Chapter 52 - Dosage Calculations
Apothecary and Household Systems
Although the metric system is preferred for dosage calculations, as a medical assistant you should have basic knowledge of the much older apothecary system, as well as the commonly known household system. The apothecary system uses units such as fluid ounces, fluid drams, pints, and quarts for volume, and drams, ounces, and pounds for weight. The only household units used for measurement are units of volume. They include drops, teaspoons, tablespoons, ounces, cups, pints, quarts, and gallons. Keep in mind that units of measurement found in both the apothecary and the household systems are equal: an apothecary ounce equals a household ounce. Apothecary and household units and equivalents you may come across in practice are outlined in Table 52-2 and Table 52-3.
Metric System
Like the decimal system, the metric system is based on multiples of 10. The greater confidence you have working with decimals, the more comfortable you will be working with metric units. See the Caution: Handle with Care feature Working with Decimals. The basic units of volume and weight in the decimal-based metric system are liters (L) to measure volume and grams (g) to measure weight. Prefixes are added to these basic units of measurement to indicate multiples, such as kilogram (kg), or fractions, such as milliliter (mL) or microgram (mcg). Common metric units and equivalents are presented in Table 52-1. Note that a cubic centimeter (cc) is the amount of space occupied by 1 mL. Although these two measurements are equal, the accepted medical abbreviation is mL. Do not use the abbreviation "cc," even though you may sometimes see it in practice. Additionally, note that the abbreviation for liters is a capital L instead of a small l. The small l can be confused with the numeral 1.
Dosages Based upon Weight
An order based on weight often states the amount of medication per weight of the patient per unit of time. For example, an order for a 34 lb child may read "Erythromycin 40 mg/kg/day po q4h." This means that over the course of a day, the patient should receive 40 mg of medication for every kilogram (kg) he or she weighs. It is to be given every four (4) hours or six (6) times during a 24-hour period. You will need to calculate the patient's weight in kilograms, the total medication to administer in 24 hours, and the amount of medication to administer in each dose. Use these steps. 1. Calculate the weight in kilograms using the proportion method. For accuracy, round the results to the nearest hundredth (two places after the decimal point). a. Set up the proportion. Recall from Table 52-4 that 2.2 lb × 1 kg. b. Cross multiply. Remember to multiply the bottom left number by the top right number, and multiply the top left number by the bottom right number. c. Solve for x (the unknown). 2. Calculate the desired dose (D) for 24 hours by multiplying the dose ordered by the weight in kilograms. 3. Calculate the desired dose (D) for the one dose you have been asked to administer. This is done by dividing the amount to be received in 24 hours by the number of times the medication will be received in 24 hours. In this case, the medication is to be given six times in 24 hours. 4. Calculate the amount to administer. On hand you have the medication shown in Figure 52-6. a. Set up the equation. You want to give 103 mg of medication, and the label shows there are 200 mg in 5 mL of medication. b. Cross multiply. Remember to multiply the bottom left number by the top right number, and multiply the top left number by the bottom right number. c. Page 1071 Solve for x to determine the amount of liquid medication to administer to this patient.
Dosage Calculations
As a medical assistant you may be called upon to calculate medication doses. Remember to follow your scope of practice. You may be able to calculate these using either the proportion method or a formula method. No matter what method you use, you must be aware that the patient's health or life can depend on your calculations. Always take the time to check and recheck your arithmetic. For a quick review of basic math, see Points on Practice: Math Review. If you have a question or you are not sure about your calculations, check the problem again and then have a coworker check. If you are not 100% sure you know how to do dosage calculations correctly, consider buying and using a dosage calculation workbook or searching the Internet for extra practice.
Working with Decimals
Consider the following when working with decimals to prevent errors in dosage calculations. 1. Writing decimals: Write the whole-number part of the decimal to the LEFT of the decimal point. Write the decimal fraction part to the RIGHT of the decimal point. Decimal fractions are equivalent to fractions that have denominators of 10, 100, 1000, and so forth. Use zero as a placeholder to the RIGHT of the decimal point just as you use zero for whole numbers. The decimal number 1.203 represents 1 ones, 2 tenths, 0 hundredths, and 3 thousandths. 2. Using zeros: Always write a zero to the left of the decimal point when the decimal number has no whole-number part. Using the zero makes the decimal point more noticeable. Never place a trailing zero after the decimal point when working with medication dosages. 3. Rounding decimals: Underline the place value to which you want to round. Look at the digit to the RIGHT of this target place value. If this digit is 4 or less, do not change the digit in the target place value. If this digit is 5 or more, round the digit in the target place value up one unit. Drop all digits to the right of the target place value.
