What is covered on this page →
Converting between Arabic and Roman Numerals.
Understanding the systems of measurement in pharmacy.
Accuracy and precision in pharmacy calculations.
Considerations for safety and accuracy in dosing.
Mastery of pharmacy calculations is an essential foundational skill in pharmacy practice, serving as the bedrock upon which safe and effective patient care is built. These calculations encompass a range of tasks, from determining medication dosages to preparing compounded formulations, and are crucial for protecting the public’s health. Accuracy in pharmacy calculations is paramount. A minor error in dosage or formulation can have severe consequences for patient well-being. Incorrect calculations can lead to underdosing, rendering a medication ineffective, or overdosing, potentially causing injury to health or even death.
Pharmacists play a pivotal role in ensuring the safe and effective use of medications. They must meticulously calculate and double-check dosages, especially for high-risk populations such as children, the elderly, and patients with chronic illnesses. Incorrect calculations can result in adverse drug reactions, reduced treatment efficacy, or medication-related problems that compromise patient safety. Furthermore, compounding pharmacies within community and hospital settings rely heavily on precise calculations to customize medications for individual patient needs. Errors in compounding can lead to inconsistent potency, contamination, or even toxic formulations, putting patients at risk.
Learners must understand, pharmacy calculations are foundational to pharmacy practice, with their importance rooted in patient safety. Accurate calculations are vital for preventing medication errors, protecting the public from harm, and ensuring that patients receive the right treatment at the right dosage. Pharmacists, pharmacy technicians and other support staffs must continuously hone their calculation skills to fulfill their responsibility in safeguarding the health of the public.
Numbering Systems in Pharmacy
Roman numerals and the Arabic numbering system (also known as the Hindu-Arabic numeral system) are two distinct methods of representing numbers. Each system has its own set of symbols and rules for representing numbers.
Roman Numerals
Roman numerals use a combination of letters from the Latin alphabet to represent numbers. The basic symbols are:
Note carefully
The Roman numeral abbreviation “ss” for 1/2 is not a standard Roman numeral abbreviation. The Latin term semis meaning one half has been associated with roman numerals and represented as such in some medical literature or text. However, Roman numerals are typically used for whole numbers, and fractions were not represented using Roman numerals in the same way they are in modern decimal notation.
If you encounter “ss” in a Roman numeral context, it is likely an informal or non-standard representation for 1/2, but it does not have an official counting designation. Roman numerals were primarily used for counting whole units, not fractions.
Roman numerals are usually written in additive form, where you add the values of the symbols together to get the total [symbols are read from left to right].
Example
XVII = 10 + 5 + 1 + 1 = 17
DCXV = 500 + 100 + 10 + 5 = 615
However, subtractive notation is also used in certain cases, where a smaller value is placed before a larger value to indicate subtraction [symbols are read from left to right].
Example
XIV = 10 + (5 – 1) = 14
CMXXIX = (1000 – 100) + 10 + 10 + (10 – 1) = 929
Roman numerals are often used in formal contexts, such as numbering chapters in books (e.g., Chapter II) or representing the year on the copyright page (e.g., MMXXI for 2021). They are not well-suited for arithmetic calculation. In modern pharmacy practice Roman numerals are not typically used as a primary numerical system. The Arabic numbering system (symbol 0 – 9) is the standard numerical system used in pharmacy and healthcare settings worldwide. This system is far more practical for accurately representing dosages, quantities, and measurements, as well as for conducting precise calculations, which are essential in pharmacy. However, Roman numerals may have limited and specialized uses in pharmacy or healthcare. In some cases, prescription doses, historical pharmaceutical documents or recipes may use Roman numerals for dosages or measurements. Pharmacists and researchers may need to interpret these documents accurately to understand historical and contemporary practices.
Arabic Numbering System
The Arabic numbering system uses ten symbols (0 – 9) to represent numbers. These symbols are used to create all other numbers. The Arabic system relies on the concept of place value, where the position of a digit in a number determines its value. Similarly to Roman numerals the string of symbols is read from left to right.
Example
123, the “1” represents one hundred, the “2” represents two tens (twenty), and the “3” represents three ones (three). Figure 1.1 provides visual representation of the Hindu-Arabic numbering system.
The Arabic system is highly efficient for arithmetic calculations, making it well-suited for everyday use. It allows for easy addition, subtraction, multiplication, and division. The Arabic numbering system is the standard numerical system used worldwide for most mathematical, scientific, and practical applications.
Roman numerals are a historical numeral system with limited modern-day applications, often used for formal or decorative purposes. In contrast, the Arabic numbering system is the universal standard for everyday mathematics and is highly efficient for performing mathematical operations. The Arabic system’s simplicity and versatility have made it the preferred choice for most numerical needs across the globe.
Systems of Measurement in Pharmacy
Table 1.2 Historic and Contemporary Systems of Measurement in Pharmacy practice
The Apothecaries System of Measurement
The Apothecaries’ system, also known as the apothecary system or apothecaries’ weight, is an older system of measurement used in pharmacy and medicine for dosing and measuring various substances. While it has largely been replaced by the metric system in most countries, it still has some historical significance and is occasionally used in the United States and a few other places.
