## How To Calculate Percentage Change Between Two Values

So I'm a total math n00b, but I wanted to know how much of a change there was between some benchmarking numbers, in percentages. I thought that this was really basic, but I was wrong. So I Googled and found an article describing how to calculate the percentage change between two values. I wrote this Perl script so that I'd just have it in my toolbox:

#!/usr/local/bin/perl -w use strict; print "\nUsage: $0 from to\n" unless @ARGV == 2; my ($from, $to) = @ARGV; my $diff = (($to - $from) / $from) * 100; my $label = $diff < 0 ? 'greater' : 'less'; printf "$from is %.2f%% $label than $to\n", abs $diff;

When I run this script, I get values that agree with Dr Math's answers:

% percent_diff 7 5 7 is 28.57% larger than 5 % percent_diff 5 7 5 is 40.00% smaller than 7

So far so good. But then when I ran it on my benchmark numbers, I got different numbers than I would intuitively expect:

% percent_diff 13.67 40.73 13.67 is 197.95% smaller than 40.73 % percent_diff 40.73 13.67 40.73 is 66.44% greater than 13.67

Now, to me, it seems like you can fit roughly three 13.67s in 40.73. So then why isn't it 300% smaller?

Pardon my total ignorance, but if anyone knows the answer to this question, I'd greatly appreciate a simple explanation. Thanks!

**Update:**Mark Jason Dominus was kind enough to respond very lucidly to an email linking to this blog entry. With his permissin, I've pasted his comments below. All is now clear.

## Backtalk

Mark Jason Dominus wrote:

Theory wrote: