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### Determining File Compression Ratio

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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/
```
Associated Topics:
High School Calculators, Computers

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