Medications and Calculations

Overview

This chapter on medications and calculations is subdivided into six sections: (A) systems of measurement with conversion, (B) methods for calculation, (C) calculations of oral dosages, (D) calculations of injectable dosages, (E) calculations of intravenous (IV) fluids, and (F) pediatric drug calculations. The nurse may proceed independently through Sections A to F to practice and master calculation of drug dosages during the fundamental nursing or pharmacology course. This chapter also serves as a review of drug calculation for nurses in practice settings.

Numerous drug labels are used in the drug calculation problems to familiarize the nurse with important information on a drug label. This information is then used in correctly calculating the drug dose.

Six calculation methods are explained. Four are general methods: (1) basic formula, (2) ratio and proportion, (3) fractional equation, and (4) dimensional analysis. The nurse should select one of these general methods for the calculation of drug dosages. The other two methods are used to individualize drug dosing by body weight and body surface area. Each calculation method has a color-coded icon that identifies the method used in the chapters.

The drug calculation chart in Table 14A-3 may be used in the clinical setting. The nurse might find it helpful to review Chapter 13 on medication administration.

Keeping in mind that the goal is to prepare and administer medications in a safe and correct manner, the following recommendations are offered:

• Think. Focus on each step of the problem. This applies to simple and difficult problems.

• Read accurately. Pay particular attention to the location of the decimal point and to the operation to be done, such as conversion from one system of measurement to another.

• Picture the problem.

• Identify an expected range for the answer.

• Seek to understand the problem. Do not merely master the mechanics of how to do it. Ask for help when unsure of the calculation.

Section 14A: Systems of Measurement with Conversion

Outline

Key Terms

Metric System

Conversion within the Metric System

Metric Conversion

Household System

Household Conversion

Metric, Apothecary, and Household Equivalents

Objectives

• Discuss the two systems of measurement.

• Convert measurement within the metric system, larger units to smaller units, and smaller units to larger units.

• Convert measurements within the household system, larger units to smaller units, and smaller units to larger units.

• Convert metric, apothecary, and household measurements among the three systems of measurement as appropriate. See Table 14A-3.

Key Terms

apothecary system, p. 150

gram, p. 149

household measurement, p. 149

liter, p. 149

meter, p. 149

metric system, p. 149

minim, p. 150

ounce, p. 149

Two systems of measurement—metric and household—are used to measure drugs and solutions. The metric system, developed in the late eighteenth century, is the internationally accepted system of measure. It is replacing the apothecary system, which dates back to the Middle Ages and had been used in England since the seventeenth century. Household measurement is commonly used in community and home settings in the United States.

Metric System

The metric system is a decimal system based on the power of 10. The basic units of measure are gram (g, gm, G, Gm) for weight; liter (l, L) for volume; and meter (m, M) for linear measurement, or length. Prefixes indicate the size of the units in multiples of 10. Table 14A-1 gives the metric units of measurement in weight (gram), volume (liter), and length (meter) in larger and smaller units that are commonly used.

TABLE 14A-1

METRIC UNITS OF MEASUREMENT

UNIT	NAMES AND ABBREVIATIONS	MEASUREMENTS
Gram (weight)	1 kilogram (kg, Kg)	1000 g
	1 gram (g, gm, G, Gm)	1 g
	1 milligram (mg)	0.001 g
	1 microgram (mcg)	0.000001 g
	1 nanogram (ng)	0.000000001 g
Liter (volume)	1 kiloliter (kl, KL)	1000 L (l)
	1 liter (L, l)	1 L (l)
	1 milliliter (mL)	0.001 L (l)
Meter (length)	1 kilometer (km)	1000 m
	1 meter (m, M)	1 m
	1 centimeter (cm)	0.01 m
	1 millimeter (mm)	0.001 m

NOTE: 1 mL (milliliter) = 1 cc (cubic centimeter). Values are the same in drug and fluid therapy. 1 mg (milligram) = 1000 mcg (micrograms).

Kilo is the prefix used for larger units (e.g., kilometer), and milli, centi, micro, and nano are the prefixes used for smaller units (e.g., millimeter). The prefix stands for a specific degree of magnitude; for instance, kilo stands for thousands, milli for one thousandth, centi for one hundredth, and so on. Because the difference between degrees of magnitude is always a multiple of 10, converting from one magnitude to another is relatively easy.

