# How to calculate the percentage of increase/decrease with negative numbers?

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?

• I don't see what's wrong here? For your second one it's a 161% decrease not a -161% decrease. – Module Mar 18 '14 at 13:28
• The Wikipedia page Relative change and difference has more on this. – Ninjakannon May 15 '15 at 23:10

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 $0.6$:

$$\dfrac{-2.1 - 0.6}{-2.1}\times 100\% \approx 128.6\% \;\;\text{INCREASE}$$

• Thank you for you answer...BUT why then ((6.11-(-3.73))/6.11)*100 gives 161 indicating an increase - but (((-3.73)-(-10.85))/(-3.73))*100 gives -190.9? Does that mean that with 2 negative numbers this equation does not apply? – master of puppets Mar 18 '14 at 15:31
• The important thing to look at is how the original value and the final value compare: If the original value is greater than the final value, then the absolute value of the the result indicates the percent decrease. If the original value is less than the final value, then the absolute value of the result indicates the percent increase. – Namaste Mar 18 '14 at 15:44
• thanks I am accepting your answer, the bit I could not understand trying to rewrite this algorithm was the signs. I decided to reverse the signs for further calculation ( another library that uses the algorithm ) and everything works fine now. Also I needed to handle 0s but thats not part of the question. thanks – master of puppets Mar 18 '14 at 16:26
• You're welcome. Glad things are working for you! – Namaste Mar 18 '14 at 16:28
• With the formula $$\frac{final-original}{|original|}$$ you have always a meaningful result, though a bit counterintuitive when final and original have not the same sign. Your definition above would not work if final and original have the same sign (the sign of percent change is reversed). – Jean-Claude Arbaut Sep 24 '14 at 8:48

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.

(the section named Net Income)

• If it is defined, what is, according to you, the explanation that an increase from a smaller number to x can be a lesser percentage than an increase from a larger number to x. And what is your position on the Wall Street Journal article I linked to. Are they completely wrong? – Hans Knudsen Sep 23 '14 at 16:15
• Would you then be so kind as to tell me what you think about the section Net Income in the WSJ-article? I take it you will not claim that it is a completely unreliable site. – Hans Knudsen Sep 23 '14 at 19:34
• Maybe you should take a look here before being so cocksure - and that's it for my part. mathforum.org/library/drmath/view/55720.html – Hans Knudsen Sep 24 '14 at 8:27
• I agree that speaking of percent increase or decrease when original and final values are not of the same sign is dangerous and counterintuitive. However, you can always define the relative variation as $$\frac{B-A}{|A|}$$ if $A\neq0$. That's (along with sens of subtraction) the missing absolute value that is causing trouble in amWhy's answer, I didn't pay enough attention to it. With this, you get $-161%$ and $+128%$ respectively, so the decrease/increase is ok. And +1 of course. – Jean-Claude Arbaut Sep 24 '14 at 8:45
• And really sorry for my misunderstanding of your answer. Even though I use often (constantly I may say) such percentages for work, with correct formula, I managed to get it wrong mentally when reading answers here. How uncomfortable :/ – Jean-Claude Arbaut Sep 24 '14 at 8:52

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