TB vs TiB: Why a 16 TB Drive Shows 14.55

Updated

Drive makers count in powers of 1,000 and some software counts in powers of 1,024. Here is the conversion, a table for common drive sizes, which tools use which, and how to keep the units straight when you plan footage.

7 min readBeginner
  • Decimal vs binary
  • TB to TiB
  • Mbps vs MB/s
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Two ways to count a terabyte

Nothing is missing from your drive. A terabyte (TB) is 10¹² bytes, one trillion, and that is how every drive and card maker labels capacity: Seagate's data sheets say so in their footnotes. A tebibyte (TiB) is 2⁴⁰ bytes, 1,099,511,627,776, which is about 10% more. Software that divides by 1,024 at each step reports the drive in tebibytes, and much of it still prints “TB” next to the number.

The binary names (kibi, mebi, gibi, tebi, with symbols Ki, Mi, Gi, Ti) were approved by the IEC in December 1998 so the two could be told apart. They are not SI units: in SI, kilo, mega, giga and tera always mean powers of 1,000.

Decimal (SI) and binary (IEC) prefixes
DecimalBytesBinaryBytes
1 kB1,0001 KiB1,024
1 MB1,000,0001 MiB1,048,576
1 GB1,000,000,0001 GiB1,073,741,824
1 TB1,000,000,000,0001 TiB1,099,511,627,776

Converting TB to TiB

Decimal to binary
TiB = TB × 10¹² ÷ 2⁴⁰ ≈ TB × 0.9095 GiB = GB × 10⁹ ÷ 2³⁰ ≈ GB × 0.9313

Example: A 16 TB drive

Calculation:
16 × 10¹² ÷ 1,099,511,627,776 = 14.552
Result:
14.55 TiB, which a binary tool may print as "14.55 TB"
Binary to decimal
TB = TiB × 2⁴⁰ ÷ 10¹² ≈ TiB × 1.0995

Example: An array that reports 87.3 TiB

Calculation:
87.31 × 1.0995 = 96.0
Result:
96 TB: an eight-drive RAID 6 of 16 TB drives, exactly as specified

Drive sizes in TiB

What a binary-counting tool shows for common drive and tape sizes, before any file-system overhead.

Labeled capacity and binary equivalent
LabelTiBGiB
1 TB0.91931.3
2 TB1.821,862.6
4 TB3.643,725.3
8 TB7.287,450.6
12 TB10.9111,175.9
16 TB14.5514,901.2
18 TB (LTO-9 native)16.3716,763.8
20 TB18.1918,626.5
24 TB21.8322,351.7

A formatted volume shows a little less again, because the file system reserves space for its own structures. That loss depends on the file system and the volume size; the unit gap above is the larger part of what people notice.

Why the gap grows

Each binary step is 1,024 rather than 1,000, so the difference compounds with every prefix. At the kilobyte it is 2.4%; at the terabyte it is almost 10%.

How much larger the binary unit is
PrefixBinary ÷ decimalDecimal figure looks smaller by
kilo / kibi+2.40%2.34%
mega / mebi+4.86%4.63%
giga / gibi+7.37%6.87%
tera / tebi+9.95%9.05%
peta / pebi+12.59%11.18%

Which tools count which way

  • Drive, card and tape makers: decimal. A 16 TB drive holds 16 trillion bytes.
  • macOS and iOS: decimal. Apple says the binary reporting belonged to OS X Leopard and earlier and iOS 10 and earlier, so a 16 TB drive shows as about 16 TB in Finder.
  • Windows File Explorer: typically divides by 1,024 but labels the result GB and TB, so the same drive appears as about 14.5 TB.
  • Linux and the command line: GNU df -h and du -h use powers of 1,024 and print a bare “T”; df --si switches to powers of 1,000.

Bits, bytes and data rates

The second mix-up is bits against bytes. Codec and network rates are in bits per second and are always decimal: Apple's ProRes tables give Mb/s, where 1 Mb is a million bits. Copy speeds are usually in bytes per second. One byte is eight bits:

Rates and sizes
MB/s = Mbps ÷ 8 GB per hour = Mbps × 3,600 ÷ 8,000 = Mbps × 0.45

Example: UHD ProRes 422 HQ at 24p, 707 Mb/s (Apple white paper)

Calculation:
707 ÷ 8 = 88.4 MB/s; 707 × 0.45 = 318 GB per hour
Result:
318 GB per hour, the figure Apple publishes

The bitrate guide works through file size from bitrate in more detail.

What it means for footage

Keep a plan in one system from end to end. Codec rates and drive labels are both decimal, so plan in decimal and the numbers line up:

Hours of footage on a drive
Hours = Drive TB × 1,000 ÷ GB per hour

Example: UHD ProRes 422 HQ 24p on a 16 TB drive

Calculation:
16,000 ÷ 318 = 50.3
Result:
About 50 hours, before file-system overhead

The free bitrate calculator runs this in your browser, in decimal units. The mistake to avoid is mixing the two: taking the 14.55 that a binary tool shows for a 16 TB drive and multiplying it by a decimal GB-per-hour figure undercounts by 9%. In the other direction, a camera card sold as 512 GB is 476.8 GiB; if your tool shows that figure, the card is not short.

The same applies to arrays and tape. See RAID capacity for usable space after parity (the free RAID capacity calculator works it out), and LTO archiving for tape counts. CineMath's Data & Storage calculator works in decimal units throughout, matching the labels on your media.

Calculators for this guide