# Dimensional analysis

Dimensional analysis is a method for converting one unit to another using the relationships between various physical quantities. Dimensional analysis is a skill that is used widely in science and engineering. It can help with understanding how to convert between different units of measurement.

Converting between different units of measurement typically involves the use of a conversion factor. When you convert between different units of measurement, you are using dimensional analysis, even if you are not doing so explicitly.

Examples

1. In the United States, weight is most commonly referenced in terms of pounds. In most other countries, kilograms are used instead. In order to convert from pounds to kilograms, or vice versa, we use a conversion factor that relates pounds and kilograms, along with dimensional analysis.

1 kilogram ≈ 2.2 pounds

We can rearrange this relationship and say that there are 2.2 pounds per kilogram, where the "per" indicates division:

This is the conversion factor we can use to convert betweeen these two measurements of weight. Convert 135 pounds to kilograms using dimensional analysis:

The unit of pounds cancels out, leaving us with just kilograms.

2. Time is another quantity that we convert frequently. There are 60 seconds in one minute, 60 minutes in 1 hour, and 24 hours in 1 day. Convert 1.5 days to minutes:

As can be seen from the examples above, dimensional analysis, though sometimes tedious, can be very helpful for helping us see the relationships between various quantities, as well as for converting quantities from one to another using basic algebra.

### Did you know?

In science and engineering, it is common to perform dimensional analysis to confirm that a derived equation or computation has the expected dimensions. If it does, then it makes the result more plausible. If however, the dimensions are not the expected dimensions, it is likely a mistake was made along the way.