Kilobytes to kibibytes (kB to KiB)

One kilobyte is exactly 0.9765625 kibibytes. That is the definition of the prefixes, not a measurement: the decimal SI prefixes (kilo, mega, giga, tera) step by exactly 1,000, and the binary IEC prefixes (kibi, mebi, gibi, tebi) step by exactly 1,024. The two families are both exact; the trouble is only that software and storage labels do not always say which one they mean.

Worked through: 128 kB x 0.9765625 = 125 KiB.

Going the other way, one kibibyte is 1.024 kilobytes.

For mental arithmetic: Multiply by 0.977, or take off about 2.4%.

One kilobyte is exactly 0.9765625 KiB, because 1,000 divided by 1,024 terminates. This direction comes up when a limit is set in decimal kilobytes and a tool reports binary ones: a 500 kB upload cap is 488.28 KiB, so a file shown as 490K by ls -lh is over it. The gap is only 2.4%, small enough to ignore unless something is sized to fit exactly.

Precision is worth matching to the input. A measurement given as 1 kB carries one or two significant figures, and reporting its conversion to six implies a precision the original never had.