What is the mathematical formula to convert binary bytes into metric bytes, and vice versa?

The reason I ask this is because I can’t seem to develop the equation myself. I know that 1 metric kilobyte=1000 bytes, and 1 binary kilobyte=1024 bytes, but even knowing this, my equations don’t seem to be correct, according to online conversion sites. I wish to know this equation as unfortunately I can’t find any conversion app for Windows Phone 8 that will convert the two, and wish to have it handy whenever I need to calculate how much storage there is. For instance, all advertized sizes for hard drives and other devices are in metric bytes, for some reason. However, the actual disk space you have to store files on is less then that, since computers use binary bytes. Therefore, it’s good to have a mathematical equation in order to convert metric storage over to binary storage, and see how much space you actually have to use. So if there are any of you that are good at math and computer storage, I’d appreciate the help! :)

There is a good calculator here: http://www.gordonengland.co.uk/conversion/binary.htm

Thanks for your response! While I'm looking for something I could use on my phone (I do not use cellular data, unfortunately), I noticed that there was a table towards the end of the the page that featured how to calculate the size in bytes, and then the difference between metric and binary units. So thank you for sending me back to that page, as I now have that table to help me calculate the sizes! :)

The 'formula' is exactly what you said, for decimal conversion it is 1000, for binary conversion it is 1024.

So a drive sold as 100GB has 100.000.000.000 bytes of storage.

Divide by 1024*1024*1024 to get the binary = 93.13GiB storage

The reason this still doesn't add up e.g. for hard drives is because even with binary conversion, we are talking unformatted space. Once you format it to actually store things on it other factors add to it like the file system chosen.

If you were to install Windows 8 on an (U)EFI system onto that drive you lose another 400MB (Windows Recovery, EFI Boot, Windows Reserved).

Anyway, the most accurate calculation you can do is using 7%, so 100GB*0.93 = 93GiB.

For Solid States Drives it gets even wilder as some manufacturers state decimal GB, some binary GiB and some applications may perform user over-provisioning resulting in even less space than advertised or calculated.

Thanks for your answer. :) Using the converter Alan supplied (which was the one I was using before as well), I concur that subtracting 7% from the metric value will give you a close estimate to the binary number (for gigabytes, anyways.) While I'm somewhat disgruntled I cannot find the actual equation used to make this conversion, the one you supplied will serve good enough whenever I need a ballpark estimate. I know that there are a lot of factors that will affect disk space as well, however when calculating for say upgrading a hard disk: I know that the disk is 120 GB according to Windows Explorer (and that's just the size of the partition.) Since that's big enough to hold the system and some programs, I'd probably go with a hard drive that's at least over 150 metric GBs. But anyways, I appreciate your help, and your response. Thank you!

I'm not sure what you expect to find but the equation to "convert" unformatted metric storage to unformatted binary storage is right there in front of you?

from kB to KiB = capacity * 1000 / 1024

from MB to MiB = capacity * 1000^2 / 1024 ^2

from GB to GiB = capacity * 1000^3 / 1024^3

from TB to TiB = capacity * 1000^4 / 1024^4

If you want to go from binary to metric it's just the other way around

from GiB to GB = capacity * 1024^3 / 1000^3

If you were looking for something like "metric - 46 = binary storage" then I'm afraid this is mathematically not possible. I guess my 7% estimation is the closest you will get to an easy "on-the-fly" calculation.

Those help as well! And actually, I was expecting something like an algebraic equation, which turn out to be your answers, really. X*(1000/1024) for kB to KiB, and so forth. Sorry for the trouble, but I appreciate your help! :)