Conversion within the Metric System

The metric units most frequently used in drug notation are the following:

1 g=1000 mg

1 L=1000 mL

1 mg=1000 mcg

To be able to convert a quantity, one of the values must be known, such as gram or milligrams, liters or milliliters, and milligrams or micrograms. Gram, liter, and meter are larger units; milligram, milliliter, and millimeter are smaller units.

Metric Conversion

A. When converting larger units to smaller units in the metric system, move the decimal point one space to the right for each degree of magnitude change.

Note: This does not apply to micro and nano units.

Example

Change 1 gram to milligrams.

Grams are three degrees of magnitude greater than milligrams (see Table 14A-1). Move the decimal point three spaces to the right.

B. When converting smaller units to larger units in the metric system, move the decimal point one space to the left for each degree of magnitude of change.

Example

Change 1000 milligrams to grams.

Milligrams are three degrees of magnitude smaller than grams. Move the decimal point three spaces to the left.

REMEMBER: When changing larger units to smaller units, move the decimal point to the right, and when changing smaller units to larger units, move the decimal point to the left.

Practice Problem 1

Metric Conversion

Larger to Smaller Units	Smaller to Larger Units
1. Change 2 g to mg	4. Change 1500 mg to g
2. Change 0.5 () g to mg	5. Change 3 g to kg
3. Change 2.5 L to mL	6. Change 500 mL to L

Household System

Household measurement is not as accurate as the metric system because of the lack of standardization of spoons, cups, and glasses. The measurements are approximate. A teaspoon (t) is considered to be equivalent to 5 mL according to the official United States Pharmacopeia. Milliliters (mL) are the same as cubic centimeters (cc) in value. Three teaspoons equals 1 tablespoon (T). Ounces (oz) are fluid ounces in the household measurement system; the word fluid in front of ounce is usually not used. One milliliter of water fills a cubic centimeter exactly.

Table 14A-2 gives the household equivalents in fluid volume. The measurements with asterisks are frequently used in drug therapy and should be remembered.

TABLE 14A-2

HOUSEHOLD EQUIVALENTS IN FLUID VOLUME

1 MEASURING CUP	=	8 OUNCES (oz)
1 medium-size glass (tumbler size)	=	8 ounces (oz)
1 coffee cup (c)	=	6 ounces (oz) (varies with cup size)
1 ounce (oz)	=	2 tablespoons (T)
1 tablespoon (T)	=	3 teaspoons (t)
1 teaspoon (t)	=	60 drops (gtt)*
1 drop (gt)*	=	1 minim (min, or m)

*Varies with viscosity of liquid and dropper opening.

Household Conversion

A. When converting larger units to smaller units within the household system, multiply the requested number by the basic equivalent value.

Example

Change 2 glasses of water to ounces.

The equivalent value is 1 medium-sized glass = 8 oz (fl oz)

2 glasses × 8 oz = 16 oz (fl oz)

With discharge teaching for a patient who requires liquid medication(s) at home, the nurse may find it necessary to convert metric measurements to household measurements.

Practice Problem 2

Household Conversion

REMEMBER: To change larger units to smaller units, multiply the requested number of units by the basic equivalent value. To change smaller units to larger units, divide the requested number of units by the basic equivalent value. Refer to Table 14A-2 as needed.

Larger to Smaller Units	Smaller to Larger Units
1. Change 3 oz to T ______	4. Change 3 T to oz ______
2. Change 5 T to t ______	5. Change 16 oz to a measuring cup ______
3. Change 3 coffee cups to oz ______	6. Change 12 t to T ______

Metric, Apothecary, and Household Equivalents

Although the apothecary system is no longer used, Table 14A-3 is included to show metric and apothecary equivalents by weight, and metric, apothecary, and household equivalents by volume.

Practice Problem 3

Summary: Metric and Household Measurements

Metric System: Refer to Table 14A-1 as needed.

1. 2 g = _________ mg	5. 500 mg = _________ g
2. 1.2 kg =________ g	6. 10,000 mcg = _____ mg
3. 5 mg = _______ mcg	7. 2400 mg = ________ g
4. 2.5 L = _______ mL	8. 1500 mL = ________ L

Household System: Refer to Table 14A-2 as needed.

