# Percent change: Know the formula

**Here’s a question** I posed to some college students recently:

*Let’s say you cover the Town of East Middleburgtown. The mayor announces that this year’s town budget comes in at $12.6 million. Last year’s budget was $11.4 million. What is the percent change? Better yet, what’s the formula for figuring it out?*

If you don’t know the answer, or how to obtain it, you’re not alone. This kind of problem — which is in my son’s 7th grade math textbook — routinely stumps most journalists in most of the newsrooms across America.

I’ll avoid the temptation to moralize here. If you’re a journalist — if you have a pulse — you need to know this very basic operation. With it, you’ll have the power to analyze all kinds of data and even double-check the mayor’s math.

Here it is:

`(the_new_number - the_original_number) / the_original_number`

or, in the case of East Middletownburg:

`(12.6-11.4) / 11.4`

Remember (and you learned this in fifth grade) that operations in parentheses come first. That gives you this:

`1.2 / 11.4 = .105 = 10.5%`

So, the mayor’s new budget is a 10.5% increase over last year’s. Now you have something to write about!

my math-savvy wife was just explaining this to me the other day, now i can bookmark your post so I’ll never have to ask her again. great site Tony, added to my google reader!

Social comments and analytics for this post…This post was mentioned on Twitter by seattlesketcher: A math formula every journalist should know (via @TonyDB) http://bit.ly/1KNNyq…

It amazes me that kids come through 12 to 16 years of academics with no understanding of statistics at all, which greatly hampers your ability to make sense of the world. I take every opportunity to use and explain things like “right edge of the bell curve” and “two standard deviations” and go over ways to interpret raw data with the kids… Invaluable tools mental modeling and turning “knowledge” into “wisdom.”

I’m glad I remembered how to do this type of problem!

Alternate approach:

Divide larger number by the smaller smaller number, subtract 1 and move the decimal point two positions to the right.

Or . . . in the case of Middletownburg: 12.6/11.4=1.105

I.e . . . the new budget is 110.5% of the old budget . . . or 10.5% larger. I find this easier . . . but . . . different strokes.

What REALLY freaks folks out is that having one’s salary move from $100K to 150K a year is a 50% increase . . . but if the boss takes back the $50k, it’s only a 33% decrease.

Ahhhh . . . a 17% raise? (50-33?) . . . that costs the boss . . . nothing !

Dan,

Yes, math is funny that way — different routes can lead to the same destination. As long as it’s accurate! That’s always the main thing.