5.6 Using Dimensional Analysis

A common method used to perform calculations with different units of measurement is called dimensional analysis. Dimensional analysis is a problem-solving technique where measurements are converted to equivalent units of measure by multiplying a given unit of measurement by a fractional form of 1 to obtain the desired unit of administration. This method is also referred to as creating proportions that state equivalent ratios. Equivalencies described in Section 5.7 are used to set up ratios with the fractional form of 1 to achieve the desired unit the problem is asking for. The units of measure that must be eliminated to solve the problem are set up on the diagonal so that they can be cancelled out. Lines are drawn during the problem-solving process to show that cancellation has occurred.^[1]

When setting up a dosage calculation using dimensional analysis, it is important to begin by identifying the goal unit to be solved. After the goal unit is set, the remainder of the equation is set up using fractional forms of 1 and equivalencies to cancel out units to achieve the goal unit. It is important to understand that when using this problem-solving method, the numerator and denominator are interchangeable because they are expressing a relationship.^[2] Let’s practice using dimensional analysis to solve simple conversion problems of ounces to milliliters in Section 5.7 “Conversions” to demonstrate the technique.