Two prefix systems, one byte count
Every quantity of data has exactly one honest description: a byte count. Everything else is a label applied to that count, and there are two competing sets of labels.
The decimal prefixes are the ordinary SI ones defined by the BIPM: kilo is 10³, mega is 10⁶, giga is 10⁹, tera is 10¹², peta is 10¹⁵. Storage vendors, network equipment and the SI-conforming parts of the computing world use these. A drive advertised as 1 TB contains 1,000,000,000,000 bytes.
The binary prefixes are kibi, mebi, gibi, tebi and pebi, standardised in IEC 60027-2 in 1999 and carried forward into IEC 80000-13:2008. Each is the nearest power of two: 2¹⁰ = 1,024, 2²⁰ = 1,048,576, 2³⁰ = 1,073,741,824, and so on. Memory addressing is binary, so RAM sizes, page sizes, block sizes and most operating-system file listings are naturally binary quantities.
The trouble is that for thirty years before IEC acted, the computing industry used the decimal names for the binary values. JEDEC's terminology standard for semiconductor memory still defines kilo, mega and giga as the binary powers in memory contexts, and Windows still divides by 2³⁰ and prints the label “GB”. So the word “gigabyte” genuinely means two different numbers depending on who wrote the software you are reading, and this calculator makes that ambiguity explicit by keeping the two families separate.
Why the gap grows with every prefix step
Conversion itself is trivial: multiply into bytes, divide out of bytes. What deserves explanation is the size of the discrepancy, because it is not constant.
At prefix level k, the decimal unit holds 103k bytes and the binary unit holds 210k bytes. Their ratio is (10³/2¹⁰)k = (1000/1024)k = 0.9765625k. Because the ratio is raised to the power of the prefix level, the gap compounds one step at a time.
Run it out. At k = 1 a decimal kilobyte is 1000/1024 = 0.9765625 of a kibibyte, a shortfall of 2.344%. At k = 3 it is 0.9765625³ = 0.931323, a shortfall of 6.868%. At k = 4 it is 0.909495, a shortfall of 9.051%. At k = 5, 0.888178, a shortfall of 11.182%.
Read the same ratio the other way and the numbers differ, which is the source of endless confusion. A tebibyte is 2⁴⁰/10¹² = 1.099512 terabytes, so it is 9.951% larger than a terabyte. A terabyte is 10¹²/2⁴⁰ = 0.909495 tebibytes, so it is 9.051% smaller than a tebibyte. Both statements are correct and they are not the same percentage, because the denominators differ. Whenever you quote one of these gaps, write the division that produced it.
The gap you actually see on screen depends on which unit the software displays, not on the drive. A 1 TB drive shown in GiB reads 10¹² ÷ 2³⁰ = 931.32 GiB against a nominal 1000 GB, which is the level-3 shortfall of 6.87%. The same drive shown in TiB reads 0.909495 TiB against a nominal 1 TB, the level-4 shortfall of 9.05%. Same drive, same bytes, two different-looking losses.
Worked example: the missing space on a 2 TB drive
You buy a drive labelled 2 TB. Windows reports 1.81 TB. Nothing has been lost. Here is the arithmetic, one step at a time.
- What the label promises. The vendor defines 1 TB as 10¹² bytes, so the drive holds 2 × 1,000,000,000,000 = 2,000,000,000,000 bytes.
- What Windows divides by. Windows computes its “TB” figure as 2⁴⁰ = 1,099,511,627,776 bytes, which is properly a tebibyte.
- The division. 2,000,000,000,000 ÷ 1,099,511,627,776 = 1.818989 TiB, which Explorer rounds to 1.81 TB.
- Express the loss. 1 − 1.818989 ÷ 2 = 1 − 0.909495 = 9.051% of the labelled figure, exactly the level-4 shortfall from the table below.
- Cross-check in gibibytes. 2,000,000,000,000 ÷ 1,073,741,824 = 1,862.645 GiB. Divide by 1,024 to return to tebibytes: 1,862.645 ÷ 1,024 = 1.818989. The two routes agree.
- Bits, for completeness. 2,000,000,000,000 × 8 = 16,000,000,000,000 bits, which is what matters if you are timing a transfer rather than filling a disk.
Formatting overhead is a separate, smaller effect layered on top. Reserved system areas, the file-system metadata and the partition table consume real bytes, typically well under 1% for a modern NTFS or APFS volume on a large drive. The 9.05% is not overhead; it is arithmetic.
Which convention applies to what
Match the convention to the thing you are measuring, and most of the confusion disappears.
Decimal, always: hard drives and SSDs as sold, network and interface rates (a gigabit link is 10⁹ bits per second), optical media capacities, and anything quoted in a datasheet that cites SI. Vendors print a footnote defining 1 GB as 1,000,000,000 bytes precisely because the ambiguity is real.
Binary, always: RAM, because address lines are binary and a memory module cannot be built with a round decimal capacity. Also file-system block sizes, memory page sizes, and the buffer sizes in most software.
Mixed, and you must check: operating-system file and volume listings. Windows divides by binary powers and prints decimal labels. macOS switched to decimal reporting in Mac OS X 10.6, so a Mac and a Windows machine report different numbers for the same drive. Most Linux tools accept a flag: df -h gives binary, df -H gives decimal, and ls -l --si differs from ls -lh for the same reason.
