# Why does my 500GB hard drive have a capacity of exactly 500,107,862,016 bytes?

Why does my 500 GB hard disk show up to have exactly 500 107 862 016 Byte?

I'm aware of the GiB vs. GB issue and know that manufacturers of hard drives use 1000 as factor. But I cannot find an explanation for the weird looking number. It is not a power of 2, neither it seems to be any other simple product of numbers (factorization is 2^13 ⨉ 3^4 ⨉ 7 ⨉ 67 ⨉ 1607).

First I thought it is dependent on the manufacturer but than I checked a second drive and it has exactly the same amount of bytes (according to Mac OS X Disk Utility).

So what's the reason for this number?

• Down votes seem unfair here. OP clearly researched, and isn't complaining, he's researched and is just trying to understand
– Dave
Feb 8, 2016 at 21:10

The answer is IDEMA formula, as described in the IDEMA Standard LBA 1-03 specification (specs available here, or direct PDF download).

LBA counts = (97,696,368) + (1,953,504 * (Advertised Capacity in GBytes – 50))
LBA counts = (97,696,368) + (1,953,504 * (500 – 50))
LBA counts = 976,773,168

Capacity in Bytes = 512 Bytes * LBA counts
Capacity in Bytes = 500,107,862,016 Bytes

• Don't ask me how the formula is firstly formed though. It appears to be some black magic that the vendors never revealed its rationale. Feb 9, 2016 at 4:18
• Welcome to Super User. People are security conscious and get concerned when clicking a link immediately downloads an unknown file. It's a good idea to include a notice on live download links. Feb 9, 2016 at 4:21
• @fixer1234 It's quite common for hardware specs and datasheets to come as PDF, and often as download-only too. Anyway, I've cleaned up the 'warning' a bit.
– Bob
Feb 9, 2016 at 4:32
• Thank you, that explains it. So every complying hard drive will have the exact same amount of bytes. Would be interesting to know where the black magic came from, but we will probably never know ;-) Feb 9, 2016 at 20:04
• After simplification it's Bytes = 1000194048*AdvertisedGB + 10838016. The difference between 1000194048 and 1e9 seems arbitrary, so does the offset 10838016 (which equals 10 MiB + 344 KiB); still in this representation the formula is not that insane. I wouldn't be surprised if it turned out the original formula was derived (a posteriori) from some existing HDD models of the era and designed to exactly match certain two of them. Dec 15, 2022 at 15:32

You're right, it's not the GiB vs. GB issue.

If you check several 500GB drives, you'll find they're all* slightly different. In most cases, it won't be exactly 500 000 000 000 Bytes. Yours has 500 107 862 016 Bytes, another might be 500 107 946 218... That's the actual usable space the manufacturer ended up with given the precise disk layout and it varies slightly from drive to drive.

(*as far as I've seen)

• The real question is why would anyone care so long as it meets the minimum size that it's sold as.
– user35787
Feb 8, 2016 at 20:45
• @Iain I don't think op does care, more about just understanding
– Dave
Feb 8, 2016 at 21:14