75 ℎ𝑜𝑢𝑟𝑠

Or1 ℎ𝑟

1.33 𝑚𝐿× 100 𝑚𝐿 = ~75 ℎ𝑜𝑢𝑟𝑠

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?

Drip Rate Calculations: Example #2

What rate in mL/hr should be ordered?

95 𝑘𝑔 ×0.2 𝑚𝑐𝑔/𝑘𝑔

𝑚𝑖𝑛×

60 𝑚𝑖𝑛

1 ℎ𝑟= 1140 𝑚𝑐𝑔 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

1140𝑚𝑐𝑔

ℎ𝑟×

1 𝑚𝑔

1000 𝑚𝑐𝑔= 1.14 𝑚𝑔 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

1.14𝑚𝑔

ℎ𝑟×

250 𝑚𝐿

8 𝑚𝑔= 35.6 𝑚𝐿 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

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 𝑚𝐿 ÷ 35.6𝑚𝐿

ℎ𝑜𝑢𝑟= ~ 7 ℎ𝑜𝑢𝑟𝑠

Or

1 ℎ𝑟

35.6 𝑚𝐿× 250 𝑚𝐿 = ~ 7 ℎ𝑜𝑢𝑟𝑠

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) = (ℎ𝑒𝑖𝑔ℎ𝑡 𝑥 𝑤𝑒𝑖𝑔ℎ𝑡) ÷ 3600

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

BSA Based Dosing: Example

5 ft 2 inches: 5 𝑓𝑡 ×12 𝑖𝑛𝑐ℎ𝑒𝑠

1 𝑓𝑜𝑜𝑡= 60 𝑖𝑛𝑐ℎ𝑒𝑠 + 2 𝑖𝑛𝑐ℎ𝑒𝑠 = 62 inches

62 𝑖𝑛𝑐ℎ𝑒𝑠 ×2.54 𝑐𝑚

1 𝑖𝑛𝑐ℎ= 157.48 𝑐𝑚

108 lbs ×1 𝑘𝑔

2.2 𝑙𝑏= 49.09 kg

BSA equation:

157.8𝑐𝑚 × 49.09𝑘𝑔 ÷ 3600 = 1.47 m2

Dose: 10 mg/m2 X 1.47 m2 = 14.7 mg/day

14.7 𝑚𝑔 ×1 𝑡𝑎𝑏𝑙𝑒𝑡

5 𝑚𝑔= 3 𝑡𝑎𝑏𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 𝑋 7 𝑑𝑎𝑦𝑠 = 21 𝑡𝑎𝑏𝑙𝑒𝑡𝑠

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

Pediatric Dilutions

Gentamicin available in 40 mg/mL vial for injection but…

We need Gentamicin 10 mg/mL concentration

How do we make this dilution?

Pediatric Diltuions

Use 40 mg/mL

Withdraw 10 mL =

10 𝑚𝐿 ×40𝑚𝑔

1𝑚𝐿= 400 𝑚𝑔

Add NS 30 mL for a total of 40 mL

Final concentration is 400 mg/ 40 mL = 10 mg/mL

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

Pediatric Dilutions

Need Insulin aspart 10 units/mL concentration

Use 100 units/mL

Withdraw 1 mL =

1 𝑚𝐿 ×100 𝑢𝑛𝑖𝑡𝑠

1 𝑚𝐿= 100 𝑢𝑛𝑖𝑡𝑠

Add 9 mL of diluent

Final concentration = 100 units/10 mL = 10 units/mL

Questions?