Why a 1 TB drive shows as 931 GB
Drive makers count in powers of ten and operating systems count in powers of two. Neither is lying; they are using different prefixes with confusingly similar names.
Size in gibibytes
931.32GiB
- Size in tebibytes
- 0.9095 TiB
- Size in mebibytes
- 953 674 MiB
- Size in decimal gigabytes
- 1000.00 GB
- Apparent shortfall
- 6.868 %
- Apparent loss
- 68.68 GB
- Bytes
- 1 000 000 000 000
Show the working
- Advertised size = 1
- Bytes = 1 * 1e12 = 1 000 000 000 000
- Size in gibibytes = 1 000 000 000 000 / 2^30 = 931.323
- Size in tebibytes = 1 000 000 000 000 / 2^40 = 0.909 495
- Size in mebibytes = 1 000 000 000 000 / 2^20 = 953 674
- Size in decimal gigabytes = 1 000 000 000 000 / 1e9 = 1000
- Apparent shortfall = 1000 > 0 ? (1 - 931.323/1000) * 100 : 0 = 6.867 74
- Apparent loss = 1000 - 931.323 = 68.6774
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- 1 GB = 10^9 bytes; 1 GiB = 2^30 bytes = 1 073 741 824 bytes
- the ratio is 2^30 / 10^9 = 1.073 741 824, a fixed 7.374% gap at the gigabyte scale
The gap widens with each prefix: 2.4% at kilobytes, 4.9% at megabytes, 7.4% at gigabytes, 10.0% at terabytes.
Formatting overhead and filesystem metadata take a further slice on top of this.