[math] Converting bytes to megabytes

I've seen three ways of doing conversion from bytes to megabytes:

1. megabytes=bytes/1000000
2. megabytes=bytes/1024/1024
3. megabytes=bytes/1024/1000

Ok, I think #3 is totally wrong but I have seen it. I think #2 is right, but I am looking for some respected authority (like W3C, ISO, NIST, etc) to clarify which megabyte is a true megabyte. Can anyone cite a source that explicitly explains how this calculation is done?

Bonus question: if #2 is a megabyte what are #1 and #3 called?

BTW: Hard drive manufacturers don't count as authorities on this one!

Use the computation your users will most likely expect. Do your users care to know how many actual bytes are on a disk or in memory or whatever, or do they only care about usable space? The answer to that question will tell you which calculation makes the most sense.

This isn't a precision question as much as it is a usability question. Provide the calculation that is most useful to your users.

In general, it's wrong to use decimal SI prefixes (e.g. kilo, mega) when referring to binary data sizes (except in casual usage). It's ambiguous and causes confusion. To be precise you can use binary prefixes (e.g. 1 mebibyte = 1 MiB = 1024 kibibytes = 2^20 bytes). When someone else uses decimal SI prefixes for binary data you need to get more information before you can know what is meant.

The answer is that #1 is technically correct based on the real meaning of the Mega prefix, however (and in life there is always a however) the math for that doesn't come out so nice in base 2, which is how computers count, so #2 is what people really use.

Divide by 2 to the power of 20, (1024*1024) bytes = 1 megabyte

1024*1024 = 1,048,576   
2^20 = 1,048,576
1,048,576/1,048,576 = 1  

It is the same thing.

Here is what the standard (SI) says:

http://physics.nist.gov/Pubs/SP330/sp330.pdf#page=34

Megabyte means 2^20 bytes. I know that technically that doesn't mesh with the SI units, and that some folks have come up with a new terminology to mean 2^20. None of that matters. Efforts to change the language to "clarify" things are doomed to failure.

Hard-drive manufacturers use it to mean 1,000,000 bytes, because that's what it means in SI so they figure technically they aren't lying (while actually they are). That falls under lies, damn lies, and marketing.

There's an IEC standard that distinguishes the terms, e.g. Mebibyte = 1024^2 bytes but Megabyte = 1000^2 (in order to be compatible to SI units like kilograms where k/M/... means 1000/1000000). Actually most people in the IT area will prefer Megabyte = 1024^2 and hard disk manufacturers will prefer Megabyte = 1000^2 (because hard disk sizes will sound bigger than they are).

As a matter of fact, most people are confused by the IEC standard (multiplier 1000) and the traditional meaning (multiplier 1024). In general you shouldn't make assumptions on what people mean. For example, 128 kBit/s for MP3s usually means 128000 bits because the multiplier 1000 is mostly used with the unit bits. But often people then call 2048 kBit/s equal to 2 MBit/s - confusing eh?

So as a general rule, don't trust bit/byte units at all ;)

BTW: Hard drive manufacturers don't count as authorities on this one!

Oh, yes they do (and the definition they assume from the S.I. is the correct one). On a related issue, see this post on CodingHorror.