Conversions and Calculations
Apothecary System
Avoirdupois system
Metric system
Common Household Measurements
Start with what you know…
Household
measurements: Teaspoonful, Tablespoon, cup, etc.
Most doctors will not write in teaspoonful, but use the other systems
Do not assume that people understand what a millimeter or an ounce is.
You must make instructions easy enough for a child to understand.
Used throughout pharmacy because of its accuracy.
Units include milliliters (ml), cubic centimeters (cc), and liters (L) for volume.
Kilograms (kg), grams (g), milligrams (mg) and micrograms (mcg) for weight
Millimeters (mm) and meters (m) for distance. Millimeters are used in body surface area calculations and reserves for physicians and pharmacist.
Remember : Volume refers to liquids
Weight refers to dry ingredients
Length refers to distance
The most common household measurement is the teaspoon.
Household Measurement (volume) 
Metric Volume

Household

1 teaspoon 
5ml or cc 
1 teaspoon 
1 tablespoonful 
15ml or cc 
3 teaspoons 
1 cup 
240 ml or cc 
8 ounces 
1 pint 
480 ml or cc 
2 cups 
1 quart 
960 ml or cc 
4 cups 
1 gallon 
3840ml or cc or 3.84 L 
16 cups 
Originated in
The units used are grains (gr.)
Dry Weight 
Fluid Weight 
1 grain= 60mg 
1
dram= 60 minims 
15 grains= 1 gram 
8
drams= 480 minims 
20 grains= 1 scruple 
3
scruples= 1 dram 
1 dram= 3 scruples 

1 ounce= 8 drams 
= dram (apothecary) 
1 ounce= 24 scruples 
= ounce (apothecary) 
1 ounce= 480 grains 

1 ounce= 31.1 grams 
= scruple 
1 pound= 16 ounces 
= minims 
1 pound= 96 drams 

1 pound= 288 scruples 

1 pound= 5760 grains 

1 pound= 454 grams 

Conversion Table:
Apothecary/Metric/ Household
Apothecary Volume 
Apothecary Weight 
Metric Volume 
Metric Weight 
Common Household 
1 ounce 
1 ounce 
30 ml 
30 g 
2 tbsp 
4 drams 
4 drams 
15 ml 
15g 
1 tbsp 
2 drams 
2 drams 
7.5 ml 
7.5 g 
½ tbsp 
1 dram 
60 grains 
4 ml 
4 g 
1 tsp 
½ dram 
30 grains 
2 ml 
2 g 
½ tsp 
When using the apothecary system, the measurement is placed before the amount; for example, 1 grain is written
as gr 1. ½ grain is written as gr ss. (ss= ½)
Avoirdupois 
Metric Equivalent 
Dry
Weights 

