Learning Objectives
By the end of this section, you will be able to:
 Define common systems of measurements
 Perform mathematical calculations to solve dosage equations
 List the stages of the nursing process for safe dosing
Medication administration involves ensuring the right dose of medication is administered to the patient. Medication calculations are an important skill for the nurse to perform correctly to ensure the patient receives the right dose. Miscalculating drug dosages is a frequent source of medication administration errors (Tariq et al., 2023). To provide safe administration of medications, it is important for the nurse to be aware of the various systems of measurement and to be equipped with the skills to perform accurate calculations. These skills will help the nurse to be confident in their ability to calculate medication dosages.
Systems of Measurement
Collections of measurement units and how they are associated with one another are known as systems of measurement. These collections of measurement are based on a standard reference point. Without a measurement standard, there is an increased likelihood of incorrect measurements. There are three systems of measurement used for drug dosages: the metric system, household system, and apothecary system.
Metric System
The metric system is the most widely used international system of measurement and is considered to be the most accurate of the three systems of measurement. It is a decimalbased system based on units of 10. The gram is used to measure weight, liter is used to measure volume, and meter is used to measure length. Table 11.6 displays metric measurements and their equivalents. Though the FDA recommends using milliliter (mL) as the standard measurement for liquid medications, it is important to note that you may still see cubic centimeter (cc) used in practice. Should you see “cc” used, 1 cc is the equivalent of 1 mL.
Measurement  Equivalent 

Weight  
1 kilogram (kg)  1,000 grams (g) 
1 gram (g)  1,000 milligrams (mg) 
1 milligram (mg)  1,000 micrograms (mcg) 
Volume  
1 liter (L)  1,000 milliliters (mL) 
1 milliliter (mL)  1 cubic centimeter (cc) 
Length  
1 kilometer (km)  1,000 meters (m) 
1 meter (m)  100 centimeters (cm) 
1 centimeter (cm)  10 millimeters (mm) 
Household
The household system utilizes everyday household items, such as measuring cups and tablespoons, to serve as measuring devices. Due to variations in the size of household items, it is considered to be the least accurate system of measurement. Table 11.7 displays common household units and their equivalent conversions.
Measurement  Equivalent 

1 cup  8 ounces (oz) = 16 tablespoons (tbsp or T) 
2 tablespoons (tbsp or T)  1 ounce (oz) 
3 teaspoons (tsp or t)  1 tablespoon (tbsp or T) 
1 teaspoon (tsp or t)  60 drops (gtt) 
Apothecary
The apothecary system utilizes fractions as a part of the whole to measure weights and volumes. Due to the confusion that may arise with the use of fractions, the ISMP recommends using the metric system for medications. Although the apothecary system is not frequently used today, there are some providers who may continue to use apothecary measurements in their orders. Table 11.8 displays frequently used apothecary weight and volume measurements and their equivalents.
Measurement  Equivalent 

Weight  
1 pound (lb)  16 ounces (oz) 
1 ounce (oz)  8 drams (dr) 
1 dram (dr)  60 grains (gr) 
Volume  
1 gallon (gal)  4 quarts (qt) 
1 quart (qt)  2 pints (pt) 
1 pint (pt)  16 ounces (oz) 
1 ounce (oz)  8 fluid drams (fl dr) 
1 fluid ounce (fl oz)  1 ounce (oz) 
1 fluid dram (fl dr)  1 dram (dr) 
Dosage Calculations
Dosage calculations are critical skills for the nurse to develop. The nurse must know how to accurately calculate drug dosages to ensure the correct amount of the drug is administered to the patient. Accurately calculating dosages enhances patient safety and reduces the risk of drug errors and potential harm. Dosage calculations may require units of measurement to be converted to a different system of measurement as well as dosages to be determined according to the patient’s weight or serum levels. This section prepares you with the knowledge needed to confidently perform dosage calculations.
