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I am trying to work out the percentage difference between two numbers (one of which is negative), NOT PERCENTAGE CHANGE. I have done quite a bit of reading, but there doesn't appear to be a definitive answer. Where both numbers are positive, I have been using the formula listed on the following site (https://www.calculatorsoup.com/calculators/algebra/percent-difference-calculator.php). If both numbers are negative, I simply input the absolute values, making them positive. I have issues arise when one of the numbers is negative - for instance:

The percentage difference between 1.6 and -8.8. If I use the formula in the link above, it provides me a result of -293%, but I'm not sure if this is correct - from a methodological stand point. Is this something that would be frowned upon in the mathematics world?

Cheers, Bosshard

BossHard
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  • You can always take the percentage difference of their absolute values. – K.defaoite Dec 23 '20 at 00:31
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    The calculator used a weird definition. My definition would have only the original number in the denominator. This idea is not important in the "mathematics world", or even the "physics world", or even the accounting and finance worlds. The only relevant example I could think of is the oil price crashing to negative, but then again, commodities traders don't usually think in terms of percentage change of the asset per se. – Benjamin Wang Dec 23 '20 at 00:34
  • When talking about percentage, you always need to specify what the percentage is of. What the percentage is in reference to. If you can adequately phrase the statement, there should be no question as to what formula is to be used. – JMoravitz Dec 23 '20 at 00:54

1 Answers1

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The percentage difference is defined as the difference of the values, divided by the average and written in percentage. If you have two values, the formula is $\frac{|x-y|}{\frac{|x+y|}{2}} \times 100$. This also holds for negative numbers.
Remark:
(1) It is better known as relative change in percentage, for example here https://en.m.wikipedia.org/wiki/Relative_change_and_difference.

jojobo
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  • @SeanXie, thanks for editing the formatting, I had problems with it. – jojobo Dec 23 '20 at 06:55
  • Your definition of "percentage difference" differs from the "percentage change" concept that you linked to. Your definition does make sense, except that I would absolute-value the denominator too, so that the formula works not just when the two values' average is positive, but also when it is negative. – ryang Jul 16 '22 at 08:54