Convert TB to TiB

A terabyte is a trillion bytes. A drive sold as 1 TB is exactly that — the space that seems to go missing is a unit disagreement, not a defect.

A tebibyte is 1,024 gibibytes. The gap against the terabyte has grown with each step: 2.4% at kilo, 4.9% at mega, 7.4% at giga, 10% at tera.

The factor is 0.909495, and almost nobody carries that around. Rounded to 0.91 it is off by 0.06 % — which stays invisible on small numbers and turns into a whole unit somewhere around 10,000 TB.

That is the number worth knowing before you round: not the error itself, but where it stops being ignorable. Below that point the shorter factor is the sensible one; above it, use the field above, which never rounds until it prints.

One TiB is 1,024 of the unit below it; one TB is 1,000. On this page that is the difference between 1.0995 TB and 1 TB — 10 % — and the gap grows at every step up the scale, which is why it is a rounding error on a photograph and a visible chunk of a hard disk.

This is the whole of the missing-storage mystery, and on this page it is worth 10 %. A drive sold in TB holds exactly what the label says; Windows divides by 1,024 instead of 1,000, keeps the decimal name, and reports 1 TB where the box said 1.0995. macOS has counted these in the decimal units since 10.6, which is why the same drive can look two sizes on two machines — nothing is missing and nobody is rounding, the same bytes have two names.

A drive sold as 4 TB contains four trillion bytes, and the manufacturer means exactly that. Windows takes the same four trillion bytes and divides by 1,099,511,627,776, because that is what it calls a terabyte, and gets 3.638. Then it formats the volume, which costs a fraction of a percent, and prints 3.63 TB. Every byte is present and countable; the label above them changed unit without changing name.

Nine percent is large enough that people reasonably suspect a defect or a partition that failed to appear. It is neither, and the test is quick: the exact byte count in the drive properties should be at or slightly above four trillion. If it is, the drive is the size it was sold as and the summary line is the only thing that disagrees.

The disagreement is a single substitution — 1,024 where 1,000 was meant — applied once per step up the scale. One step gives 2.4 percent, two gives 4.9, three gives 7.4 and four gives 10. A terabyte is four steps up from a byte, so it carries the substitution four times, which is why nobody argues about kilobytes and everybody notices terabytes.

That also means the gap will keep growing. The next step, the petabyte against the pebibyte, is 12.6 percent, and an array quoted in one unit and provisioned in the other is out by an eighth before anything is stored on it. The arithmetic has not changed since the 1960s; only the scale at which people meet it has.

Every drive box and product page carries a footnote defining 1 TB as one trillion bytes, and it is there because the wording was litigated in the United States in the mid-2000s. That footnote is now the most reliable sentence on the packaging: it tells you the capacity you are buying in the only unit that has one meaning. Compare drives on bytes and the whole question disappears.

What it cannot do is change what your operating system prints afterwards. Windows will continue to divide by 1,024 four times and label the result TB, so a 4 TB drive will always read as roughly 3.63 there, an 8 TB as 7.27 and an 18 TB as 16.37. Budget for the unit before you buy rather than being surprised by it after: multiply the advertised figure by 0.909 and that is what the machine will show you.

Some capacity genuinely does go, and it is worth separating from the unit question so that neither is blamed for the other. A filesystem has to store its own structures — on NTFS the master file table, on ext4 the inode tables and journal, on APFS the metadata containers — and those are real bytes that are no longer available for files. On a multi-terabyte volume they come to a fraction of a percent.

There is a second, subtler cost once files start arriving: everything is stored in whole blocks, typically 4 KiB, so a file of 100 bytes occupies 4,096. On a drive holding a million small files that rounding is measured in gigabytes. Neither effect is anywhere near the size of the unit difference, but both are why the free-space figure on a working drive is never quite the clean number the conversion above gives.

Anyone assembling several of these drives meets the conversion twice. Eight 4 TB drives are 32 TB decimal, which the array will report as 29.1 TiB before any redundancy, and a single-parity configuration then hands back the capacity of one drive, leaving 25.5 TiB usable. A plan made in decimal terabytes and checked against a pool reported in tebibytes will be short at both stages.

ZFS adds a third subtraction, because it is designed to be told about free space and behaves badly when it runs out. The usual working advice is to keep a pool comfortably below full rather than filling it, so the capacity you can actually plan on is lower again. None of that is the unit disagreement, but it stacks on top of it, and a pool sized on the number printed on the drive boxes will be the tightest of the three.

The rule that survives contact with every vendor is to convert everything to bytes before comparing anything. A NAS advertising 16 TB of raw capacity and a backup service quoting 16 TiB of quota are not offering the same amount, and the difference is 1.6 TB, which is a drive. Bytes are the only figure both sides are using the same way, and every specification eventually states one.

The second rule is to distrust a bare capital-letter unit and trust one with an i in it. TiB can only mean 1,099,511,627,776 bytes; TB means a trillion when a manufacturer writes it and 1,099,511,627,776 when Windows does. When a document uses TiB it has told you which convention it is on, which is worth more than any assumption about the kind of vendor who wrote it.

Once the unit is accounted for, a genuine shortfall usually has one of three causes, and all are visible in the disk management tool. An unallocated region at the end of the disk means the partition was created smaller than the drive; a drive appearing as 2 TB when it is larger means it has been given an MBR partition table, which cannot address beyond that; and a capacity that is a clean fraction of the expected one usually means a fault or, occasionally, a counterfeit.

The check that settles it is the byte count against the manufacturer's stated figure, not the rounded summary. If the raw disk reports four trillion bytes and the volume on it reports substantially less, the problem is the partition rather than the hardware and is fixable without losing anything. If the raw disk itself is short, the conversion on this page is not the explanation and the drive should go back. Worth doing before the drive is filled rather than after: a capacity check on an empty disk takes a minute, and the same check on one holding a backup set is an afternoon.