How to calculate drugs for a patient

1. Dosage
Calculations

2. Dosage Calculations
• Measurement systems
– Metric
– Apothecaries
– Household
• Most doctors use the metric
system

3. Three Systems
of Weight andMeasure
• Metric (simple system based on units of 10).
• Apothecary (based on the weight of one
grain of wheat).
• Household (drops, teaspoons, tablespoons,
etc.).

4. Metric System
• Meter is used for linear measure, Meter for
length, gram for weight and liter for
volume

5. Metric System
• The metric, or decimal, system is a simple system of
measurement based on units of 10. The basic units can be
multiplied or divided by 10 to form secondary units.
• The decimal point is moved to the right for calculating
multiples, and the decimal point is moved to the left for
division.
• The basic units of measurement in the metric system are
the meter (linear), the liter (volume), and the gram (mass).
• When the metric system is used, a zero is always placed in
front of the decimal for values less than 1 (e.g., 0.5) to
prevent error.

6. Apothecary System
• Grains, minims, drams, ounces, pounds,
pints, and quarts

7. • The apothecary system, is based on the weight
of one grain of wheat. Therefore, the basic unit
of weight is the grain (gr), and the basic unit of
volume is the minim (the approximate volume
of water that weighs a grain).
• The grain is expressed in fractions such as
morphine gr 1/4.
• The minim (m) is the smallest unit of volume,
followed in ascending order by the fluid dram
(D), fluid ounce (Z), pint (pt), quart (qt), and
gallon (gal).
Apothecary System

8. Household Measures
• Drops, teaspoons (tsp), tablespoons (tbsp) ,
ounce (oz)and cups
• Important since this is often how people
take medications
• 60 drops (gtts) = 1 teaspoon (tsp)
• 3 tsp = 1 tablespoon (tbsp)

9. • The household system of measurement is similar to the
apothecary system of liquid measures and is the least
accurate of the three systems.
• The units of liquid measure are drop (gtt), teaspoon
(tsp), tablespoon (Tbsp), cup, and glass.
• Household units are often used to inform clients of the
size of a liquid dose. The USP recognizes the use of the
teaspoon as the ordinary practice for household
medication administration and states that the teaspoon
may be regarded as representing 5 ml. Household
spoons are not appropriate when accurate measurement
of a liquid dose is required; therefore, the USP
recommends that a calibrated oral syringe or dropper be
used for accurate measurement of liquid drug doses.
Household Measures

10. Units
• mEq – drugs ordered in number of units
per dose
– Insulin
– heparin

11. Milliliters
• mL = milliliter. This is a VOLUME
measurement. it is 1/1000 of a liter. when
talking about water or similar liquids, it is
equivalent to one cubic centimeter.

12. Cubic Centimeter
• cc = cubic centimeter. This is also a
VOLUME measurement. Most syringes
measure their capacity in cc's. If you have
a 5cc syringe, it will hold ~5mL of liquid in
it.

13. ML And CC’S
• 1 mL = 1cc
• 1 cc = 15 to 16 minims
• 1 cc = 15 to 16 drops (gtt) so
• 1 mL= 15 to 16 drops (gtt)
• Fluids are generally written in cc’s to
standardize the abbreviation – you may
see mL’s written but this abbreviation is
being eliminated

14. CC’S and Household
measures
• 5 cc = 1 tsp (teaspoon)
• 15 cc = 1 tbs (tablespoon)
• 30 cc = 1 oz (ounce) = 2 tablespoons
• 240 cc = 8 oz or 1 cup

15. Milligrams
• mg = milligram. This is a WEIGHT
measurement. It is 1/1000 of a gram. the
amount of chemical substance is often
measured in milligrams. For injectable
solutions, this will be reported as a
concentration of weight to volume, such
as mg/ml (milligrams per milliliter).

16. Dosage Calculations (cont.)
• Basic units of volume and weight
• Metric system
– Liter (L) – volume
– Grams (g) – weight
• Apothecaries’ system
– Fluidounces, fluidram, pints, quarts – volume
– Pounds – weight
• Household system
– Drops, teaspoons,
tablespoons, ounces,
cups, pints, gallons,
quarts – volume

17. ConvertingUnits of Weight and
Volume
• The nurse has to apply the knowledge of measurement systems and
their conversions when the health care practitioner prescribes a
drug dosage in one system and the pharmacy dispenses the
equivalent dose in another.
• Given the above example of morphine, if the health care practitioner
orders morphine gr 1/4 and the pharmacist dispenses morphine 15
mg, the nurse is responsible for ensuring the correct dose. The nurse
knows that 1 grain equals 60 milligrams; to convert the ordered
dose to milligrams, the nurse should use the following calculation:
1 gr = 60 mg
x = 1/4 gr × 60 mg/gr
(the grains cancel out)
x = 60/4 mg
x = 15 mg

18. Measurement Conversions within the Metric
System
• Because the metric system is based on
units of 10, dose equivalents within the
system are computed by simple
arithmetic, either dividing or multiplying.

