Percent of Change

Percentage of change is used to calculate how much something has changed, whether it is day-to-day temperature, grade-point average, water level of a body of water, the cost of any given product, etc.

As long as whatever it is you're calculating the change of has a numeric value for both its original value and its new value, you can calculate the amount (in percent) it has changed and we can most certainly help.

To calculate percent of change, first subtract the value of the old quantity from the new quantity. This will give you the numerical difference between the original and new values.

Then divide this difference by the old quantity. This will tell you how much change has occurred over the original value. In other words, the division will tell you what percentage the amount of change (new – original) is of the original quantity so you can see what percent the original quantity has increased or decreased.

Lastly, multiply the value you obtain by 100 to find the percent of change.

What Exactly is the 100 For? Why Do I Care About A Percent?
The 100 in this equation is used to create a percentage so that people can more easily understand how much the component really has changed. We want a percentage because when you only divide the difference in value by the old value, you get the flat rate of how much the original value has changed which is only a number or a decimal.

To illustrate what I mean, it would be hard to tell exactly how much higher the temperature is today than it was yesterday when my answer is .02. (That wouldn't even stand for .02 degrees because subtracting the old temperature from the new temperature to get the change in degrees is only the first part of our equation. We really want to know what percent of the original value this change is.) So, to be able to understand what "the temperature is .02 higher than it was yesterday" means, I multiply .02 by 100 to find the percent in which it's changed.

.02 * 100 = 2 %

That means the temperature has increased by 2 percent since yesterday and therefore, it is two-percent hotter outside today than it was yesterday. Ah ha...that's something we can all understand a little better.

Why Only Numeric Values?
"My new watch is forty percent cooler now that I got a blue face for it."

Is attractiveness (or "cool"ness) really a measurable quality? The sentence above just shows what happens when you try to calculate the percentage of change of something that doesn't have a numeric value: it gets sticky.

Well, if you think of it this way...
"You've changed forty percent since I've known you!"
"My handwriting is thirty percent more legible than it used to be."

At first thought, these sentences seem as ridiculous as the ones used earlier; personality and legibility of handwriting don't seem very measurable. But what if Jon used to follow a daily schedule that consisted of ten things he loved doing but then he stopped doing and liking four of those things when he met Sarah? What if three more out of ten (thirty percent more) people can read Paul's new style of handwriting than his old style?

I'm sure many people use this type of reasoning to their advantage even though it's not even all that sound; just because thirty percent more people in a ten person sample can read Paul's new handwriting it doesn't mean that the handwriting itself is precisely thirty percent more legible.

This kind of reasoning helps people figure out just how much better something is than it used to be, or how much better they are at something now than they were at an earlier point in their life. Be careful when you try this trick to boast about your improvement on something because you might get called out on your flaw in logic (don't say I didn't warn you.)

Estimation
"I lost fifty percent of my concentration after you made that phone call in my office."

Concentration isn't exactly measurable, but this sentence works. That's because it's a figure of speech. Whoever said that didn't really assign a number to how well he was concentrating before and after his friend made the call. Instead, he probably noticed that after the call was made it took him thirty minutes to do something it him took fifteen minutes to do before the call was made (or something of the sort.)

Again, just because he got the same amount of work done in half the time before he was interrupted doesn't necessarily mean that precisely fifty percent his concentration was lost. Concentration isn't the only thing that affects how fast someone works.

Example 1: You've Got Voicemail
Joleen is a very busy person. When she got to work on Friday morning she had 5 new messages in her voicemail account from Thursday night. Now that it's Monday, she has 9 new messages from over the weekend. What is the percentage of increase of new messages from one weeknight to the weekend?

Original Quantity: 5
New Quantity: 9

This means that she received 80 % more messages over this weekend than over a night in the week.

Note: Be careful to avoid saying that she receives eighty-percent more messages over any given weekend than over any given night in the week. This was only one weekday night and one weekend.

Example 2: Sticker Collection
When I was younger I collected stickers. One day I decided I'd make it my goal to increase my sticker collection by at least 75 % (have 75 % more stickers than I had at that point) in only one month. At that point my sticker collection only held 24 stickers. By the end of the month, I had 61 stickers. Did I reach my goal?

Original Quantity: 42
New Quantity: 69

I increased my sticker collection by 64 % so unfortunately, I didn't quite reach my goal.

Example 3: GPA Increase
Austin's GPA at the start of the school year was 2.36 (on a 4.0 scale.) By the end of the year he managed to get it up to 3.12. He wants to know what percent increase that is.

Original Value: 2.36
New Value: 3.12

He was able to increase his GPA by 32 % in one year.

Once again, be careful not to say he became a better student by 32 %. Maybe he studied just as hard this year as he studied the previous year but he just had really hard classes the previous year.

Works Cited

Staple, Elizabeth. "Basic 'Percent of' Word Problems." Purplemath. 2000.; 12 June
2006. <http://www.purplemath.com/modules/percntof.htm>.

Back