Pharmacy Calculations – Deciphering Word Problems
Focus on what you’re solving for; ignore the extra details.
What is the dose? (Chapter 13)
250mg
Dose drug amount
=
1 tsp
Amount to make
(volume)
Drug Strength
Example: If a prescription reads: Cefaclor 250 mg/5ml, dispense 150 ml, 375 mg b.i.d. x 10d, what is the
dose in teaspoonsful? (Problem #41, page 100)
 nown values:
250mg
375mg
=
o Drug strength (250 mg/5ml)
1 tsp
X tsp
o Dose drug amount (375 mg)
250x =
375
X
=
1.5 tsp
 Solve for Amount to make (volume)
 Answer: 1.5 tsp per dose
Looking for a shortcut to cross-multiplying? Rather than write out the full equation and each step, try
using this method with you calculator:
250mg
375mg
=
1 tsp
x
Step 1: Multiply the two numbers that are diagonal from each other
(just think-when two get together, they multiply)
Step 2: Divide the answer from step 1 by the number that is diagonal to the variable you’re
solving for (just think-the lonely one will try to split up or divide the couple). X = Step 2’s answer
How much of a drug do you need? (Chapter 16) These questions may require you to do an additional
step if they want the answer in the form of how many tablets/capsules of a particular strength (how many
tablets of the drug do you need to make...?).
3 gm
X
=
500ml
total amount to make
Example: A prescription is written for allopurinol liquid 20 mg/ml in Ora-Plus:Ora-Sweet 1:1 (label with a
shelf life of 60 days). How many tablets of allopurinol 100 mg are needed to prepare 150 ml? (Problem #4,
page 121)
 Known values:
20mg
Xmg
=
o Drug strength (20mg/ml)
1 ml
150ml
o Total amount to make 150ml
X
=
3000mg *STEP 1
If
each
tablet
is
100mg,
how
=
3000/100
o Strength of available drug 100mg
many tablets are needed?
or 30 tablets *STEP 2
 Step 1: Solve for Dose Strength
 Step 2: Solve for # of tablets needed of available drug.
If the drug strength is given as a %:
*Percent roughly means “out of each one hundred” so any percentage can be depicted as a fraction where
the percentage is the numerator (number on top) in the unit of grams and “100” is the denominator
(number on bottom) in the unit of ml or grams. That percentage is the drug’s strength.
%
strength
=
100
amount
Example: A prescription is written for Dilantin 5% in zinc oxide qs 120 g. How many Dilantin 50 mg tablets
are needed to prepare this compound? (Problem #5, page 121)
 Known values:
5g
Xmg
o Drug strength (5% or 5g/100ml)
=
100 g
120g
o Total amount to make 120 g
X
=
6g *STEP 1
If each tablet is 50mg, how
=
6g/50mg or 6000mg/50mg
o Strength of available drug 50mg
many tablets are needed?
or 120 tablets *STEP 2
 Step 1: Solve for total strength
 Step 2: Solve for # of tablets needed of available drug
How many days supply is this? (Chapter 17)
Rx Max
Days supply =
Daily dose
Example: How many days supply is the following prescription?: Augmentin 500 mg #42 one t.i.d. (Problem
#2, page 129)
 Known values:
o Rx Max (42 tab)
o Daily dose (3 tab/day)
42 tab
=
o Each tablet is 500 mg (irrelevant to this problem)
3 tab/day
=
14 days
 Solve for days supply
 Answer: 14 days
What is the amount insurance plans will allow per fill? (Chapter 18)
These questions require multiple step calculations.
 Step 1: Calculate the Rx Max
 Step 2: Calculate the amount in an insurance period (usually 34 days), This is the initial fill quantity (if
it’s less than the Rx Max)
 Step 3: Calculate how many refills/partials would be allowed to meet Rx Max
 Rules of Thumb to Remember:
o Do not split up boxes, bottles or vials
o In the case of bottles, insurance will usually only allow 1 bottle to be dispensed at a time even if
it provides less than the amount in an insurance period
Example: Dicyclomine 20 mg #200, 20 mg p.o. qid, 1 refill (Problem #14, page 141)
 Known values:
o Amount to dispense=200 tablets
o Number of fills=2 (remember to count initial fill as first fill, so a Rx that states 1 refill=2 fills)
o Daily dose=4 tablets, 20mgx4= 80mg
o Dose=20mg
Step 1: Calculate the Rx Max
Rx Max = #(amount to dispense) x # of fills
=200 x2 =400 max
Step 2: Calculate the amount in an insurance
period (34 days in most cases)
Step 3: Calculate how many refills/partials
would be allowed to add up to Rx Max
Amount in an insurance period=34xdaily dose
=20mg=1 tab, qid=4 times/day, 1x4=4 tab/day
= 34x4=136 tabs, Initial fill quantity
Rx Max (Calc found in Step 1)
=
Amount in insurance period (Calc found in Step 2)
400 tabs
= 2.94
136 tabs
So, 2 full qty fills plus a partial are required to meet Rx Max
In other words 1 initial fill of 136, 1 refill of 136 and a partial fill
=
To determine partial fill quantity:
Rx Max – (Initial fill qty x 2) (2 is the whole number from above calc)
o 400-(136x2)=
o 400-272=
o 128=Partial Fill Amount
Double check your work by adding up quantities in initial fill, all refills and
partial fills. These should equal the Rx Max.
