Dimensional Analysis

Treating Units Like Variables

You can multiply and divide units much like you can algebraic variables (see derived units). You can use this property to your advantage with certain problems, especially ones that require unit conversions. Dimensional analysis is a method of solving a problem where you use units as a guide to set up the necessary steps. When using dimensional analysis, you start by looking at what given values you have and their units and apply a conversion factor in order to cancel out unwanted units and add new units. More complicated problems will require multiple conversion steps, but the goal is to end up with units that are compatible with the answer that you are looking for. For example, if you you start with 100 g of a methane (a flammable gas), and you want to find the amount of energy released when the 100 g of methane are burned, you would find conversion factors that would cancel out the units of mass and eventually work your way toward units of energy, such as joules or calories.

Examples