1 pound 
454
g 
1 ounce 
30 g 
1 grain 
64.8
mg 


Liquids 

1 fl. Ounce 
30
ml 
1 pint 
473
ml 
1 gallon 
3785
ml 
Because the metric
system is the most common system used in pharmacies, it is the measurement you
use when preparing a compounded drug.
Metric System Steps
When converting the metric system
from one unit to another you need to move the decimal either to the left or to
the right. All changes involve either dividing or multiplying by 10s. The most
common units in the metric system are kg,g,mg, and
mcg. Each unit is multiplied by 1000. example 5000mg = 5
grams (5000/1000 =5 ).
[mgs/1000= grams]
5000.→ 5.000 therefore you need to move 3 decimal places to the left.
Another way to remember this is the step approach. You should commit to memory this metric stairway in order to do some conversion problems in the metric system. (see chart)
Rarely seen with prescription, but one should have a basic understanding of fractions if ever the need arises.
Twostep process to convert simple fractions into percentages.
6/9 converted into a percentage requires dividing 6 by 9 and multiply this by 100 to get percentage. 6/9 =0.666 x 100 = 66.6% or rounded up will be 67%
To convert decimals into percentages just multiply the decimal by 100.
1.5 = 150%
Try these 1/5= __________%
10/25= ___________%
0.25= ____________%
About 90% of the problems encountered in pharmacy will be ratio/proportion equations.
3 rules to remember
HAVE = NEED
Question 1 : Prepare 240mg of a drug using the pharmacy stock concentration of 80mg/4ml
Keep
the same units across from each other
mg with mg & ml with ml
80
mg = 240 mg
4 ml X ml
FIND THE UNKNOWN “X” BY DIVIDING THE NUMBER NEXT TO IT ON BOTH SIDES OF THE EQUAL SIGN.
80 X = 960
80
80
80 X = 960
80 80
·
Q2: You need
to prepare 1 pint of 40 mcg medicated lotion. How many
milliliters of the stock solution 5mcg/ml will it take to prepare the final
product?
·
Q3: You
receive an order for clindamycin 450mg q12h (every 12 hours). You have on hand
clindamycin 150mg/ml. What quantity of clindamycin is needed
per dose?
·
Q4: You
receive an order for 0.5mg of alprazolam (Xanax) Directions: 1 to 2 tablets at
bedtime (qhs) for 7 days. You only have 1 mg tablets in stock. How many tablets
are needed to fill this order?
·
You receive
an order for erythromycin 150mg every 6 hours per day for 10 days. You have on
hand erythromycin 200mg/5ml suspension 200ml size.
1. How many milliliters of suspension will
be given per dose?
2. How many milliliters of suspension will
be given per day?
3. How many milliliters of suspension will
be given over the course of treatment?
4. How much suspension will be
discarded, if any?
·
You need to
fill a prescription for cimetidine 600mg tablets 3 times a day for 30 days. You have 400mg tablets.
How many 400mg tablets will you need to fill this
order?
You receive an order for carbamazepine suspension. You have in stock 1 bottle of 450ml Tegretol (carbamazepine) 100mg/5ml .
The order is for Carbamazepine 250mg tid (3 times a day) po (by mouth)
1. How many milliliters are needed per dose?
2. How many milliliters are needed per day?
3. How many doses can be taken from the 450ml bottle?
It is necessary to convert pounds to kg since all manufacturers provide proper dosing regimens based on kilograms.
16
ounces= 1 lb
2.2
pounds= 1 kg
To determine how many kilograms there are in 1 lb, divide.
To determine how many pounds there are in 1 kg, multiply.
Converting weight and determining pediatric dosage
The pharmacy receives an order for a baby girl weighing 7 pounds.
The order calls for 20mg/kg/dose.
Convert weight: 2.2lb = 7lb
1kg x
Cross multiply and solve for x;
7lb = 3.18kg
2.2lb
Now multiple the weight in kilograms by the recommended dosage.
20mg
= x
1 kg
3.18kg
20mg x
3.18kg = x = 63.6mg/dose
1 kg
For the same example we now have
an order for 60mg/kg/day to be given
every 8 hours
Therefore
60mg
= x
1 kg 3.18kg
x=
60mg x 3.18kg
1
kg
= 63.6 mg / dose
Hospital pharmacy technicians deliver a 24 hour supply of intravenous (IV) solutions to the nursing station daily.
Most IV piggybacks are smaller and can be given over a shorter period of time (3060 minutes)
Large volume parenterals (LVP) need to be given at a slow rate because veins can only handle a small amount of volume.
You should be able to calculate the volume needed to last over a certain period of time, or he or she may need to calculate how much longer a currently hanging IV solution will last. Drip rates are an essential way to determine this.
Drop factor is given on each set of tubing. 10gtt/ml or
15gtt/ml
Intravenous (IV) drip system
Drops are written as gtt. Amounts differ between dropper sizes. There are about 60 drops in 5 ml (cc). Also drops can be intended for drip rates
Basic conversions are as follow:
Time: 1 hour= 60 minutes, 24 hours = 1 day
* Volume: ml, gtt
* This will be determined by the size of the tubing used to deliver the medication. We will be using a common drop factor (DF) to determine the volume.
You receive an order for a 2L bag to be given over 24 hours. Your tubing says it delivers 15gtt/ml. What are the drops per minute?
Steps involved in
determining drops per minute:
2000 ml per 24 hours
2000 ml = x ml x= 83.3ml therefore 83.3ml/hr
24 hours 1 hour
3.
What will be the milliliters per minute?
83.3 ml =
x x= 1.38ml therefore 1.38ml/min
60 min 1 min
4. What will be the
drops per minute?
15gtt = x gtt
ml 1.38ml x=
20.7 gtt therefore 20.7
gtt/min
Order: 1500
ml of 20mEq KCL for 12 hours. The tubing size= 20 gtt/ml
How many
drops per minute will be delivered?
Calculations:
Do your calculations here:
Allegation is used when you need to prepare (compound) percent strength that you do not have in stock. To make this strength, you need to use two other strengths to attain the correct one.
Example A doctor orders a 20% KCl
solution but you only have 10% and 50% on hand.