Conversion Between Systems
Medications may be prescribed using one system of measurement and supplied in a form that uses a different system of measurement. When this occurs, the prescribed measurement must be converted to the supplied measurement. This calculation may involve converting a metric system measurement into a household measurement or a household measurement into an apothecary measurement. To be able to accurately calculate the dosage, the nurse must be aware of common conversion factors (Table 11.9).
1 kg  2.2 lb 
1 tsp  5 mL 
1 oz  30 mL 
1 tbsp  15 mL 
2 tbsp  1 oz 
1 cup  8 fl oz 
1 lb  16 oz 
8 oz  240 mL 
1 pt  500 mL 
1 gtt  0.5 mL 
Dimensional Analysis
A factorlabel method for solving dosage calculations is called dimensional analysis. Factors are simply another name for the unit of measurement. The goal of dimensional analysis is to set up the known information (such as amount ordered, amount supplied, and quantity supplied) in a way that like units of measurement (factors) cancel each other out so the dose is remaining. Dimensional analysis allows all calculations to be solved using the same method without having to memorize formulas, which reduces the risk of calculation errors.
To solve, the desired dose is placed over one and then cross multiplication is used to determine the dose. If the dose ordered and dose supplied are not the same unit of measurement, a conversion factor may be added to the equation. To simplify the equation, zeros may be canceled out, and fractions may reduce to the smallest form. When calculating medication dosages, rounding should not occur until calculating the final answer. When it is possible to administer a fraction of a dose, medications are typically rounded to the nearest tenth for adults and to the nearest hundredth for children, unless otherwise indicated by the agency’s policy.
Example:
 Order: Alprazolam (Xanax) 1,000 mcg PO Q8 hours
 Supplied: Alprazolam (Xanax) 0.25 mg tablets
 Calculation: $\mathrm{1,000}\phantom{\rule{0.2em}{0ex}}\overline{)\text{mcg}}/1\times 1\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}/\mathrm{1,000}\phantom{\rule{0.2em}{0ex}}\overline{)\text{mcg}}\times \text{1 tablet}/0.25\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}=\text{tablets/dose;}$ $=(\mathrm{1,000}\times 1\times 1)/(1\times \mathrm{1,000}\times 0.25)\text{;}=\mathrm{1,000}/250=\mathbf{\text{4 tablets}}$
Example:
 Order: Potassium chloride (KCl) 60 mEq PO Q6 hours
 Suppled: KCl 40 mEq/15 mL
 Calculation: $6\overline{)\text{0 mEq}}/1\times 15\phantom{\rule{0.2em}{0ex}}\text{mL}/4\overline{)0\text{mEq}}=\text{mL/dose;}=(3/1)\times (15/2)\text{;}=45/2=\mathbf{\text{22.5 mL per dose}}$
Link to Learning
Watch a demonstration of how to perform dimensional analysis in this video.
Clinical Safety and Procedures (QSEN)
QSEN Competency: Calculating Medication Dosages
See the competency checklist for Calculating Medication Dosages. You can find the checklists on the Student resources tab of your book page on openstax.org.
Formula Method
The formula method, sometimes referred to as the “desired over have method,” divides the desired amount by the amount on hand, then multiplies it by the quantity on hand to determine the dose. The desired amount (D) is the dose prescribed, the amount on hand (H) is the available dose or concentration, and the quantity (Q) is the form and amount in which the drug is supplied.
$\frac{\text{D(desiredamount)}}{\text{H(amountonhand)}}\text{}\times \text{Q(quantity)}=\text{Dose}$
Examples:
 Order: Amoxicillin (Amoxil) 500 mg PO Q8 hours
 Supplied: 250 mg tablets
 Calculation: $\mathit{\text{D}}\mathit{/}\mathit{\text{H}}\mathbf{\times}\mathit{\text{Q}}=500\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}/250\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}\times \text{1 tablet}=2\times 1\text{;}=\mathbf{\text{2 tablets}}$
 Order: Morphine (Duramorph) 1 mg IV Q2 hours PRN severe pain
 Supplied: 2 mg vials
 Calculation: $\mathit{\text{D}}\mathbf{/}\mathit{\text{H}}\mathit{\times}\mathit{\text{Q}}=1\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}/2\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}\times \text{1 vial}=0.5\times 1\text{;}=\mathbf{\text{0.5 vial}}$
Ratio Proportion Method
A ratio is a comparison of one quantity to another, often described as a division problem. Ratios can be expressed as a fraction (1/4) or as a ratio (1:4). A proportion is an equation of two ratios that are equal. Proportions can be expressed as 1/4 = 2/8 or 1:4 is proportional to 2:8.