1. 5 glasses = _____ oz	4. 4 oz = ___________ T
2. 3 T = __________ t	5. 15 t = ___________ T
3. 2 c = _________ oz	6. 5 T = ___________ oz

TABLE 14A-3

APPROXIMATE METRIC, APOTHECARY, AND HOUSEHOLD EQUIVALENTS

	METRIC SYSTEM		APOTHECARY SYSTEM	HOUSEHOLD SYSTEM
Weight	1 kg	1000 g	2.2 lb	2.2 lb
	*1 g	1000 mg	15 (16) gr
	0.5 g	500 mg	gr
	0.3 g	300 (325) mg	5 gr
	0.1 g	100 mg	gr
	*0.06 g	60 (65) mg	1 gr
	0.03 g	30 (32) mg	gr
	0.01 g	10 mg	gr
		0.6 mg	gr
		0.4 mg	gr
		0.3 mg	gr
Volume	1 L; 1000 mL		1 qt; 32 oz (fl oz)
	0.5 L; 500 mL		1 pt; 16 oz (fl oz)
	0.24 L; 240 mL		8 fl oz	1 glass
	0.18 L; 180 mL		6 fl oz	1 c
	*30 mL		1 fl oz; 8 fl dr	2 T; 6 t
	15 mL		fl oz; 4 fl dr	1 T; 3 t
	^†5 mL			1 t
	4 mL		1 fl oz; 60 (min)	1 t
	1 mL		15 (16)	15-16 gtt
Height/distance	2.54 cm		1 in	1 in
	25.4 mm		1 in	1 in

fl dr, Fluid dram; fl oz, fluid ounce; minim; cm, centimeter; g, gram; gr, grain; gtt, drops, in, inch; kg, kilogram; L, liter; lb, pound; mg, milligram; mL, milliliter; mm, millimeter; pt, pint; qt, quart; T, tablespoon; t, teaspoon; c, coffee cup.

*Equivalents commonly used for computing conversion problems by ratio.

^†5 mL = 1 t (teaspoon); official United States Pharmacopeia measurement.

Answers to Practice Problems

1 Metric Conversion

1. 2.0 g = or 2.0 g = 2000 mg
The gram is three degrees of magnitude greater than the milligram, so the decimal point is moved three spaces to the right.

2. 0.5 g = or 0.5 g = 500 mg
The gram is three degrees of magnitude greater than the milligram, so the decimal point is moved three spaces to the right.

3. 2.5 L = or 2.5 L = 2500 mL
The liter is three degrees of magnitude greater than the milliliter, so the decimal point is moved three spaces to the right.

4. 1500 mg = or 1500 mg = 1.5 g
The milligram is three degrees of magnitude smaller (less) than the gram, so the decimal point is moved three spaces to the left.

5. 3 g = or 3 g = .003 mg
The gram is three degrees of magnitude smaller than the kilogram, so the decimal point is moved three spaces to the left.

6. 500 mL = or 500 mL = 0.5 L
The milliliter is three degrees of magnitude smaller than the liter, so the decimal point is moved three spaces to the left.

2 Household Conversion

1. 3 oz = 6 T;
the equivalent value is 3 oz × 2 = 6 T

2. 5 T = 15 t;
the equivalent value is 1 T = 3 t

3. 3 c = 18 oz;
the equivalent value is 1 c = 6 oz

4. 3 T = oz;
the equivalent value is 3 T ÷ 2 or oz

5. 16 oz = 2 c;
the equivalent value is 1 measuring cup = 8 oz

6. 12 t = 4 T;
the equivalent value is 1 T = 3 t

3 Summary

Metric and Household Measurements

Metric Conversion

1. 2000 mg (1 g = 1000 mg)
2 × 1000 mg = 2000 mg
or
(three spaces to the right)

2. 1200 g

3. 5000 mcg (1 mg = 1000 mcg)

4. 2500 mL

5. 0.5 g (1000 mg = 1 g)
500 ÷ 1000 = 0.5
or = 0.5 g
(three spaces to the left)

Household Conversion