# What is the correct percent difference formula?

While googling for percent difference formulas, I got two different formulas:

1. (difference/old-value)$\times 100$.
2. (difference/average)$\times 100$.

So, for $6$ and $9$, the first one gives $-33$ and the second gives $-40$. Which one is correct and when is either formula used?

It depends on what you are trying to do.

If you start out with $6$ and then it increases to $9$, and you want to know by how much the original value increased (or decreased), then you use **[(new value - old value)/old value] * 100. So, here, it would be $\dfrac{9 - 6}{6}*100 = \dfrac{3}{6}*100 = 50$%. (If when using this formula, your percent is a negative number, then that is the percentage it decreased by.

(difference/old-value)×100 is the most commonly used formula, but isn't ideal for all situations.

(x-y/f(x,y))×100 is the generic percent difference formula, and what you put for f(x,y) could vary depending on your goals. This is especially of concern if you're dealing with negative numbers or doing further math on the percentages.

Several common choices for the function f(x, y) would be:

max(|x|, |y|),

max(x, y),

min(|x|, |y|),

min (x, y),

(x + y)/2, and

(|x| + |y|)/2.