Dimensional Analysis Made Easy

How much wood could a woodchuck chuck, if a woodchuck could chuck 557 kilograms per hour, in an eight hour work day. Give answer in megatonnes.

How much wood could a woodchuck chuck if a woodchuck could chuck 15.5 kilograms per minute in an eight hour work day? Give answer in megatonnes.

Dimensional analysis is not the first thing Mr. Spock does when the Starship Enterprise accidentally travels into a new universe or timeline. That is not what we’re here to learn about today.

Unfortunately. Because that sounds interesting.

Instead, we have what is also commonly called “the factor-label method” and simply “unit conversion.” Dimensional analysis is the method that is used to get an answer in the correct units of measurement in problems relating to math, chemistry, and other physical sciences. At its most simple, it can be solving how many minutes are in two hours, or, on the more complex end, it can be finding how many moles there are in three cubic meters of argon.

So are you stuck on your homework? We’ve assembled a few resources to help you with the factor label method.

Play an interactive exploration on Oppia.org teaching the basics of dimensional analysis.

In this video from Brightstorm, dimensional analysis is explained concisely and clearly in three neat examples using what different instructors variously call the picket fence method or the railroad track method.

In this video a dude named Schwanbeck dissects the anatomy of a conversion equation while blasting sick beats, yo.

Study.com presents a video covering both the theory and the practice. It includes an explanation with domino tiles. [Updated 3/30/15. Note: at original publication this resource was free. As of this update, it may require an account.]

And finally, here is an online presentation produced as a supplement to the textbook Chemistry: The Science in Context by Gilbert et al. and published by W.W. Norton & Co.

Good luck, dear student. May all your homework be painless and may all your conversion factors be equal to one. Until next time…


Desire more chemistry help? Master the elements, polyatomic ions, the first ten straight-chained hydrocarbons, and other topics at Study Putty.

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Image credit: “Groundhog-Standing2.jpg” by April King, under GNU Free Documentation License.

About Bret Norwood

Bret Norwood is a staff blogger for Learning Laboratory in addition to other roles, including UI design and content development for Study Putty, our free memorization tool for chemistry and many other course topics. He is also a published writer of literary fiction--see BretNorwood.com
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