# 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).

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