# Calculating the percentage of the difference between two values

If I have the following two different values for x:

x = 0.022

x = 0.020

And, if I want to calculate the percentage of the difference (change) in x, will it be?

---> 0.022 - 0.020 = 0.002

---> 0.002 x 100% = 0.2%?

And, should the percentage of the difference be always positive?

Thanks.

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I presume you have an initial value for $x$, and then a later value for $x$, and you want to calculate what percent change you have from the initial value of $x$.

So say you have two values $x_1=.02$ and $x_2=.022$. So as you've calculated, the increase in going from $x_1$ to $x_2$ is $.022-.02=.002$. But $.002/.02=.1$, so there has been a $10\%$ increase in $x$ from the initial value.

The percentage of the difference won't always be positive if your second value of $x$ is smaller than the first. For example, if instead $x_1=.022$ and $x_2=.02$, then the change is $-.002/.022\approx-9.09\%$.

In general, to find the percentage of change, you can use the formula $$\frac{x_f-x_i}{x_i}\cdot 100\%$$ where $x_i$ is your initial value of $x$, and $x_f$ is your final value of $x$.

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Does this work for negative numbers? What if your initial is -10 and your final is -5? – Ralph Winters Mar 21 '11 at 12:50
You can use the formula and find that -10 reduced by 50% is -5. I'm not sure many people would see it that way because they just don't like negative numbers. But if you were in debt by \$10 and paid off 5, you would have reduced your debt by 50%, right? – Ross Millikan Mar 21 '11 at 13:36
The percent difference of -10 to -5 is an INCREASE of 50% since you are going from a smaller to a larger number. – Ralph Winters Mar 21 '11 at 14:21
The formula should always include the Absolute Value of the Denominator! – user70447 Apr 1 '13 at 15:58