Convert TB to GiB

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 gibibyte is 1,073,741,824 bytes — about 7% more than a gigabyte. Windows measures in gibibytes and labels them GB, which is the whole of the missing-space mystery.

The factor is 931.322575, and almost nobody carries that around. Rounded to 930 it is off by 0.14 % — which stays invisible on small numbers and turns into a whole unit somewhere around 1,000 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 GiB is 1,024 of the unit below it; one GB is 1,000. On this page that is the difference between 0.0011 TB and 0.001 TB — 7.4 % — 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 7.4 %. A drive sold in GB holds exactly what the label says; Windows divides by 1,024 instead of 1,000, keeps the decimal name, and reports 0.001 TB where the box said 0.0011. 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 one terabyte contains 1,000,000,000,000 bytes. An operating system dividing that by 1,073,741,824 reports 931.32 and writes GB after it. The quantity is unchanged, the unit is 7.37 per cent larger, and the label is the same three letters in both places. That is the entire mechanism, and it explains every "my new disk is smaller than advertised" question ever asked.

It is worth knowing the expected figure rather than the rule, because the expected figure is checkable in five seconds. A 1 TB drive should report about 931 GiB, a 2 TB about 1,863, a 4 TB about 3,725, an 8 TB about 7,451. If the number you are looking at is within a per cent of one of those, the drive is exactly the size it claimed to be.

The unit gap is the first subtraction and rarely the last. A partition table takes a little, alignment takes a little more, and then the filesystem spends capacity on itself: allocation tables, a journal, inode structures reserved at format time whether or not they are used. Ext4 additionally holds back five per cent of the volume for privileged processes so that a full disk does not become an unrecoverable one, which is a setting rather than a law and can be changed.

So the honest expectation for a 4 TB drive is not 3,725 GiB of usable space but something in the high three-thousands, with the shortfall split between a unit that is bigger than the label suggests and a filesystem doing its job. Attributing the whole of it to either cause alone produces a number that never quite reconciles.

Everything upstream of the operating system speaks decimal. The manufacturer’s specification, the invoice, the SAN quotation and the drive label are all in TB. Everything downstream of the operating system speaks binary: volume managers, hypervisor datastores, filesystem summaries and most monitoring agents compute in powers of 1,024, and only some of them write the i that would say so.

The consequence is that the boundary between purchasing and operations is also the boundary between two unit systems, and neither side announces it. When a capacity figure crosses that line — into a ticket, a report, a dashboard threshold — it is worth carrying the byte count or the explicit unit with it, because a bare number will be read in whichever convention the reader happens to work in.

On a single drive the shortfall is a footnote. On an array it becomes a line item, because the absolute figure scales with the total. Twelve 8 TB drives are 96 TB of raw decimal capacity, which is 89,407 GiB, so somebody expecting to see 96,000 of something finds nearly 6,600 of it apparently absent before a single parity block has been allocated. That is a number large enough to be escalated by somebody who has not done the conversion.

The parity and hot-spare arithmetic then happens on top, and it is much larger. A twelve-drive set with double parity has ten drives of usable capacity, which is 74,506 GiB from the same 96 TB of hardware. Separating the two subtractions is the useful discipline: one is a unit conversion and is not a loss at all, the other is redundancy and is the thing you are paying for.

A memory chip is addressed by a fixed number of address lines, so its capacity is necessarily a power of two: an 8 GB module holds 8,589,934,592 bytes, which is 8 GiB, and the marketing figure and the reported figure coincide by construction. Nobody sells a 7.5 GB stick, because the hardware cannot be built that way.

A hard disk has no such constraint. Its capacity is whatever the platters, tracks and firmware come to, so a manufacturer is free to round to a decimal figure and always has. That is why one spec sheet can list memory in units that are binary and storage in units that are decimal, using the same prefix letters throughout, without either entry being incorrect.

Decimal capacity labelling matches the SI meaning of the prefixes, where tera is 10 to the twelfth and always has been. It is the computing use of the same prefixes for powers of two that is the departure, adopted because 1,024 was close enough to a thousand to borrow the word. When the two conventions collided in retail, the argument went to court in the United States and was settled rather than decided.

The visible residue is the small print. Most drives now carry a line stating that one gigabyte means one billion bytes and that the capacity reported by an operating system will be lower. It is an accurate disclosure of a real discrepancy, printed in the place people are least likely to read it, and it is why the question keeps being asked.

The multiplication worth memorising is 931 GiB per TB, and its inverse, 1.0995 TB per TiB. From those two, most reconciliations are mental arithmetic: a 6 TB volume should show about 5,588 GiB, a 10 TB about 9,313, a 20 TB about 18,626. A figure that is close is a unit difference; a figure that is ten per cent lower again is something else, and that something else is worth finding.

When it does need finding, the byte count is the tool. Every operating system will show the exact capacity in bytes somewhere — a properties dialog, blockdev --getsize64, a volume manager listing — and comparing integers removes every rounding and labelling question at once. Two byte counts either match or they do not, and the answer takes one command rather than an argument.

Solid-state drives add a subtraction that spinning disks do not. Flash wears out, blocks fail, and the controller needs somewhere to write while it erases elsewhere, so every SSD holds back a portion of its physical NAND as spare area. A drive containing 1,024 GiB of flash is frequently sold as a 1 TB drive, and the difference — about 93 GiB — is over-provisioning that the host never sees at all.

That is a design choice rather than a discrepancy, and it is why a consumer SSD and an enterprise one with the same amount of flash inside can be sold at different capacities: the enterprise part reserves more, and lasts longer under write-heavy work. The figure worth taking away is that the reported capacity of an SSD has already had two deductions applied — the vendor's spare area and then the unit conversion — before the filesystem takes its own share.