How To: Dimensional Analysis

Dimensional Analysis

What Is Dimensional Analysis?

Dimensional analysis is used to convert units. It's the process of analyzing units to decide which conversion factor to use. It's used by multiplying units by conversion factors, rates equal to 1.

How Do We Use Dimensional Analysis?

Let's say, for example, we are told to answer the question : Sixty miles/ hour is how many ft/sec? We use conversion factors to solve this problem. We multiply 60 miles/1 hour · 5280 feet/1 mile · 1 hour/60 minutes · 1 minute/ 60 seconds. Then, we cross cancel the units, and remember, don't cross out the number - only cross out the units. Since we are looking for the number of feet per second, make sure you do not cross out those units. Instead, circle them to remind you not to cross them out. After cross canceling units, we are left with 60/1 • 5280 feet/1 mile • 1/60 • 1/60 seconds. After multiplying them, we get 316800/3600. Then it needs to be simplified, which is 88/1. Do not write the answer as 88/1. Remember the units we circled? Those are needed for the final answer. Since feet is on the top and seconds is on the bottom, we know that the final answer is 88 feet/1 second.

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