What Is Dimensional Analysis?

Dimensional analysis is a method that uses conversion factors to move from one unit of measurement to another. This is because multiplying any number by 1 doesn't change its value. An example is calculating the amount of seconds in a day, done by multiplying one day by the conversion factor 24 hours and again by the factor 60 minutes and again by the factor 60 seconds.

Conversion factors are equal to 1 due to the rules of algebra. For example, since both days and hours are units of time, by stating 24 hours is equal to one day, and dividing both sides by one day, the left side becomes the ratio for the conversion factor. Using algebra fundamentals, this ratio of 24 hours (one day), equals 1. Multiplying this factor by the number of days eliminates the unit "day," and the quantity is now expressed in hours. Dimensional analysis is useful in physical science, chemistry and engineering, where quantities are expressed in different units that need to be compared. This is especially true in physics, which uses derived units that contain two or more separate units of measurements. For example, 1 Newton (unit of force) is equal to one kilogram x meter/second^2.