# Percent Increase vs. Factor By Which Something Increases

I would appreciate a quick peer check on the following.

I am currently enrolled in a class where, I think, the professor is repeatedly confusing percent increase and factor by which something increases.

There is a difference isn't there? I'm not going crazy here am I?

As I understand it, to calculate the percent increase I would do:

$$IV = initial \; value\\ FV = final \; value\\ Assume \; FV > IV\\ \% \, Inc. = \left( \frac{FV - IV}{IV} \right) * 100 = \left( \frac{FV}{IV} - 1 \right) * 100$$

If I want the factor by which the value increased with respect to the initial value I would take the ratio of the final value to the initial:

$$Inc. \; Factor = \frac{FV}{IV}$$

To reiterate, these are not the same things. I just want to make sure I'm not confusing anything before I point it out to him and ask for clarification.

• You are correct they are different - a factor of 2 is a 100% increase or a 50% decrease. But they are so closely related - and trivially interchanged - that it's a good idea not to get hung up on the precise terminology and lose sight of the basic idea being communicated. Feb 14 '17 at 11:45
• Good comment, thanks for the advice. I won't be asking my professor for clarity. You both helped me see the bigger picture. Thank you. Feb 17 '17 at 16:46

Yes, what you show is correct.

For example, a value going from 8 to 12 is a 50% increase. You can also say it was increased by a factor of 1.5.

People sometimes get a little sloppy with this. If it's clear enough from context what the professor really means, I would let it go. If you're the professor, it's OK to insist your students use the terms correctly. When you're the student, it's better to reserve picking a fight for something more important.

• Wise words. I appreciate the comment and I will be keeping any clarifications I had for my professor to myself. Thanks for the advice and the peer check. Feb 17 '17 at 16:46