# Computing Percent Differences

Information consists of the differences that make a difference.

— Edward Tufte

I have recently been computing a lot of percentage differences – mainly in variance calculations. I have been using the formula that I was taught in 7th grade, namely $\displaystyle \Delta\%=\frac{N-O}{\text{O}}$

where

• N is an updated or new number.
• O is the original number.
• Δ% is the percentage change.

I recently discovered that this formula fails miserably when dealing with negative quantities – I had never considered what happens when the O variable is negative.

Consider the case when O = -4 and N = -2. This should reflect a positive improvement of 50%, but instead the sign is negative. $\displaystyle \Delta\%=\frac{-2--4}{-4} = \frac{2}{-4}=-50\%$

Looks like I have been computing percent differences incorrectly since 7th grade. Here is how I am going to compute percent differences going forward. $\displaystyle \Delta\%=\frac{N-O}{\left| O \right|}$

I did a bit of googling and some folks prefer to the use the sign instead of the absolute value function in their percent difference formula (example).

This entry was posted in Financial. Bookmark the permalink.