The Apothecaries’ system uses various units for measuring different substances, including weight and volume. The base units of measurement include grains (gr) for wight and, minims (m) for fluid measure. See conversion table 1.2 for additional details. There is no measurement for length in this system.
The Apothecaries’ system was historically used by pharmacists and physicians in the United States and other countries for prescribing and compounding medications. It was commonly used for measuring ingredients in tinctures, solutions, and other pharmaceutical preparations.
In the late 20th century, many countries, including the United States, transitioned to the metric system for pharmaceutical and medical measurements due to its simplicity and worldwide standardization. While the Apothecaries’ system is no longer the primary system in use, it is important for pharmacists and healthcare professionals to understand it, as some older medical texts and prescriptions may still use these units. Though outdated, historical references and some traditional medicine formulations may still use the Apothecaries’ system units.
Avoirdupois System of Measurement
The avoirdupois system is a system of measurement used for measuring weight or mass in most English-speaking countries, including the United States. It is the most common system of measurement for everyday items and commodities. The term “avoirdupois” comes from the Old French term “aveir de pois” (goods of weight) and was historically used for trading goods.
The basic unit of weight in the avoirdupois system is the pound, abbreviated as “lb.” See table 1.2 for additional details. There is no measurement or volume and length in the Avoirdupois system. In the United States, it is commonly used for measuring the weight of people, animals, food items, and many other everyday objects.
While pounds and ounces are the primary units, the avoirdupois system can be further subdivided into smaller units like grains (1 pound = 7,000 grains) and drams (1 dram = 256 grains). These smaller units are more commonly encountered in the apothecaries’ system, which is used in pharmacy and medicine.
The avoirdupois system is used in the United States, Canada, and several other countries for most everyday weight measurements, including commerce and trade. In scientific and technical fields, the metric system is often preferred for its ease of use and international standardization. While the avoirdupois system is still commonly used in daily life, many countries have officially adopted the metric system for scientific, industrial, and legal purposes. Conversion factors are used to convert between the avoirdupois and metric systems when necessary.
Converting between Systems of Measurement
Express the following in grains using the Apothecaries system of measurement:
Expression 1
ʒ XIV ℥ IISS gr CMLVII
Step 1- Roman numerals are not suited for arithmetic operations hence, convert values to Hindu-Arabic.
ʒ XIV ℥ IISS gr CMLVII
= ʒ 10+(5-1) ℥ (1+1+1/2) gr (1,000-100)+50+5+1+1
= 14 ʒ 2.5 ℥ 957 gr
Step 2- Covert the different units to the basic unit of measure ‘grains’ in Apothecary.
From table 1.2 → 60 grains = 1 drachm
If, 60 gr = 1 ʒ
then, X gr = 14 ʒ → X = 840 gr
From table 1.2 → 480 grains = 1 ounce
If, 480 gr = 1 ℥
then, X gr = 2.5 ℥ → X = 1,200 gr
Add all the weights
840 gr + 1,200 gr + 957 gr = 2,997 gr
Let’s play a little more ☺!
I have 2,997 grains of Talcum for manufacturing. My machine has a capacity of 75 kg. How much Talcum will I need to acquire to manufacture one full batch of Talcum dusting powder?
Hint: The common unit of measure in Apothecaries and Avoirdupois is the ‘grains’.
Step 1 – Convert Kilograms to Grains
From table 1.2- 1 kilograms = 2.2 pounds
If, 1 kg = 2.2 lb
then, 75 kg = X lb → X = 165 lb
From table 1.2- 1 pound = 16 ounces
If, 1 lb = 16 oz
then, 165 lb = X oz → X = 2,640 oz
From table 1.2- 437.5 grains = 1 ounce
If, 437.5 gr = 1 oz
then, X gr = 2,640 oz → X = 1,155,000 gr
the capacity of the dusting powder machine is 1,155,000 grains.
Step 1 – Find the additional amount of Talcum needed for one batch
If 1 batch requires 1,155,000 gr
and the available stock is 2,997 gr
The additional amount of Talcum needed is
= 1,155,000 gr – 2,997 gr
= 1,152,003 gr
Things to note
The grains is the common unit of measure between Apothecaries and Avoirdupois. The Avoirdupois is used for mass or weight only. There is no reference units for length in Apothecaries or Avoirdupois.
The unit of measure for the UK and US metric system are similar however, their values are different. Conversions can be readily made among Apothecaries, UK-Metric and US-Metric.
The operator should denote the system of measurement to reduce the risk for ambiguity and errors.
Accuracy and Precision in Pharmacy Calculations
Accuracy in pharmacy calculations is of paramount importance due to several critical factors that directly impact patient safety, healthcare outcomes, professional trust, and legal liability. The pharmacy profession bears the responsibility of ensuring that medications are dispensed accurately and in the correct doses, as drugs, in essence, are potent substances with the potential to both heal and harm.