When using the ratio proportion method, the known ratio of drug amount to quantity is set equal to the desired amount to the unknown quantity. This proportion may be displayed as H/Q = D/x or H:Q::D:x. To solve, cross multiply and solve for x. In doing so, the equation becomes Hx = DQ, which can then be solved by dividing DQ by H (x = DQ/H).
$\frac{\text{H(haveonhand)}}{\text{Q(quantity)}}=\frac{\text{D(desiredamount)}}{\text{x}}$
Examples:
 Order: Guaifenesin (Mucinex) 400 mg PO Q4 hours
 Supplied: 200 mg tablets
 Calculation: $\mathit{\text{H}}\mathbf{/}\mathit{\text{Q}}\mathbf{=}\mathit{\text{D}}\mathbf{/}\mathit{\text{x}}\mathbf{\text{;}}\phantom{\rule{0.2em}{0ex}}200\phantom{\rule{0.2em}{0ex}}\text{mg}/1\phantom{\rule{0.2em}{0ex}}\text{tablet}=400\phantom{\rule{0.2em}{0ex}}\text{mg}/\text{x; 200x}=(400\times 1)\text{; x}=(400/200)\text{; x}=\mathbf{\text{2 tablets}}$
 Order: Ketorolac (Toradol) 15 mg IM Q6 hours
 Supplied: 30 mg/mL vial
 Calculation: $\mathit{\text{H}}\mathbf{/}\mathit{\text{Q}}\mathbf{=}\mathit{\text{D}}\mathbf{/}\mathit{\text{x}}\mathbf{\text{;}}\phantom{\rule{0.2em}{0ex}}30\phantom{\rule{0.2em}{0ex}}\text{mg}/1\phantom{\rule{0.2em}{0ex}}\text{mL}=15\phantom{\rule{0.2em}{0ex}}\text{mg}/\text{x; 30x}=(15\times 1)\text{; x}=(15/30)\text{; x}=\mathbf{0.5}\phantom{\rule{0.2em}{0ex}}\mathbf{\text{mL}}$
WeightBased Dosages
Weightbased dosages are ordered as a certain amount of drug based on the patient’s body weight. When calculating weightbased dosages, it is important to note that body weight is based on kilograms. If the weight is documented in pounds, it will need to be converted to kilograms before completing the calculation, or the conversion may be accounted for by using dimensional analysis.
