Conversions and Calculations

Apothecary System

Avoirdupois system

Metric system

Common Household Measurements

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.

## Metric System

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.

### Household Measurements

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)

#### 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

### Apothecary System

Originated in Europe, but used throughout the medical field in the USA.

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)

### Standard Weights: Avoirdupois

 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 Measurements

1. You can use cc or ml interchangeably, although ml is the preferred measurement.
2. Dry weight use microgram (mcg), milligram (mg), gram (g) and kilogram (kg).
3. Liquid volumes use millimeter (ml) and liter (L).

### Apothecary Measurements

1. Dry weights use pounds (#), ounces, drams, scruples, and grains (gr).
2. Liquid volume weights use fluidounces, fluidrams, and minims.

### Avoirdupois Measurements

1. Dry weights use pounds (#), ounces (oz), and grains (gr)
2. Liquid volumes use fluid ounces (foz), pints (pt) and gallons (gal).

### Conversions

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)

#### Fractions:

Rarely seen with prescription, but one should have a basic understanding of fractions if ever the need arises.

Two-step 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=  ____________%

### Ratio/Proportion Method

About 90% of the problems encountered in pharmacy will be ratio/proportion equations.

3 rules to remember

1. Filter out the unnecessary information
2. Find what strength you HAVE in stock and what strength you NEED.
3. Set up the equation and double check the calculation.

HAVE                                =                                  NEED

Question 1 : Prepare 240mg of a drug using the pharmacy stock concentration of 80mg/4ml

# HAVE= NEED

Keep the same units across from each other

mg with mg &  ml with ml

##### CROSS MULTIPY

80 mg                                       =                                  240 mg

4 ml                                                                                 X ml

# 80 X = 960

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

# X= 12 ml

·        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 400-mg tablets.

How many 400mg tablets will you need to fill this order?

### Pediatric Dosing

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?

### Determining Weights

It is necessary to convert pounds to kg since all manufacturers provide proper dosing regimens based on kilograms.

##### Remember

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

#### We know the weight of the child as 3.18 kg

Therefore

60mg = x

1 kg    3.18kg

x= 60mg x 3.18kg

1 kg

= 63.6 mg / dose

### Drip Rates

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 (30-60 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

### Hint for determining drops.

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.

### Calculating Drip rates

You receive an order for a 2-L 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:

1. What is the drop factor (DF)? : 15 gtt/ml
2. What will be the milliliters per hour?

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:

### Alligation

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 tic-tac-toe board

PLACE YOUR DESIRED STRENGTH IN THE

MIDDLE SQUARE

40

PUT YOUR HIGH STRENGTH IN THE TOP                      70

LEFT SQUARE

40

70

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         40-20 = 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                70-40 = 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

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 US is the Arabic System, consisting of 1,2,3 and so forth. This system is not always used by physicians when ordering medications. Instead they may use Roman numerals.

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 lower-case letters, either, so they used capital letters. You will have to, too.

Now, here are the three rules for making numbers with Roman numerals:

1. If you put numbers of the same size together, then you add them.

II=1+1=2
XX=10+10=20
XXX=10+10+10=30

1. If you put a small number to the right of a large number, then you add them, too.

XV=10+5=15
VIII=5+3=8

1. If you put a small number to the left of a large number, then you subtract the small one from the big one.

IX=10-1=9
CM=1000-100=900

That's it! Try to read these numbers:

CMV               XIV                  XC                  C                                 VIII
LXX                CIV                 XXXIX                        XL                               CCXXII
XLI                  DC                  MM                  MMIV                          MMMLV

### International Time

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------------------1:00am

0200------------------2:00am

0300------------------3:00am

0400------------------4:00am

0500------------------5:00am

0600------------------6:00am

0700------------------7:00am

0800------------------8:00am

0900------------------9:00am

1000-----------------10:00am

1100-----------------11:00am

1200-----------------12:00pm

1300------------------1:00pm

1400------------------2:00pm

1500------------------3:00pm

1600------------------4:00pm

1700------------------5:00pm

1800------------------6:00pm

1900------------------7:00pm

2000------------------8:00pm

2100------------------9:00pm

2200-----------------10:00pm

2300-----------------11:00pm

2400 or 0000--------12:00am

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 4:20PM, 7:15PM AND 12:00 AM IN INTERNATIONAL TIME:______________

_______________________          _____________________.

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

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

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 10-drop 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 10-drop kit.

a. How many ml/hr is this?

b. How many ml/minute is this?

c. How many drops/minute is this?

5.      A 220-lb male is to receive 1 liter of a medication dosed at 10mcg/kg/min. How many mg per hour will he receive?