Conversion from Kibioctets per second to Kilobits per second

Information about the Kibioctet per second (Kio/s)

The kibioctet per second is a unit of data transfer rate equal to 1,024 octets per second, and therefore to 8,192 bits per second. Its symbol is Kio/s. Unlike most of the binary rate units it is genuinely common, because the command-line tools that copy, download and synchronise files have reported in it for decades.

The reason is straightforward. Those tools count what they have moved in blocks, and blocks are powers of two. A program that reads in four-kibioctet pieces and divides the total by elapsed time produces a rate in kibioctets per second, and reporting it in decimal kilooctets would require an extra multiplication for no benefit. The unit is what the arithmetic naturally produces.

Anyone who has watched a file copy on a Unix-like system has seen the figure. Download utilities, archive tools, disc-writing commands and network file transfer programs all report progress in kibioctets or mebioctets per second, and most of them label it correctly with the lowercase i. It is one of the few places where the IEC prefixes are used consistently in everyday software.

For scale, a kibioctet per second moves about a thousand characters of text each second: a short letter in a second, a novel in about ten minutes. It is a rate at which a modern web page will not load in any reasonable time, so seeing it in a progress display usually means something has gone wrong with the connection rather than that the transfer is nearly finished.

The difference from a kilooctet per second is 2.4 per cent, which nobody notices. The value of using the binary unit here is not accuracy but honesty: the number came from a binary computation, and writing it with a binary prefix says so. A reader who wants the decimal figure can convert; a reader given a decimal label for a binary number cannot recover anything.

Comparing the reading with an advertised connection speed requires two steps: multiply by eight to get bits, and adjust by 2.4 per cent for the base. In practice the second step is beneath the noise of any real measurement, and the first is the one that matters.

One kibioctet per second equals 1,024 octets per second, 8,192 bits per second, or 1.024 kilooctets per second.

Information about the Kilobit per second (kbit/s)

The kilobit per second is a unit of data transfer rate equal to one thousand bits per second. Its symbol is kbit/s, often written kbps. It was the unit of the dial-up era, and it survives today as the unit in which audio and speech encoding rates are quoted.

The dial-up sequence is worth recalling because each number marks a technical generation. Modems ran at 300 bits per second in the late 1970s, then 1,200, 2,400, 9,600, 14,400, 28,800, 33,600 and finally 56 kilobits per second at the end of the 1990s. That last figure was the ceiling of an ordinary telephone line, set by the eight-kilohertz sampling of the digital telephone network rather than by the modem.

Audio encoding is where the unit now lives. Telephone-quality speech runs at 8 to 64 kilobits per second depending on the codec, with modern low-rate codecs producing intelligible speech at 8 and high-quality voice calls at 24 to 32. Music at 128 kilobits per second was the early standard of portable players, 192 and 256 are common, and 320 is the practical ceiling of the older lossy formats.

Those numbers reward a moment of arithmetic. Music at 128 kilobits per second is 16 kilooctets per second, so a four-minute track is about 3.8 megaoctets. Uncompressed compact-disc audio runs at 1,411 kilobits per second, so the compressed file is about a tenth the size of the original, which is the whole point of the format.

Video subtitle streams, control channels and telemetry links also work in kilobits per second. So does much of the machine-to-machine traffic that fills modern networks: a sensor reporting a reading every few seconds needs a fraction of a kilobit per second, and the protocols designed for such devices are built around keeping the radio switched off most of the time.

The unit's lower-case k marks the decimal kilo, one thousand exactly. In transmission this has never been ambiguous, because network rates have always been counted in true thousands; the binary confusion that afflicts storage units does not arise here, and a kilobit per second means the same thing in every document.

One kilobit per second equals 1,000 bits per second, 125 octets per second, or about 0.9766 kibibits per second.