19. For example,
To change milligrams to grams (1,000 mg equals 1 g) or milliliters to liters
(1,000 ml equals 1 L), divide the number by 1000:
250 mg = x g
(move the decimal point three places to the left)
x = 0.25 g
or
500 ml = x L
(move the decimal point three places to the left)
x = 0.5 L
To convert grams to milligrams or liters to milliliters, the nurse multiplies
the number by 1000:
0.005 g = x mg
(move the decimal point three places to the right)
x = 5 mg
or
0.725 L = x ml
(move the decimal point three places to the right)
x = 725 ml

20. • The nurse may need to convert the volumes
of liters and milliliters for enemas and
irrigating solutions such as for bladder and
wound irrigations. Intravenous solutions are
sterile, prepackaged solutions dispensed in
volumes as ordered by the health care
practitioner, such as 50 ml, 100 ml, 250 ml,
500 ml, and 1,000 ml (1 liter).

21. APPROXIMATE METRIC SYSTEM EQUIVALENTS:
Liquid Measure (Volume):
Metric Apothecary Household
.06 ml= 1 drop (gtt)
1 ml (1 cc)= 15 drops (gtts)
5 ml = 1 fluid dram = 1 teaspoonful
10 ml = 2 fluid drams = 1 dessertspoonful
15 ml = 4 fluid drams = 1 tablespoonful
30 ml = 1 fluid ounce = 2 tablespoonful
60 ml = 2 fluid ounces = 1 wineglassful
120 ml = 4 fluid ounces = 1 teacupful
180 ml = 6 fluid ounces = 1 teacupful
240 ml = 8 fluid ounces = 1 glass (cup)
500 ml = 1 pint = 1 pint
1000 ml = 1 quart = 1 quart
4000 ml = 1 gallon = 1 gallon

22. Weight :
Metric Apothecary
1 mg = 1/60 grain
4 mg = 1/15 grain
10 mg = 1/6 grain
15 mg = 1/4 grain
30 mg = 1/2 grain
60 mg = 1 grain
1 g = 15 grains
4 g = 1 dram
30 g = 1 ounce
500 g = 1.1 pound
1000 g (1 kg) = 2.2 pounds

23. Measurement Conversions between
Systems
• When converting grains to milligrams, the nurse must
multiply by 60.
• For example, if the physician orders nitroglycerin (anti-
anginal) 1/150 gr PO for chest pain, the dispensed dose
will be 0.4 mg:
1 gr = 60 mg
x = 1/150 gr × 60 mg/gr
(the grains cancel out)
x = 1/150 × 60/ 1 mg
x = 60/150 mg
(divide 60 by 150)
x = 0.4 mg

24. • The nurse converts between pounds and
kilograms (2.2 lb = 1 kg) by dividing or
multiplying by 2.2.
• For example, if the ordered dose is 10
mg/kg and the client weighs 150 lb:
150 lb / 2.2lb/kg X 10 mg/kg / x
(the lb and kg cancel out)
x = 68.2 × 10 mg
x = 682 mg

25. Drug Dose Calculations
• Several formulas may be used by the nurse when
calculating drug doses. One formula uses ratios based on
the dose on hand and the dose desired.
• For example, cephalexin (anti-infective cephalosporin)
500 mg PO q.i.d. (dose desired) is ordered by the health
care practitioner; the dose on hand is 250 mg/5 ml. The
formula is as follows:
250 mg (dose on hand) / 5 ml (dose on hand) = 500 mg (dose desired) / x (dose desired)
(cross-multiply)
250 x = 5 × 500
x = 5 × 500 / 250
x = 10 ml

26. • The ratio formula can be used in calculating dosages.
• For example, the health care practitioner orders heparin
(anticoagulant) 10,000 units SC; the dose on hand is
40,000 units/ml:
40,000 units / 1 ml = 10,000 units / x
(units cancel out)
40,000 x = 10,000
x = 10, 000 / 40, 000
x = 1/4
x = 0.25 ml

27. • Metabolism and absorption altered
• Require precise calculations
– BSA – body surface area
– Weight
Dosage Calculations:
PediatricandGeriatric

