Unit Analysis

In physics, it is not uncommon to change from one system of measurement to another. The best method to accomplish this change is unit analysis.

In physics calculations, the units are very important and must be treated in the same way as constants and variables are treated in algebra.

Notice in the example how the units multiply, divide and cross cancel just like numbers and variables.


Physics calculations require close examination of the units. Therefore, you must know the conversion factors that allow you to make the desired calculations.

Common Conversion Factors

 1 inch = 2.54 centimeters  1 foot = 12 inches  1 pound = 454 grams
 1 liter = 1.057 quarts  1 yard = 3 feet  1 hour = 60 minutes
 1 calorie = 4.18 joules  1 mile = 5,280 feet  1 minute = 60 seconds
 1 atm = 101.3 kilopascals  1 mile = 1,760 yards  1 pound = 16 ounces
This Per That Problems

The common type of physics problem is a "this per that" or what is called a conversion problem. An example of a this per that would be 12 inches per 1 foot.

The hardest part of a this per that is knowing the conversion factor (this per that). Once you know the conversion factor all you have to do is set up the equation, verify your units, and plug&chug (put it in the calculator).


There are 500 monkeys and you can put 5 monkeys in a cage.
How many cages will you need?

500 monkeys 5 monkeys per cage How many cage?

Reasoning tells me that if I divide 500 by 5 I will need 100 cages.

this per that

The above example is a this per that problem and similar in logic to the types of problems you will do in physics. So, let's look at it set up like a physics problem.

this per that

 Notice that monkeys cancel out and cages is our new unit.