The practical consequence: when you are comparing a capacity figure to a requirement, confirm both are in the same convention before you conclude anything. A 32 GB image that will not fit on a 32 GB card is usually a convention mismatch, not a defect — 32 GiB is 34.36 GB, which no 32 GB card holds. If you are sizing a transfer rather than a volume, the Mbps to MB/s and download time calculator applies the same byte-versus-bit care to rates.
Decimal and binary prefixes side by side
| Level k | Decimal unit | Bytes | Binary unit | Bytes | Binary unit is larger by | 1 decimal unit reads as |
|---|---|---|---|---|---|---|
| 1 | kB | 1,000 | KiB | 1,024 | 2.400% | 0.976563 KiB |
| 2 | MB | 1,000,000 | MiB | 1,048,576 | 4.858% | 0.953674 MiB |
| 3 | GB | 1,000,000,000 | GiB | 1,073,741,824 | 7.374% | 0.931323 GiB |
| 4 | TB | 1,000,000,000,000 | TiB | 1,099,511,627,776 | 9.951% | 0.909495 TiB |
| 5 | PB | 1,000,000,000,000,000 | PiB | 1,125,899,906,842,624 | 12.590% | 0.888178 PiB |
The shortfall implied by the last column — 2.344%, 4.633%, 6.868%, 9.051%, 11.182% — is what the calculator reports as the prefix gap, because it is the direction a user experiences when a labelled capacity is displayed in binary units.
IEC 80000-13 is the standard that settles it
IEC 60027-2 introduced kibi, mebi and gibi in 1999, and IEC 80000-13:2008 — Quantities and units – Part 13: Information science and technology — carries the definitions today. Under that standard, the SI prefixes on a byte mean exactly what they mean everywhere else in SI: kilo is 1,000 and nothing else. The binary quantities get their own names and symbols, with a lower-case “i” in the symbol: KiB, MiB, GiB, TiB, PiB.
Adoption has been partial. The Linux kernel documentation, the IEEE, and most storage and networking specifications follow it. Consumer operating systems and the memory industry largely do not, and JEDEC's terminology standard for semiconductor memory continues to define the decimal-named prefixes as binary powers in that context. Write KiB and GiB when you mean binary values and you will never be misread; write GB and mean 10⁹.
Mistakes that produce a wrong data-size figure
- Assuming a capacity shortfall is formatting overhead. The 6.87% or 9.05% you see is prefix arithmetic. File-system overhead is a separate, much smaller number on a large modern volume.
- Confusing the bit and the byte. Lower-case b is bits, upper-case B is bytes, and the factor is 8. Storage is quoted in bytes; network and bus rates are quoted in bits.
- Quoting the gap in the wrong direction. A TiB is 9.951% larger than a TB, but a TB is 9.051% smaller than a TiB. Write the division rather than the remembered percentage.
- Chaining conversions through rounded intermediates. Convert once, through the exact byte count. Going TB → GB → GiB with rounding at each step loses precision that the direct division does not.
- Comparing a Mac figure to a Windows figure. They use different conventions for the same drive, so the two numbers will never agree. Compare byte counts.
- Sizing memory in decimal units. RAM is manufactured in binary quantities; there is no 8 GB module holding 8 × 10⁹ bytes. Use GiB when you mean memory, and see the number base conversion calculator if you need the underlying powers of two written out.
Key terms
- Byte
- Eight bits, the smallest individually addressable unit of storage on essentially all modern hardware. Standards sometimes use octet to make the eight-bit width explicit.
- Kibibyte (KiB)
- 2¹⁰ = 1,024 bytes. Defined by IEC 60027-2 and IEC 80000-13 so that “kilobyte” can keep its SI meaning of 1,000 bytes.
- Gibibyte (GiB)
- 2³⁰ = 1,073,741,824 bytes. What Windows and many tools compute when they print “GB”.
- Prefix level (k)
- How many prefix steps up from the byte you are: 1 for kilo/kibi, 2 for mega/mebi, and so on. The decimal-versus-binary ratio is 0.9765625 raised to this power.
- Formatted capacity
- The usable space after the file system claims its metadata, reserved areas and partition structures. Smaller than raw capacity, and a separate effect from prefix arithmetic.
Related conversions and where this stops
This calculator converts a static quantity of data. It says nothing about how long that quantity takes to move, which depends on a rate and on protocol overhead — the data transfer time calculator covers that, and rates bring their own bit-versus-byte trap because a 1 Gbps link moves at most 125 MB/s.
It also says nothing about compression or deduplication. A backup catalogue reporting 4 TiB of protected data on a 2 TB volume is not broken; it is reporting logical size against physical size, and those are different quantities that happen to share a unit.
Two adjacent cases worth naming. Flash media reserve some capacity for wear levelling and over-provisioning, so a 512 GB SSD may expose slightly less than 512 × 10⁹ bytes to the host, on top of the prefix effect. And RAID and file-system redundancy consume capacity by design: eight 4 TB drives in RAID 6 present 24 TB of usable space, not 32 TB, before any prefix conversion is applied at all.
For availability and capacity planning that combines these figures with uptime targets, the uptime SLA downtime calculator handles the time side of the same planning problem.