28. Pediatric Dosages
• The body surface area method of determining
pediatric doses is based on the body surface area
of an adult weighing 150 lb. The body surface
area of an adult weighing 150 lb. is 1.73 square
meters. The approximate child dose is calculated
as follows:
Body surface area of child / Body surface area of adult X adult dose
= approximate child dose
Body surface area of child (m2) / 1.73 m2 X adult dose
= approximate child dose

29. • Younge’s rule: for children over 1 year of
age upto 12 year
Age of the child (in years) / Age of the child (years) + 12 X Adult dose = Child’s dose
Pediatric Dosages

30. • Clark’s rule: according to the weight of the
child, can be used for children of all ages.
Weight of the child in pounds / 150 X Adult’s dose = Child’s dose
Pediatric Dosages

31. • Fried’s rule: for children under 1 year of
age
Age of the child (in months) / 150 X Adult dose = Child’s dose
Pediatric Dosages

32. Dosage Calculations (cont.)
• Conversions between systems
– Approximate equivalents
– Charts
– Calculations
•Ratio method
•Fraction method

33. Dosage Calculations:
FormulaMethod
Desired dose
Dose on hand
The physician orders aspirin, 10 grains
On hand are 5-grain aspirins
10 grains
5 grains
× Quantity of dose on hand
× 1 tablet = 10/5 or 2 tablets

34. Work these problems:
1. The physician has ordered ampicillin
500 mg, on hand 250 mg capsules. How
much would you give?
2. You have 50 mg metropolol as a scored
tablet on hand and the doctor tells you
to give 25 mg. How much would you
give?
2 capsules
½ tablet
Dosage Calculations:
FormulaMethod(cont.)

35. 1. Doctor orders 500 mg of ampicillin. You have 250
mg on hand.
2. Set up a ratio with the unknown number of
capsules needed and the amount of drug ordered
X:500 mg
3. Set up a ratio with a single capsules and the
amount of drug in a single capsule 1 tab:250 mg
4. Create a proportion, multiply the outer and then
the inner parts, and solve for X.
X:500 mg :: 1cap:250 mg
Answer = 2 capsules
Dosage Calculations:
RatioMethod

36. 3. Set the second
fraction with the
amount of drug in a
capsule
10 mg
1 cap
4. Then use both
fractions in a
proportion:
30 mg 10 mg
x = 1 cap
1. The doctor orders 30
mg of Adalat. Each
capsule contains 10
mg.
2. Set up the first
fraction with the dose
ordered and the
unknown number of
capsules
30 mg
x Solve for X = 3 capsules
Dosage Calculations:
FractionMethod

37. Apply Your Knowledge
1. Which measuring system is used by most
physicians?
ANSWER: Most doctors use the metric
system when working with pharmacology
principles.
2. Convert 25 grams to milligrams.
ANSWER:
1. Add a decimal point to the measurement: 25. g
2. Add 3 zeros so you can move the decimal point three
places to the right: 25.000 g
3. Move the decimal point to the right three places:
25,000

38. Apply Your Knowledge
3. Calculate the dose to
give for 500 mg
Augmentin®.
ANSWER:
20 mL

39. DRUG CALCULATIONS
To calculate a drug dose, use the following
formula:
What you want X The amount it’s in
What you have got

40. What you want X The amount it’s in
What you have got
Example: If you need to give 1000mgs of a
drug which comes as 500 mgs tablets,
how many tablets will you need to give
the patient
1000 X 1 = 2 X 1 = 2 Tablets
500 1

41. What you want X The amount it’s in
What you have got
Example: If you need to give 250mgs of a
drug which comes as 125 mgs in 5mls
liquid format, then you need
250 X 5 = 2 X 5 = 10 mls
125 1

42. What you want X The amount it’s in
What you have got
Example: If you need to give 24mgs of a
drug which comes as 30 mgs in 5mls
liquid format, then you need
24 X 5 = 4 X 5 = 4 mls
30 5

43. Preparing Solutions Using Proportion
Method

44. Q. Prepare 250 cc of 4% solution of boric acid.
Ans: (4% solution means 4gms of boric acid in
100cc of water)
4: 100 :: X : 250
100 X = 1000
X = 1000 / 100 = 10
So to Prepare 250 cc of 4% solution of boric
acid, dissolve 10 gms of boric acid in 240 cc
of water (250-10=240 cc).

45. Q. If 153 gms of sucrose is dissolved in
enough water to make an 85% solution how
many cc syrup is made?
Ans: 85 : 100 :: 153 : X
153 x 100 / 85 = 180
So 180 cc of 85% syrup can be made by
dissolving 153 gms of sucrose.