Patient Safety and Well-being
One of the foremost reasons for the emphasis on accuracy in pharmacy calculations is the well-being and safety of patients. Medications have the power to treat various health conditions, but they can also act as poisons when administered incorrectly. A miscalculation in dosage or formulation can result in severe health consequences, including toxic overdoses, adverse reactions, or inadequate therapeutic effects. Patients rely on pharmacists to provide them with the right medications in the right amounts to facilitate their recovery and manage their conditions safely.
Trust in the Healthcare Professionals
Patients place a high degree of trust in pharmacists as experts in medication management. This trust can create an imbalance in the pharmacist-patient relationship, where patients often rely on the pharmacist’s knowledge and expertise without question. Any mistake in pharmacy calculations can lead to a breach of this trust, undermining the patient’s confidence in the healthcare system. Patients may become more vulnerable to harm when they assume that the medications they receive are accurate and safe, as they are less likely to question their healthcare providers.
Legal Consequences and Professional liabilities
Accuracy in pharmacy calculations is not only crucial for patient health but also for the legal and ethical standing of the profession. Errors in dosage or formulation can result in serious harm to patients and may lead to legal actions against pharmacists and healthcare institutions. Such legal cases can have far-reaching consequences, including the tarnishing of reputations, financial penalties, and professional sanctions. Therefore, pharmacists and pharmacy institutions must prioritize accuracy to minimize the risk of legal disputes and liabilities.
Accuracy in pharmacy calculations is fundamental to safeguarding patient health and trust in healthcare professionals. The consequences of inaccuracies in medication dispensing can be severe, ranging from patient harm to legal and professional repercussions. It is imperative that pharmacists and pharmacy teams adhere to strict protocols and quality control measures to ensure precision in every step of the medication dispensing process.
Factors Contributing to Errors in Practice
All pharmacy staff must be mindful of various factors that contribute to errors and take proactive steps to mitigate them. By being mindful of these factors and actively addressing them, pharmacists can significantly reduce the risk of errors in their practice and enhance patient safety. Continuous education, quality improvement initiatives, and a commitment to patient-centered care are essential elements of error prevention in pharmacy practice.
Work Environment
The work environment in a pharmacy can be fast-paced and high-pressure, which may increase the likelihood of errors. Factors such as interruptions, distractions, noise, and crowded workspaces can divert a pharmacist’s attention away from important tasks. Pharmacists should strive to create a conducive work environment by minimizing distractions, organizing their workspace efficiently, and implementing strategies to manage interruptions.
Workload and Fatigue or Burnout
Excessive workload and long hours can lead to pharmacist fatigue and burnout. Fatigue impairs cognitive function, attention, and decision-making abilities, increasing the risk of errors. Pharmacists must manage their workload effectively, take regular breaks, and prioritize self-care to reduce the impact of fatigue. Additionally, pharmacy employers should ensure reasonable staffing levels to prevent overburdening their staff.
Technical Competence
Pharmacists should have a strong foundation of technical competence, including knowledge of medications, drug interactions, dosage calculations, and compounding techniques. Continuous education and training are essential to stay updated with evolving pharmaceutical practices. Understanding one’s strengths and weaknesses is critical. When faced with tasks or situations beyond their training or skill level, pharmacists should seek guidance from colleagues, mentors, or refer patients to specialists when necessary. It’s essential to recognize when to ask for help and not hesitate to do so.
Medication Dispensing Systems
Errors can occur in the use of automated medication dispensing systems and technology. Pharmacists and pharmacy staff should be well-trained in the operation of these systems, conduct regular maintenance checks, and have contingency plans in place in case of system failures.
Communication and Handoff Errors
Miscommunication between healthcare providers, pharmacy staff, and patients can lead to errors. Effective communication is crucial for accurate medication dispensing. Pharmacists must ensure that they understand and convey information clearly, particularly when discussing drug instructions, allergies, and potential side effects. They should also pay attention to handoff procedures when transferring patient care responsibilities
Quality Assurance and Double-Check Systems
Implementing quality assurance measures, such as double-triple-check systems for high-risk medications, can help catch errors before they reach the patient. Pharmacists should adhere to established protocols for verification and double-checking, particularly for high-alert medications. Prescriptions are checked at data entry, during picking and packing, and finally by the pharmacist before packing for patients. Other pharmacy staff also play a critical role in this process to ensure the right product get to the right patient.
Documentation Errors
Accurate documentation of medication dispensing and patient counseling is essential for patient safety and legal compliance. Pharmacists should maintain meticulous records to track medication orders, dispensing, and patient interactions. It is also crucial to document errors in dispensing because this information can inform significant process improvements and quality control measures. These documented errors will also provide valuable insights for risk mitigation strategies.
References
American Pharmacists Association. (2015). Medication Errors. PharmacyLibrary. Link
Strand, L. M., Morley, P. C., Cipolle, R. J., Ramsey, R., & Lamsam, G. D. (1983). Drug-related problems: Their structure and function. The Annals of Pharmacotherapy, 17(6), 802-803. DOI: 10.1177/106002808301700605
By: Dwight L. Baker (BPharm, MBA, MPH, Dip.Ed.)
Published: 2023- Sept- 14, Last updated 2024- Jan- 14