Converting within the Metric System
Converting one metric unit of measurement to another is similar to multiplying and dividing decimal numbers. When you convert a quantity from one unit of metric measurement to another, you should follow these rules: 1. Move the decimal point to the right when you convert from a larger to a smaller unit. This is dividing. 2. Move the decimal point to the left when you convert from a smaller to a larger unit. This is multiplying. Use Table 52-1 and Figure 52-1 to help determine both the direction and the number of places to move the decimal point when you convert between units of metric measurement. For example, milliliter is three decimal places to the right of liter, the basic unit. To convert a quantity from liters (larger) to milliliters (smaller), move the decimal point three places to the right, or three steps down the stairs shown in Figure 52-1. Similarly, to convert a quantity from grams (smaller) to kilograms (larger), move the decimal point three places to the left, or three steps up the stairs.
Conversions within and between Measurement Systems
Frequently you will need to convert units of measure within a system of measure or between systems of measure. Most commonly you will convert within the metric system. For example, you may need to determine how many milligrams of medication to give a patient when the medication only comes in grams. Sometimes you may need to convert from one measurement system to another. For example, a patient may need to take five milliliters of medication and the only device she has is a teaspoon.
Body Weight and Body Surface Area Calculations
In certain cases, a drug dose is determined based on the body surface area (BSA) or the weight of the patient. This is more common with pediatric and geriatric patients. These patients are at greater risk of harm from medication because of the way they break down and absorb medications. Calculations for these individuals must be precise. Although BSA and weight dosage calculations are usually done by the physician or other licensed healthcare personnel, you may be asked to perform calculations, depending on your area of practice.
Ensuring Safe Dosage Calculations
In order to be able to calculate dosages, you must understand and be able to perform basic math accurately. Whether you are using a calculator or doing it by hand, accuracy is key. Remember that a minor mistake in basic math can mean major errors in the patient's medication. When you perform any calculation, think about the answer you obtain and determine if it is reasonable. Consider this example: While performing a calculation, a medical assistant adds the following numbers: 21¾, 12½, and 1½. He calculates an answer of 49¼. Before he accepts this answer as correct, however, he asks himself, "Is this reasonable?" In order to answer this question, he does a quick estimation. First, he adds the whole numbers from each of the mixed numbers in the problem: 21 + 12 + 1 = 34. Then he rounds each mixed number up to a whole number and adds them: 22 + 13 + 2 = 37. He recognizes that the correct answer to the problem must be between 34 and 37, so his original answer is incorrect. He probably entered one of the numbers into his calculator incorrectly. When he repeats the original calculation, he now comes up with an answer of 35¾. This is between the values that he expected based on his estimate, so it is a reasonable answer to the problem. Think about the example. When performing calculations, there are many steps in which an error might be made. In this case, a number had been entered incorrectly into a calculator. While errors like this can happen to anyone, they can usually be detected by performing a quick check to see if the answer is reasonable. You should develop the habit of asking yourself the same question every time you perform a calculation. When performing a calculation, analyze the problem and try to estimate a reasonable range for the answer. This critical thinking skill can help you to detect errors and should become a part of every calculation you perform.
Formula Method for Dosage Calculations
In some instances, you can use a basic formula to calculate drugs that have the same label as the dose ordered—such as milligrams and milligrams—and therefore do not require a conversion. When you use the formula method, you substitute the correct numbers for what each of the letters represents. The basic formula that you would use looks like this: D/H × Q Using this formula, you will need to know the following: D = Desired dose or the amount of medication the physician has ordered the patient to take. H = Dose on hand or the amount of medication in each unit of the drug; for example, the number of mcg, mg, or g in each unit dose. Q = Quantity of the dose on hand or dosage unit; for example, a pill or an amount of liquid.