Calculate the amount of each solution needed to attain a 20% solution.
This can be done
using any two strengths as long as only one is less than
the final solution.
Water is another
element you might use as one of these solutions.
(To dilute
the higher strength.)
Problem:
You have in stock a 70% solution of
dextrose (glucose) and a 20% solution of dextrose. How much of each do you need
in order to create 1 L (1000ml) of a 40% solution.
Basic rules
for alligation :
Draw a tictactoe board
PLACE YOUR DESIRED STRENGTH IN
THE
MIDDLE SQUARE
40
PUT YOUR
HIGH STRENGTH IN THE TOP 70
40
70
PUT YOUR
LOWER STRENGTH SOLUTION
ON THE BOTTOM LEFT SQUARE.
If you are using water, place
a zero in this square 40
20
Take the difference between
top left square 70 20 4020 = 20
And middle square number &
place the new
number in the bottom right square.
Do the
same with the bottom left
number and place 40
this result in the top right
square.
20 30
7040 = 30
70 20
Create
a fraction by adding the two new
20
figures (top & bottom
both). Place the top 40 20+30
number
over the denominator and do the
same for the bottom right number. 30
20 30 20+30
70 20 20X1000ml=400
50
Divide
out each fraction and then multiply
by the total volume you need. 40
20 30
30X1000ml=600
50
70 20 400ml
Check
your answer by adding the two parts
They
should equal the total volume. 40
20 30 600ml
1000ml
Answer: 400ml of the 70%
solution, and 600ml of the 20% solution will prepare 1
liter (1000ml) solution of 40%
ROMAN NUMERALS
The number system
commonly used in the
Roman Numerals
M=1000 
D=500 
C=100 
L=50 
X=10 
V=5 
I=1 
(There's no
zero). 
Obviously, Romans did not have special symbols for numbers, so they used letters. They did not have lowercase letters, either, so they used capital letters. You will have to, too.
Now, here are the three rules for making numbers with Roman numerals:
II=1+1=2
XX=10+10=20
XXX=10+10+10=30
XV=10+5=15
VIII=5+3=8
IX=101=9
CM=1000100=900
That's it! Try to read these numbers:
CMV XIV XC C VIII
LXX CIV XXXIX XL CCXXII
XLI DC MM MMIV MMMLV
Also known
as military time. Used exclusively in hospitals.
The system is based on 100.
Below is a list showing how the times match up.
0100
0200
0300
0400
0500
0600
0700
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400 or 0000
FILL IN THE BLANKS:
FROM 0800 TO 1500 HOURS IS _______________HOURS
A DOSE GIVEN AT 0600, 1400 AND 2200 HOURS IS
_______________HOURS APART
A DOSE GIVEN AT 0005,1430, AND 2045
WOULD BE GIVEN AT _________,____________,AND ____________ ON A 12 HOUR CLOCK
WRITE
_______________________ _____________________.
Ratio & Proportion
Word problems
1. A manufacturer wants to prepare 500,000 diazepam (Valium) tablets
containing 5 mg of diazepam per tablet. How many
kilograms (kg) of
diazepam powder will be required to prepare this batch?
2. If a drug contains 25mg of an expectorant per tablespoonful, how much
expectorant would be found in a quart of this
mediction?
3. An antiflatulent medication contains 20mg of Simethicone per infant
dose of 0.3ml. How many grams of simethicone are in 1
fluid ounce (avoidupois)?
4. The average aspirin tablet contains 5 grains of acetylsalicyclic acid
(ASA). How many grams of aspirin would be found in a 250
tablet size bottle?
5. A technician prepared a large batch of zinc oxide (ZnO) ointment
containing
10 grams of zinc oxide in every 100 grams of
ointment. How much ointment was prepared if the technician used 3/8 lb. of zinc
oxde powder?
6. A pint of cough medicine contains 960 mg of dextromethorphan
(antitussive). How many grams of the medication would be in a 2 teaspoonfuls dose?
7. How many milligrams (mg) of NTG (nitroglycerin) would be contained in
30 tablets each containing 1/150 grain?
8. A patient weighs 186 lbs. and
the dosing of the medication is in kg. How many kg does the patient weigh?
9. If 2 grains (gr) of phenobarbital are divided
into 90 capsules, how many micrograms (mcg) of phenoarbital would be present in
each capsule?
Reducing & enlarging formulas (Use the rule of proportions)
Rx
Zinc
oxide USP 50g
Pine
Tar 120g
Petrolatum 284 g
1. How much pine tar would be needed to prepare 1 kg of this product?
2. How much Zinc Oxide would
be in 100 grams of this ointment?
If the order is written as such:
Rx
Zinc
Oxide USP 50g
Pine
Tar 120g
Petrolatum
qs ad 500g
“qs ad” = quantity
sufficient to… or to make…
How much petrolatum is needed
to prepare this formula?
Rx
Benzyl
Benzoate 250ml
Triethanolamine 5 ml
Oleic
Acid 20ml
Puified
Water qs ad 1000ml
1.
How much benzyl benzoate would be needed to
prepare 1 pt of the lotion?
2.
If the “qs ad” were not present in this script, how much water would you
use?
Alligations
You receive a prescription to make 4 oz. of a 10% solution. On your shelf you find both 25% and 5% solutions. What proportions
of each will you use?
Your pharmacy receives a medication order to prepare a 15% ointment
weighing 2 oz. Your pharmacy stocks a 50% ointment and a 10% ointment. How much
of each are require to make this compound?
What amount of 90% alcohol and distilled water are
needed to make 1 liter of 25% alcohol?
A physician orders a prescription for 4 oz. of 1.5% hydrocortisone cream.
The pharmacy stocks a 0.5% and 2.5% cream. How much of each cream should be used to make this compound?
Flow Rates
1. How many ml would a
patient receive in 1 hour if it takes 45 minutes for 100ml to be infused?
2. If a patient is given 1 liter of an intravenous solution and the infusion
rate is 125ml/hour, how long will the intravenous bag last?
3. An intravenous is to flow
at 100ml/hour using a 10drop set (10 drops/ml), how many drops per minute are administered?
4. A patient is to receive 2
liters of normal saline infused over 24 hours using a 10drop kit.
a. How many ml/hr is this?
b. How many ml/minute is this?
c. How many drops/minute
is this?
5. A 220lb male is to
receive 1 liter of a medication dosed at 10mcg/kg/min. How many mg per hour
will he receive?