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## Formatted capacity confusion clarified

From time to time some meticulous customer will ask us how come a fresh formatted hard disk or RAID array volume is smaller than the nominal capacity.  For example when you format a 1TB hard disk the resulting drive appears to have 931 GB even though the hard disk label claims 1000GB. Where is the “missing” 69GB?

The problem is much more pronounced if someone formats a 16TB RAID volume and instead of the expected 16000 GB they only see 14896GB. This looks like a significant loss: 1104 GB. “We paid for 16000GB!” exclaimed one company controller.

This phenomenon arises because hard-disk manufactures and RAID array controllers count the capacity in a different way than the file system does. The prefixes kilo, mega, giga, and tera are used to state powers of ten. However in computer software the data being handled is typically organized based on powers of 2, so it became customary to call 2**10 a kilobyte, which was really 1024 bytes, not exactly 1000.

Storage hardware is using the base 10 system and software is using the base 2 system. So no storage is actually lost, it is just a question of how the information is represented.

The IEC has created a system of prefixes to differentiate between the base 10 and the base 2 systems. In base 2 the proper terms are kibibyte, mebibyte, gibibyte, and tebibyte. The “-bi-” refers to binary. In short they are KiB, MiB, GiB, TiB. But these are not frequently used.

But we need exact proof and want to know the math behind it.

Hard disk manufacturers assume:   Kilo = 10 3 = 1000 (kB)

File system assumes:   Kilo = 2 10 = 1024 (KiB)

Let us calculate kB, MB, and GB to KiB, MiB and GiB factors:

kB – KiB:  1000 / 1024  = 0.977

MB – MiB:  (1000 * 1000)  /  (1024 * 1024)  = 0.954

GB – GiB:  (1000 * 1000 * 1000)  /  (1024 * 1024 * 1024)  = 0.931

Now we can easy find out formatted capacity for 1TB hard disk or 16TB (16000GB) array:

1000GB * 0.931 = 931GiB

16000GB * 0.931 = 14896GiB

Typically software will display GB as the storage unit size, but actually it is GiB. Until this is changed there will always be this confusion about the exact size of storage devices.

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• ### marko

August 24, 08 2010 12:40:11

This should be taught at schools 🙂

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• ### Nash

August 22, 08 2011 08:11:16

Your answer was just what I neeedd. It’s made my day!

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• ### RichardS

September 03, 09 2010 05:25:28

@marko

Yes should be, but some of the people still doesn’t understand it 😉

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• ### Loodienny

November 30, 11 2012 08:08:53

I have signed up for any future notifications of posts. I really like this post, keep up the good blogs

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• ### Corrine Hely

June 07, 06 2015 03:36:49

Very good post! We will be linking to this particularly great post on our website.
Keep up the good writing.

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• ### Ewan

July 23, 07 2015 01:49:03

Excellent web site you have here.. It’s hard to find high-quality
writing like yours nowadays. Take care!!

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• ### Bryan Clare

October 27, 10 2015 11:25:00

Very good but . . . surely your calculations give the UN-formatted capacity. So a 4GB memory card will have an actual capacity of 4*0.931=3.724GiB. I may be wrong but doesn’t the card then have to be formatted using FAT32, FAT16 or whatever which will use some memory so the usable (ie formatted) capacity wil be even lower. I’d like to know how much as I am hoping to fit 3.48G(i?)B of pics on a 4GB card.

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• ### Shashank

January 08, 01 2016 09:53:05

Excellent article! Cleared my confusion and was simple to understand.
Great job guys.

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• ### Santhana Krishnan

February 07, 02 2016 06:31:13

Yes.

I loved your article. It cannot be explained so simple than this to any one.

Great Post !!

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