Preventing Errors during Dosage Calculations
Medication errors are a serious problem in healthcare. The possibility of error occurs several times during medication administration. Error can occur when performing calculations, when selecting the medication to administer, and when reading the label to perform the calculation. Always pay close attention to the dose and the route of administration (how the medication is given). You must check and recheck the ordered form of the drug as well as the amount of drug per dose of the drug. In the following example, this crucial relationship is illustrated. Prochlorperazine (Compazine) is an antiemetic drug for acute nausea and vomiting. It is given to both children and adults. When the vomiting is so severe that a tablet or capsule cannot be swallowed, the drug is administered in injectable or suppository form. This drug is available in multiple forms: 10 mL multidose vials with 5 mg of drug per mL, written as 5 mg/mL 2 mL single-dose vials with 5 mg/mL 4 fl oz bottles of syrup with 5 mg/5 mL (5 mg/1 tsp) 5 mg tablets 10 mg tablets 2 mL prefilled disposable syringes with 5 mg/mL 2½ mg suppositories 5 mg suppositories 25 mg suppositories 10 mg extended release capsules 15 mg extended release capsules Because so many forms of this drug are available, there is a high risk of error in choosing the correct form. In addition, the route of administration can determine how much drug is delivered in one dose. For example, note that suppositories are available in 2½ mg, 5 mg, and 25 mg forms. If the 2½ mg dose were written as 2.5 mg, there might be confusion with the 25 mg dose suppository. Thus, the 2½ mg suppository is always written this way, even in the PDR. This clarification helps prevent a child from receiving the adult dose of 25 mg, which could result in serious complications to the central nervous system. This possible confusion is one example of how much difference a decimal point can make. Note also that in the syrup there is a 5 mg dose of drug per 5 mL (1 tsp), whereas in the other liquid forms (vials and prefilled syringes), there is a 5 mg dose of drug per 1 mL. The injectable form is five times more concentrated than the syrup. Therefore, if you were to administer the same amount of injectable liquid as syrup to a patient, you would give the patient five times more drug than in the syrup. Just as a child could be endangered with the 25 mg suppository, an adult could be endangered with the wrong form of liquid. Because elderly patients often receive syrup forms of medication, this instruction could be particularly confusing.
Math Review
Recall the following math rules while performing dosage calculations. 1. Order of operations: When solving a math problem, first divide or multiply from left to right, then add or subtract from left to right. For example: For the equation you would need to divide 650 by 325 first. This equals 2 2 × 3 = x Now multiply second: 6 = x. 2. Proportions: Proportions are two fractions that are equal to each other. When 3 of the 4 values in a proportion are known, the unknown value can be calculated. Proportions using fractions are solved by cross multiplying. For example: To solve for the unknown in 2/3 = x/12, cross multiply (3 × x = 2 × 12) and then solve for the unknown (x = 8). 3. Rounding: When rounding, you must look at the first digit to the right of the place value that you are rounding to. If this digit is 5 or more, round up. If it is less than 5, round down. For example, to round 2.7384 to the hundredths place, you look at the digit to the right of the 3. This digit, 8, is greater than 5, so you round the number up to 2.74.
Dosages Based upon Body Surface Area
The total surface area of the body, or body surface area (BSA), is used to calculate very precise medication dosages. Pediatric patients, as well as burn victims or patients undergoing chemotherapy or radiation therapy, may need BSA dosage calculations. A complex formula or a nomogram, shown in Figure 52-7, may be used to determine the BSA. A nomogram is a set of scales arranged so that a ruler aligned with two of the values shows the corresponding value on the third scale. In Figure 52-7, aligning the ruler with a person's height and weight shows the body surface area.
Measurement Systems
Three systems of measurement are used in the United States for pharmacology and drug administration. These include metric, apothecary, and household systems. Metric is the most commonly used system. Although apothecary and household systems are rarely used, basic knowledge of these systems may be needed. To understand drug measurement, focus primarily on remembering the basic unit of volume and weight. Volume refers to the amount of space a drug occupies. Weight refers to its heaviness. Length, which is also a basic unit, is discussed in the Vital Signs and Measurements chapter.
Converting between Systems of Measurement
When performing dosage calculations, sometimes it will be necessary to convert units from one system to another. In order to do this, you must become familiar with their equivalent measures. Because of the difference in basic units of measure, you must remember that conversions between systems are only approximate equivalents. If you use a conversion chart, read it carefully before administering a drug. Check it several times and place a ruler under the line you are reading to be absolutely sure you are reading the chart properly. Table 52-4 provides equivalent measures for the metric, apothecary, and household systems.