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Formula to Calculate Percent Increase

Date: 01/31/2005 at 16:58:20
From: Rachel
Subject: How do I calculatre percentage increases


I want to compare two figures and show the percent increase that has
been made.  For example, if 55 has increased to 75, what percentage
increase is that?

Whenever I get a figure, I am never sure if there is a way of checking 
back that it is correct.

Date: 02/01/2005 at 16:05:06
From: Doctor Ian
Subject: Re: How do I calculatre percentage increases

Hi Rachel,

When we say

  Q increased by P percent

what we _mean_ is that the new value of Q is 

  Q' = Q + (P percent of Q)

which is to say, 

  Q' = Q + (P/100 * Q)

So far, so good? 

If you have Q (the old value) and Q' (the new value), then you want to
find P.  If we solve the equation for P, we get

            Q' = Q + (P/100 * Q)

        Q' - Q = P/100 * Q

        Q' - Q
        ------ = P/100

  Q' - Q
  ------ * 100 = P

So you subtract the old value from the new one, and divide the 
difference by the old value.  Then multiply by 100 to get the 

Another way to think of that is:

  amount of change
  ---------------- x 100 = percent change
  original amount

If you want to check your work, you can go back to the definition, 
plug the numbers in, and see if what you get is true.  For example,
suppose I have an increase from 40 to 50.  The formula gives me

       50 - 40         10
   P = ------- * 100 = -- * 100 = 25
         40            40

So I think it's 25%.  Let's go back to the definition:

  50 = 40 + (25% of 40)

     = 40 + 10

     = 50

This is true, so I have the right percentage increase. 

Does this make sense? 

- Doctor Ian, The Math Forum 
Associated Topics:
Middle School Fractions

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