Example:
 Order: Amoxicillin (Amoxil) 40 mg/kg/day PO BID
 Supplied: 400 mg/5 mL
 Weight: 66 lb
 Calculation:

Step 1: Convert pounds to kilograms $66\phantom{\rule{0.2em}{0ex}}\overline{)\text{lb}}\times 1\phantom{\rule{0.2em}{0ex}}\text{kg}/2.2\phantom{\rule{0.2em}{0ex}}\overline{)\text{lb}}=30\phantom{\rule{0.2em}{0ex}}\text{kg}$ Step 2: Calculate the dose in milligrams $30\phantom{\rule{0.2em}{0ex}}\overline{)\text{kg}}\times 40\phantom{\rule{0.2em}{0ex}}\text{mg}/\overline{)\text{kg}}\text{/day}=\mathrm{1,200}\phantom{\rule{0.2em}{0ex}}\text{mg/day}$ Step 3: Divide the dose by the frequency $\mathrm{1,200}\phantom{\rule{0.2em}{0ex}}\text{mg/day}\phantom{\rule{0.2em}{0ex}}/\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}\text{(BID)}=600\phantom{\rule{0.2em}{0ex}}\text{mg/dose}$ Step 4: Convert the milligrams to milliliter $600\phantom{\rule{0.2em}{0ex}}\text{mg/dose}=400\phantom{\rule{0.2em}{0ex}}\text{mg}/5\phantom{\rule{0.2em}{0ex}}\text{mL; x}=(600\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}\times 5\phantom{\rule{0.2em}{0ex}}\text{mL})/400\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}=(\mathrm{3,000}/400)$$=\mathbf{7.5}\phantom{\rule{0.2em}{0ex}}\mathbf{\text{mL per dose}}$
Using dimensional analysis:
$66\phantom{\rule{0.2em}{0ex}}\overline{)\text{lb}}/1\times 1\phantom{\rule{0.2em}{0ex}}\overline{)\text{kg}}/2.2\phantom{\rule{0.2em}{0ex}}\overline{)\text{lb}}\times 40\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}/1\phantom{\rule{0.2em}{0ex}}\overline{)\text{kg}}\times 5\text{mL}/400\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}=\text{mL/day;}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0ex}{0ex}}(66\times 1\times 40\times 5)/(1\times 2.2\times 1\times 400)$ $=(\mathrm{13,200}/880)=15\phantom{\rule{0.2em}{0ex}}\text{mL/day;}\phantom{\rule{0.2em}{0ex}}15\phantom{\rule{0.2em}{0ex}}\text{mL/2 doses}=\mathbf{\text{7.5 mL/dose}}$
Serum Drug Level Dosing
Serum drug level dosing, also known as therapeutic drug monitoring, allows the medication to be dosed according to the amount of drug found in the blood system. This type of dosing is sometimes necessary to ensure safe and effective levels of medications are prescribed. Serum drug level dosing is typically indicated when there is a known relationship between the drug and the serum level, a narrow therapeutic window, high variability in pharmacokinetics, or potential for severe doserelated adverse effects.
Movement of drug molecules within the body based on how the drug is distributed, metabolized, absorbed, or excreted is known as pharmacokinetics. Common drugs that require serum drug level dosing include antiepileptics (phenobarbital, phenytoin, valproic acid), antiarrhythmics (digoxin, procainamide), antibiotics (vancomycin, gentamycin), antimanics (lithium), bronchodilators (theophylline), and immunosuppressants (cyclosporine, tacrolimus).
Nursing Process for Safe Dosage
The nursing process provides a systematic guide for nurses to deliver optimal care. This framework encourages critical thinking and may be applied to all facets of nursing care. This section examines how the nursing process may be applied to clinical practices to ensure safe medication dosages are accurately calculated and administered.
Assessing
The first step of the nursing process is assessment. During the assessment phase, the nurse collects data and utilizes critical thinking skills. For example, the nurse checks the medication record and makes sure the patient’s diet and fluid orders do not interact; for medication administration when a patient is NPO, the nurse looks at the patient’s ability to swallow and checks labs that may affect whether to give medication or not. Using the nursing process for safe dosing, the nurse collects data from the medication order. The data needed to safely dose the medication include the drug name, dosage, route, frequency, and any administration instructions. For example, the nurse may assess that the order is for furosemide (Lasix) 40 mg PO Q12 hours.
Diagnosing
Diagnosing involves utilizing clinical judgment to form a diagnosis that can be used for care. Within medication dosing, diagnosis occurs when the nurse identifies how the medication is supplied. Using the same example, the nurse determines that furosemide (Lasix) is available in 20 mg tablets.
