1. Chapter 8: Mathematical Calculations Used in Pharmacology
Jennifer Kean MSN,RN,CCRN

2. Apothecary system
Grains: gr (solids)- rarely used nowadays but still need to be familiar with
A few meds are expressed in grains (aspirin, Tylenol (acetaminophen), quinidine) and drops (gtts) are used in intravenous calculations
Drams and minims are no longer used
To convert grains to grams, divide by 15 or 16
To convert grains to milligrams, multiply by 60 or 64
1 grain = 60 or 64 mg
Expressed in lowercase Roman numerals ( i,v,x)
Common fractions (1/2 gr, 1/5 gr)

3. Metric System Built around multiples of 10
Most commonly used drug measurement system; used internationally
Uses meter (m) for unit of length, liter (l) for unit of volume, and gram (g) for the unit of weight

4. Metric Measure
Kilogram, gram, milligram, microgram: each group has three places, just like money does
So, ones, tens and hundreds would be in the microgram section
Thousands would be like the milligram
Millions would be like the gram
Billions would be like the kilogram

5. Metric measure Kilogram Gram Milligram Microgram Billions Millions
Thousands
Hundreds
Tens
Ones

6. Apothecary measure 60 mg = gr 1 45 mg = gr 3/4 30 mg = gr ½

7. Household measure 1 teaspoon = approx. 5 ml
1 tablespoon = 3 teaspoons= 15 ml
1 ounce = 30ml
1 cup = 8 ounces = 240 ml
1 pint = 2 cups = 16 ounces = 480 ml
1 quart = 4 cups = 32 ounces = 960 (1000) ml

8. Metric measure Measures of length (meter) Measures of volume (liter)
1 meter (m) =100 centimeters (cm) = 1000 millimeters (mm)
1 centimeter (cm) = 0.01 meter (m)
1 millimeter (mm) = meter
Measures of volume (liter)
1 decaliter (daL) = 10 liters (L)
1 liter = 1000 milliliters (ml) or 1000 cubic centimeters (cc)
Measures of weight (grams)
1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
1 milligram (mg) = 1000 micrograms

9. Metric Measure It is easy to change measures within the metric system
To change milligrams to micrograms, move the decimal point three places to the right (multiply by 1000): =
To change micrograms to milligrams, move the decimal point three places to the left (divide by 1000): =
To change grams to milligrams, move the decimal point three places to the right (multiply by 1000): =
To change milligrams to grams, move the decimal point three places to the left (divide by 1000): =

10. Converting temperature readings
Fahrenheit- used for years by nurses to measure temperature
212 degrees = boiling point
32 degrees = freezing point
Normal body temp = 97.6 degrees to 99.4 degrees
Celsius
100 degrees = boiling point
0 degrees = freezing point
Normal body temp = 36.5 degrees to 37.5 degrees

11. Celsius to Fahrenheit (C x 9/5) + 32 = F OR (C x 1.8) + 32 = F
C is a cold scale. To transition up to the hot scale you need to multiply by a fraction greater than one then add 32 to finish the calculation
EX: 36.8 C x 9/5 = = 98.2 F

12. Fahrenheit to Celsius C = (F – 32) x 5/9 OR
C = (F – 32) divided by 1.8
You started with the hottest scale, so you need to subtract 32 and then multiply by a fraction (less than 1) or divide to lower the number toward the cold scale
C =101.2 – 32 = 69.2 x 5/9 = 38.4 C
Normal Celsius body temp is 37 degrees

13. Pounds to Kilograms
To convert pounds to kilograms, divide the number of pounds by 2.2
185 lb. = 92.5 kg
To convert kilograms to pounds, multiply the number of kg by 2.2
98.2 kg = kg ( round to 216 kg)

14. Question
50 mcg = ___ mg

15. Question A patient weighs 198 pounds. How much is this in kilograms?kg kg kg kg