Determining File Compression Ratio

Date: 04/11/2001 at 09:24:59
From: Nusen Tsung
Subject: Determining File Compression Ratio

Hi Dr.Math,

I am having a problem. The answer is on the tip of my noodle, but I'm 
having total mind clog.

If you have a file A whose size is x bytes in size, and you compress 
it into a file we'll call B whose size in bytes is now y, what is the 
equation to find the compression ratio, disgregarding the time 
it took to compress?  I can find the percentage that the file was 
compressed, but I can't remember how to figure out the ratio.

Thank you for all your help in the past. Dr. Math rules!
Sincerely,
Nusen

Date: 04/11/2001 at 13:09:23
From: Doctor Twe
Subject: Re: Determining File Compression Ratio

Hi Nusen - thanks for writing to Dr. Math.

A ratio is simply a comparison of two numbers. The file compression 
ratio, then, would be expressed as x:y. 

Usually, the latter value is reduced to 1. To do that, we divide both 
numbers by y, so the ratio is then expressed as (x/y):1. This is 
really the same ratio, but it is easier to compare two ratios if they 
both use the same basis. For example, if an 875 kB file is compressed 
to 25 kB, then the compression ratio is:

     r = (875 k): (25 k)

       = 35:1

A word of caution: be sure that the units are the same in both parts. 
Suppose, for example, a 2.25 MB file is compressed to 384 kB. Since 
one is measured in megabytes and the other in kilobytes, we have to 
find a common unit. There are 1024 kilobytes in one megabyte, so I'll 
convert the 2.25 MB to kB:

     2.25 MB * 1024 kB/MB = 2304 kB

Now I can compute the compression ratio:

     r = (2304 kB):(384 kB)

       = 6:1

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/