o 136 (initial fill) + 136 (1 refill) + 128 (partial refill)=400
Compounding Fees (Chapter 20)
Formula to calculate cost to compound:
60 min
Min it took to compound
=
$ hourly salary
Cost to compound $
Add cost to compound to cost of materials
(Ratio & Proportions) How many ml should be dispensed?, What is the dose that the patient received?
(Chapter 27)
In a simple ratio & proportion problem, there are 4 elements. Usually 3 are known & you solve for the 4 th.
mg
Amount of drug
=
ml
Total amount to make
Drug strength = Specific Dose
Example: How many ml of aminophyllin solution (500mg/20ml) is needed to prepare 350 mg aminophyllin
in 100 ml of D5W? (Problem #17, page 214)
500mg
350 mg
 Known values:
=
20ml
X ml
o Drug strength (500mg/20ml)
500X
=
7,000
o Amount of drug (350mg)
X
=
14 ml
o Diluent (100ml of D5W)-irrelevant to this problem
 Solve for total amount to make
 Answer: 14 ml
Example: A patient is given 10.8 ml of phenytoin as a loading dose. Phenytoin is available as 50 mg per ml
in 2 ml and 5 ml vials. What is the dose in mg that the patient received? (Problem #25, page 215)
 Known values:
50mg
X mg
=
o Drug strength (50mg/1ml)
1ml
10.8 ml
X
=
540 mg
o Total amount to make (10.8ml)
o Available vial sizes 2ml & 5 ml-irrelevant for this problem
 Solve for Amount of drug
 Answer: 540 mg
Powdered Drug Preparations (Chapter 28)
diluent volume + powdered volume = total volume
Sometimes a 2 step process:
 provided 2 out of 3 of the volumes above, solve for third volume
 What’s the final concentration of the drug?
 Problem may provide how much you’re putting that dose into-irrelevant to the problem at handfirst you have to determine the dose.
Example: You add 10 ml of sterile water for injection to 1 g of a drug that has a powder volume of 0.8ml.
What is the concentration of the drug in mg/ml in the final solution? (Problem #7, page 224)
 Known values:
o Diluent volume (10 ml)
o Powder volume (0.8ml)
o Amount of drug (1 g)
 Solve for concentration of final solution
Step 1: Calculate total volume
Step 2: Calculate concentration of final
solution
Diluent volume + powder volume = total volume
10 ml + 0.8 ml = 10.8 ml
Concentration is g/1ml or ml/1ml or g/1g
Amount of drug
1g
1,000mg
=
=
Total volume
10.8 ml
10.8ml
=
92.6 mg
1 ml
Answer: 92.6 mg/ml
Example: A 1.5 g vial of antibiotic has a powder volume of 1.4ml. You need a concentration of 125 mg/ml.
How many ml of sterile water for injection will you need to add to obtain this concentration? (Problem
#17, page 225)
Step 1: Calculate total volume based on
concentration
Step 2: Calculate diluent volume based on
powder volume & total volume
125 mg
1.5g or 1500mg
=
1 ml
X (total volume)
12 ml
= x
Diluent volume + powder volume = total volume
X + 1.4ml=12ml
X=12ml-1.4ml
X=10.6ml
Example: 5 g of the medication (powder volume=0.7ml) is reconstituted with 9.3 ml of sterile water for
injection. Then 3 ml of an antibiotic is added to a 50 ml IVPB. How many g of the medication was added to
the IVPB? (Problem #43, page 230-problem mis-worded in book)
Step 1: Calculate total volume
Step 2: Calculate the amount of drug that
was in the 3ml that was added to the IVPB
Diluent volume + powder volume = total volume
9.3 ml + 0.7ml = 10ml
5g
x
=
10 ml
3 ml
1.5g
= X
Drug Strength in Percentages (Chapter 29)
% strength is always
grams
100 ml
Example: What percent strength solution would result if you mixed 3 g of NaCl in enough water to make 25
ml? (Problem #2, page 235)
3g
25 ml
12%
=
=
X%
100 ml
X
Example: How many grams of glucose are contained in 1,500ml of a 10% glucose solution? (Problem #10,
page 236)
10g
100 ml
150 g
X grams
1,500 ml
X
=
=
Ratio Solutions (Chapter 30)
First number of a ratio is typically 1 (sometimes a 2). Ratios are always in units:
g:ml
ml:ml
g:g
To convert a ratio to a fraction:
 Place first number in numerator
 Place second number in denominator
Ex: 1:20 becomes 1/20
To convert a ratio to a percent:
First number
Second number

=
X%
100ml
Solve for X
Ex: 1:20
1
20
5%
=
=
X%
100ml
x
To convert a percent to a ratio:
 Place the percentage in the first number field and 100 in the second number field
 Divide both sides of the ratio by the first number (this will make the first number a 1)
Ex: 0.08% becomes 0.08g:100ml which becomes 1:1,250
0.08g
0.08
1g
:
:
100ml
0.08
1,250
Example: You need to prepare 750 ml of a 1:500 w/v potassium permanganate solution. How many g are
needed? (Problem #4, page 245)
1g
500ml
1.5g
Xg
750ml
x
=
=
Example: Adrenalin injection is also available as a 1:100,000 w/v strength. Express this concentration in
mcg/ml. (Problem #22, page 247)
1g
100,000ml
=
1000mg
100,000ml
=
1mg
100ml
=
1,000mcg
100ml
=
10mcg
ml
Dosage Calculations Based on Body Weight (Chapter 31)
1 kg = 2.2 lb
Example: A patient weighs 44 pounds and is receiving ampicillin at a rate of 100 mg/kg/day. What is the
total daily dose in grams?