Outcome Identification
Once the problem has been diagnosed, the next step in the nursing process is to identify the intended outcome, or goal. The intended outcome in relation to medication dosing is the amount of medication to be administered to the patient. For example, we could use the ratio proportion method to determine the following medication calculation: $20\phantom{\rule{0.2em}{0ex}}\text{mg}/1\phantom{\rule{0.2em}{0ex}}\text{tablet}=40\phantom{\rule{0.2em}{0ex}}\text{mg}/\text{x;}\phantom{\rule{0.2em}{0ex}}20\text{x}=(40\times 1)\text{; x}=(40/20)\text{; x}=\text{2 tablets}$. Through this calculation, it is determined the outcome (goal) is to administer 2 tablets of furosemide (Lasix). The formula method (D/H × Q) could also be used: $40\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}/20\phantom{\rule{0.2em}{0ex}}\overline{)\text{mg}}\phantom{\rule{0.2em}{0ex}}\times 1\phantom{\rule{0.2em}{0ex}}\text{tablet;}=(2\times 1)\text{;}=\text{2 tablets.}$
Planning
The planning phase involves formulating a plan to achieve the intended goals and outcomes. For example, when calculating the required dose, the nurse may make a mental note or write down that two tablets of furosemide (Lasix) are needed instead of just one. In other cases, the nurse may recognize that additional supplies are needed to ensure the proper dose, such as a pill splitter, syringe, or measuring cup.
Implementing
Once a plan is in place, the next step is implementation. In the case of medication dosing, the planning phase involves the nurse collecting and preparing the required dose. For example, the nurse goes to the patient’s medication drawer or automated dispensing cabinet and removes two tablets of furosemide (Lasix). While preparing the medication, the nurse recalls the “rights” of medication administration by doublechecking to ensure it is the right medication, right dose, right frequency, and right route for the right patient.
Evaluating
Evaluation is a critical component of the nursing process. Within this phase, the nurse should assess the intervention to ensure the desired outcome was achieved. Prior to administering the dose, the nurse must ensure the accurate dose was prepared. The first step in evaluating safe dosages is to confirm the medication calculations. You may ask yourself, “Does this dose make sense?” “Was the calculation set up so that units of measurement were canceled out?” and “Was the correct conversion factor used?” If ever in doubt, ask a colleague to doublecheck the calculation to ensure the dose is accurate. The pharmacist is another excellent resource when questions arise, especially if the pharmacist's calculations differ from those of the nurse. Many times, the pharmacist is available on the specific nursing units.
Patient Education
Patient education is not only a provisional standard of nursing care, but it is also important for enhancing the patient’s knowledge and understanding of their health as well as an explanation of why certain care is being provided. Not only does patient education engage the patient in their care, but it can also reduce errors and improve patient outcomes. For example, the nurse may educate the patient that the provider ordered 40 mg of furosemide (Lasix), the pharmacy only supplies 20 mg tablets, therefore two tablets are being administered to equal the ordered dose. After receiving this education, the patient is then better equipped with an understanding of their dose and may question the nurse if only one tablet is administered next time.
Patient Conversations
Educating Patients on Safe Dosages Prior to Discharge
Nurse: Mrs. Fisher, your provider is sending you home with a prescription for Lasix. Lasix is the “water pill” that you have been getting here in the hospital to help reduce your swelling.
Patient: Oh, that’s the one that makes me go to the bathroom all the time.
Nurse: Yes, Lasix does increase the frequency of urination. Your provider would like you to take 40 mg of Lasix by mouth every 12 hours once you go home from the hospital.
Patient: 40 mg? Is that what I’ve been taking since I’ve been here?
Nurse: Yes, you have been taking 40 mg of Lasix at 6 a.m. and again at 6 p.m. Here in the hospital, we have been giving you two 20 mg tablets to equal the 40 mg that was prescribed. However, once you leave the hospital, you will need to carefully review the information on the prescription label to determine how many pills to take with each dose at home. If the pharmacy gives you 20 mg tablets, then you will take two tablets with each dose. However, if the pharmacy gives you 40 mg tablets, you will only need to take one tablet with each dose. It is important that you take the correct number of tablets to ensure you are getting the right dose of medication. What questions can I help to answer?
Patient: I don’t have any questions at this time.
Nurse: Just to recap, Mrs. Fisher, if the pharmacy supplies you with 40 mg tablets, how many tablets would you take with each dose?
Patient: I would only need to take one pill each time.