I feel like an idiot for asking this but i can't get my formula to work with negative numbers
assume you want to know the percentage of an increase/decrease between numbers
2.39 1.79 =100-(1.79/2.39*100)=> which is 25.1% decrease
but how would i change this formula when there are some negative numbers?
6.11 -3.73 =100-(-3.73/6.11*100) which is 161% but should be -161%
the negative sign is lost.. what I am missing here?
also
-2.1 0.6 =100-(-3.73/6.11*100) which is 128.6% ??? is it?
3 Answers
Perhaps this "formula" will be easier to understand (this formula is equivalent to your formula - each can be derived from the other):
$$\dfrac{\text{original value} \;- \;\text{final value}}{\text{original value}} \times 100\% = \text{percent change}$$
That change will be
an increase if the original value is less than the final value,
a decrease if the original value is greater than the final value.
Original value $6.11$, final value $-3.73$:
$$\dfrac{6.11 -(-3.73)}{6.11}\times 100\% \approx 161\% \;\;\text{DECREASE}$$
Original value $-2.1$, final value $0.6$:
$$\dfrac{-2.1 - 0.6}{-2.1}\times 100\% \approx 128.6\% \;\;\text{INCREASE}$$
I know this is a very old thread, but I am here for the first time so I hope it is OK to comment.
Let's take an example:
Original value $-10$, final value $10$:
$\frac{Original\ value - Final\ value}{Original\ value} = 200\% \ increase $
Original value $-1$, final value $10$:
$\frac{Original\ value - Final\ value}{Original\ value} = 1100\% \ increase $
How can an increase from a smaller number ($-10$) to $10$ be a lesser percentage than an increase from a larger number ($-1$) to $10$?
I’m not a mathematician, but I don’t think percent change with values of opposite signs is defined.
See also:
(the section named Net Income)
Conventional Formula
The conventional formula for computing the relative growth between two values $a$ and $b$ is $\displaystyle \frac{b-a}{a}$.
For example, if $a = 50$ and $b = 60$, the relative growth is $\displaystyle \frac{60-50}{50} = 0.2 = 20\%$.
So far, so good. But what if $a$ and $b$ have different signs? For example, $a = -10$ and $b = 20$?
The conventional formula would return a negative growth of $-300\%$, which does not make much sense.