Step 1: What is the patient’s weight in kg?
44 lbs
2.2 kg/lb
=
20 kg
Step 2: Calculate the dose based on the rate & patient’s weight.
100 mg
Kg/day
x
20 kg
=
2,000 mg
day
=
2g
Dosage Based on Body Surface Area (Chapter 32)
A Nomogram chart is used to calculate body surface area (BSA) as a function of height and weight. Either
the BSA will be provided in the problem, or the weight & height are provided along with a Nomogram and
you determine the BSA on the Nomogram.
BSA unit of measure is m2. This unit of measure is cancelled out thru the math.
Example: A patient with a BSA of 2.1 m2 is to receive 7.5 mg/ m2/week of methotrexate. The MTX is
available as 25mg/ml. How many ml are needed for the weekly dose? (Problem #45, page 274)
 Known values:
o Patient’s BSA (2.1 m2)
o Weekly dose amount (7.5 mg/ m2)
o Available Drug strength (25 mg/ml)
Step 1: Calculate total drug needed based on
BSA.
Step 2: Calculate how many ml will deliver
that total drug amount based on available
drug strength
7.5 mg
1 m2
15.75 mg
25 mg
1 ml
0.63 ml
=
=
=
=
X mg
2.1m2
X
15.75 mg
X
X
Infusion Rates/Drip Rates (Chapter 33)
There are a couple ways to complete these calculations.
Method A: Multiply a series of fractions, placing like-units diagonal from each other so they cancel out &
you’re left with the desired units
Method B: Use a series of equations, using ratio & proportion to cross multiply solving for the unknown as
we have been solving most problems.
Example: Calculate the infusion rate in ml/hr for a drip, concentration 5g/500ml. The rate is 25
mcg/kg/min. The patient weighs 112 kg. (Problem #13, page 281)
 Known values:
o Drug strength (5g/500ml)
o Infusion rate (25 mcg/kg/min)
o Patient’s weight (112kg)
 Solve for Infusion rate in ml/hr
o Additional known values (60 min/1 hr, 1,000 mg/mcg, )
Method A:
25mcg
Kg/min
x
112kg
1
=
2,800mcg
1 min
,
2,800 mcg
1 min
x
1 mg
1,000 mcg
=
2.8 mg
1 min
,
Then,
2.8 mg
1 min
x
60 min
1 hr
=
168 mg
1 hr
,
168 mg
1 hr
500 ml
5,000 mg
(which is 5 g)
x
=
16.8 ml
1 hr
Method B:
Step 1: Solve for the rate based on patient’s
weight
25 mcg
Kg/min
Step 2: Convert 2,800 mcg to g (since the
drug strength is in grams)
2,800 mcg = 2.8 mg = 0.0028 g
Step 3: Calculate the rate in grams per hour
(1 hr = 60 min)
Step 4: Calculate how many ml will deliver
0.168 g of the drug based on the strength.
x
112 kg
1
=
2,800 mcg
1 min
0.0028 g
X
=
1 min
60 min
0.168 g
= X
So, the rate is 0.168 g/60 min or 0.168g/1 hr
5g
0.168g
=
500 ml
X
16.8 ml
= X
Dilutions (Chapter 34)
When you dilute a drug, that means the amount of the drug in the solution remains constant, but the
volume of that solution increases. Therefore, there’s an inverse proportion between the volume and the
% strength of a drug within a solution.
What’s the final percentage strength of a drug when it’s diluted with an amount of diluent?