46. Q. Prepare 500 cc of 5% solution of Dettol
lotion.
Ans: 5 : 100 :: X : 500
100 X = 2500
X = 2500 / 100 = 25
To Prepare 500 cc of 5% solution of Dettol
lotion, take 25 parts of pure dettol and add
475 parts of water (500-25)

47. Q. How much salt must be added to one
liter of water to make a solution of normal
saline?
Ans. (Normal saline = 0.9 gms per 100 ml)
0.9 : 100 :: X : 1000
0.9 x 1000/100
900/100 = 9 gms
9 gms of salt is needed to make a liter of
normal saline.

48. Q. How many mL of 4% boric acid solution
can be prepared from 1 ounce of boric acid
powder?
Ans: (1ounce = 30 gms)
4 : 100 :: 30 : X
100 x 30 / 4 = 750
With 1 ounce of boric acid powder 750 mL of
4% boric acid solution can be prepared.

49. Q. What percent of solution would be
prepared if 4 drams of drug is added to
100 mL of solution?
Ans: (4 drams = 16 grams)
16 : 100 :: X : 100
16 x 100 / 100 = 16%

50. Q. How many drams of fluid lysol are
needed to make 1000 mL of 9% solution?
Ans:
9 : 100 :: X : 1000
9 x 1000 / 100 = 90 mL

51. Q. How much mercuric chloride is required
to prepare 1 liter of 1 in 2000 solution?
Ans:
1 : 2000 :: X : 1000
1 x 1000 / 2000
½ or 0.5 gram
0.5 gram of mercuric chloride is needed to
prepare 1 liter of 1 in 2000 solution.

52. Q. How much drug is contained in 100 mL
of 1 in 1000 solution?
Ans:
1 : 1000 :: X : 100
1 x 100 / 1000
1 / 10 = 0.1 gram

53. Q. How many grains of a drug would be
needed to prepare 500 mL of a 1 : 250
solution?
Ans:
1 : 250 :: X : 500
1 x 500 / 250
2 grams = 30 grains
(1 gram = 15 grains)

54. Q. How much of sodium bromic solution
labelled 0.5 gm/ 5 mL is required to
administer 15 grains of the drug?
Ans:
0.5 : 5 :: 1 : X
5 x 1 / 0.5 = 10 mL
(15 grains = 1 gram )

55. Q. How much of 15% solution is required to
give 100 mg of the drug?
Ans:
15 : 100 :: 0.1 : X
100 x 0.1 / 15
10 / 15 = 0.67 or 0.7 mL
(100 mg = 0.1 gm)

56. Q. From a dry powder from of penicillin
which is supplied in vials containing 10
lakhs unit, prepare a solution containing 2
lakh/mL.
Ans:
2 (lakh) : 1 (mL) :: 10 (lakh) : X (mL)
1 x 10 / 2 = 5 mL
Dissolve the penicillin powder in 5 mL of
solution to have a solution of penicillin
containing 2 laks/mL

57. Q. From a solution of penicillin containing
30,000 units/ mL. How much is required to
give 1.5 lakh dose?
Ans:
30000 : 1 :: 150000 : X
150000 x 1 / 30000 = 5 mL

58. Q. How much solution is needed to give 10
gm of the drug from a solution labelled 12.5
gm / 50 mL?
Ans:
12.5 : 50 :: 10 : X
50 x 10 / 12.5 = 40 mL

59. Q. Prepare 1/120 grain Atropine from 1
mgm tablets
Ans: (1 grain = 60 mgm)
1 (gr) : 60 (mg) :: 1/20 (grain) : X (mg)
60 x 1/120 = ½ mg
Dissolve the tablet in 2 mL & use 1 Ml of
the solution.

60. Q. What would be the dose of insulin in mL. If
24 units of insulin is given using U-40
insulin? (1 mL = divisions)
Ans:
40 (units) : 10 (div) :: 24 (units) : X (div)
10 x 24 / 40 = 6 divisions
Take 6 divisions (0.6 mL) to give 24 units of
insuline from U-40 Insulin. U-40 Insulin =
There are 40 units of insulin in 1 mL of the
solution

61. Q. The physician orders 12 units of plain
insulin and 32 units of lente insulin. On hand
are U-40 strengh of both types. What would
be the dose of each?
Ans:
12 : X :: 40 : 10
12 x 10 / 40 = 3 division (0.3 mL) of plain
insulin.
32 : X :: 40 : 10
32 x 10 / 40 = 8 division (0.8 mL) of lente
insulin.

62. PREPARATION OF THE
SOLUTION USING A FORMULA