# How to calculate percentage change?

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Fritz Isaacsposted 5 years ago

How to calculate percentage change?

How do you calculate percentage change and what is it useful for?

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SidKempposted 5 years ago

The key to calculating percentage change is to identify the base valuee from which the percentage will be calculated.

For example, if an object was worth \$100 on January 1, 2012. We start here, so this is the base value. A year later, on 1/1/2013, it was re-appraised at \$140, it's value has increased \$40. The change is \$40. The percentage change is (change in value)/(base value) then times 100, to make it a percentage. That is 40/100, or 0.40, times 100, or 40%.

The tricky issue with percentage change is, if the base (that is, the base value) is changed, the numbers come out phoney. This can happen by accident, or on purpose. Here is an example: I work for a company, and make \$100,000 / year. The company hits hard times and calls for a 10% salary reduction for everyone. We accept. That means, for me, the 10% change is 10% of my base salary, \$100,000, or \$10,000. The change is downward, so my new salary is (\$100,000 - \$10,000) or \$90,000. So far, so good.

A year later, the company says, "we're doing better now, and we're restoring the prior salary reduction. Everyone gets a 10% raise. But they calculate from the current salary, not my original salary. So I get a raise of 10% of \$90,000, or \$9,000, and my new salary is \$99,000.

I used to make \$100,000. I got a 10% cut then a 10% raise. But I now make only \$99,000, and I'm out a thousand dollars. How did that happen? The raise was a percentage of a smaller base than the base used to calculate the cut.

Boy, am I pissed.

This kind of error or trickery happens all the time with percentage change.

Percentage change is very useful for seeing rates of change and making projections about growth. But assuming a rate of change will be steady is risky business.

Percentage change is also useful for comparisons. Say a company trains its salespeople. One person's monthly sales increase by \$10,000, another by \$5,000. It looks like the training was twice as effective for person #1. But now we look, and, before the training, salesperson #1 was making \$100,000/month in sales, and #2 was making \$50,000/month. The percentage change was a 10% increase in both cases. The training was equally effective for both salespeople.

There are two good books to read to learn more. One is Business Statistics Demystified by Steve Kemp and Sid Kemp (that's me), and the other is a classic called How to Lie With Statistics by Huff (1954).

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suranjith_eposted 5 years ago

take the different between two values and divide it by 100. easy

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m4ryposted 5 years agoin reply to this

no, you divide the difference by the original amount, then you multiply by 100.  going from 15 to 17 is a 13% change since ((17-15)/15)*100 = 13.

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suranjith_eposted 5 years agoin reply to this

my apology. you are correct

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