# Dose Calculation Dimensional Analysis Factor-Label Method

#### Introduction

Three primary methods for calculation of medication dosages exist, and these include dimensional analysis, ratio proportion, and formula or desired-over-have method. This article explores dimensional analysis in more detail.

Dimensional analysis, as the name represents, explores dimensions or units of measurements called factors. Commonly used in solving chemistry and physics problems, dimensional analysis is fast becoming the go-to method for dosage calculations in nursing and the medical profession.

One equation leads to the answer. Clinicians do not need to memorize this complicated formula. Chances for error are diminished, thus increasing the popularity of these dosing calculations. More than one approach can be used to build an equation using this factor-label method.[1][2]

#### Indications

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#### Indications

A formula is used to calculate the dose of a drug, often utilized when converting different units of measurements such as pounds to kilograms or kilograms to grams.

The dimensional analysis approach or the factor-label method can be used to provide an additional safety check with the other methods of calculation. The correct dose should be the same regardless of the method for dosage calculation applied.

#### Contraindications

Converting degrees Celsius to degrees Fahrenheit is not possible with this unit-factor method of calculation. A comparison is not feasible between units that have different dimensions and do not have a linear relationship.

#### Preparation

Preparing for the need for conversion factors if measurement units are different is essential to use this form of dosage calculation properly. For multiplication and division to be accurate, strategic placement of the units of measure is vital, and its exploration occurs in the proper technique of setting up a long equation in the next section.

#### Technique or Treatment

**Dimensional Analysis or Factor-Label Method**

First, one must organize these elements or units used to express size into fractions. This section examines the definition of a factor/element and its relationship to drug calculations. A relationship began on the fundamental principle that a factor is a unit of measurement or amount that is closely related; 10 mg/mL or 1 tablet/200 mg or 5 mcg/5 mL.

Second, clinicians must write these elements in such a way that they can get to the answer or unknown quantity (dose). Form an equation using a fraction to denote factors needed to multiply or cancel out. In the Dimensional Analysis Approach or Factor-Label Method, as it is also known, clinicians use factors to multiply and divide to get the answer. This method of drug calculation can be employed with other methods of calculation to determine if an answer is logical or makes sense.

Basic math or chemistry constructs a fraction with a numerator (top) number and a denominator (bottom) number. Factors (units of measurement) are placed in the primary locations in the fraction so that like units cancel out, and the desired units of measurement/factors remain. Placement of units or factors in the correct spot in the equation is critical for accurate results. One cannot have the same unit of measurement in both top or bottom numbers, numerators, or denominators, or they will never cancel out.

Any individual unit of measure, the amount you want to figure out, is placed over a denominator of one. The equation conceived at this point then grows into a solvable, single line of fractions, each multiplied across numerators and divided across the denominators. Ultimately, the birth of a desired dose or amount is the result.

An example, using an order placed by a provider for lorazepam 4 mg IV PUSH for CIWA score of 25 or higher, follow CAGE Protocol for subsequent dosages based on CIWA scoring.

- The supply is with 2 mg/mL vials in the automated dispensing unit. How many milliliters are needed to arrive at the ordered dose?
- The desired dose gets placed over 1. Remember, (x mL) = 4 mg/1 x 1 mL/2 mg x (4)(1)/2 x 4/2 x 2/1 = 2 mL, the clinician kept multiplying/dividing until they got the desired amount, 2 mL in this problem example.
- Notice, the fraction was set up with mg and mg strategically placed so like units could cancel each other out, making the equation easier to solve for the unit desired (milliliters). The answer seems plausible, so the work is done.

Zeros can be canceled out in the same way as like units. For example:

- 1000/500 x 10/5 = 2, the 2 zeros in 1000 and 2 zeros in 500 can be crossed out since like units in numerator and denominator, leaving 10/5, a much easier fraction to solve, and the answer makes sense.

Zeros have been addressed, and now, look at 1.

- If you multiply a number by a 1, then the number is unchanged. In contrast, if you multiply a number by zero, the number becomes zero.
- Examples listed below are as follows: 18 x 0 = 0 or 20 x 1 = 20.

#### Complications

According to Williams and Davis, math anxiety may play a role in the accuracy of dosage calculations and ease in which carried out; however, based on limited research in this area, results are inconclusive. The assumption that when a clinician is anxious, their thought processes are potentially interrupted, causing memory lapses, leading to inaccurate dosage calculations. Inaccuracy and inability to problem solve further heighten the distress of the individual, leading to additional anxiety. A vicious cycle of math anxiety and dosing calculation errors may ensue.[3]

#### Clinical Significance

Calculating the correct dose is crucial as the consequences of error can be devastating. Picking one method and becoming skilled at this method is essential for patient safety.

The dimensional analysis method is easy to grasp and assures that clinicians provide the patient with an accurate dose.

Today's technological advances assist healthcare providers in safe medication administration, for example, prefilled medication syringes, adapter-based safety injection systems, multi-infusion systems, electronic medication reconciliation records, barcode scanning, and automatic dose configurations by pharmacists.[4] However, these advances do not take away from the importance of knowing basic medical math and dosage calculations.

High-risk medications such as heparin and insulin often require a second check on dosage amounts by more than one provider the drug is administered. Follow institutional policies and recommendations on the confirmation of dose calculations by another licensed provider.

#### Enhancing Healthcare Team Outcomes

When calculating doses of medications, the pharmacist and nurse should always double-check and cross-check to ensure that the right numerical values and formulas have been used.

#### References

Yang Y, Xing L, Boyer AL, Song Y, Hu Y. A three-source model for the calculation of head scatter factors. Medical physics. 2002 Sep:29(9):2024-33 [PubMed PMID: 12349923]

Shin HC. On a scale as a sum of manifest variables. Annals of epidemiology. 2018 Oct:28(10):736-738. doi: 10.1016/j.annepidem.2018.08.003. Epub 2018 Aug 9 [PubMed PMID: 30143354]

Williams B, Davis S. Maths anxiety and medication dosage calculation errors: A scoping review. Nurse education in practice. 2016 Sep:20():139-46. doi: 10.1016/j.nepr.2016.08.005. Epub 2016 Aug 22 [PubMed PMID: 27589091]

Level 2 (mid-level) evidenceCho YC, Lee SH, Cho YH, Choy YB. Adapter-based Safety Injection System for Prevention of Wrong Route and Wrong Patient Medication Errors. Journal of Korean medical science. 2017 Dec:32(12):1938-1946. doi: 10.3346/jkms.2017.32.12.1938. Epub [PubMed PMID: 29115074]