Metric Prefixes, Bits and Bytes

How SI prefixes work

Every metric unit you meet is a base unit with a decimal prefix in front of it: a kilometre is a metre multiplied by 1,000, a milligram is a gram divided by 1,000. Because every prefix is a power of ten, converting between prefixed units only ever means shifting the decimal point. The km in the length converter and the kg in the weight converter come from the same list.

Case matters: m and M

The symbols are not interchangeable. Lowercase m means milli, one thousandth, and uppercase M means mega, one million. A 3 mW indicator draws 0.003 watts; a 3 MW generator supplies 3,000,000 watts. One letter out of place makes the answer out by a factor of one billion, which is the sort of error no rounding will rescue.

Bits and bytes

A bit is the smallest unit of information, a single on or off. A byte is exactly 8 bits. File sizes are written in bytes, network speeds are written in bits per second, and reconciling the two is the most common calculation error in this area. The fix is one division: take a speed in bits per second and divide by 8 to get a rate in bytes per second.

The UnitUtils data storage converter keeps bits, bytes, decimal prefixes and binary prefixes as separate units, so you state which one you mean instead of inferring it. Frequency prefixes are decimal only, so 1 kilohertz is exactly 1,000 hertz and 1 gigahertz is exactly 1,000,000,000 hertz, with no 1,024-based variant in the frequency converter.

Decimal and binary prefixes

Two sets of prefixes both claim to mean a thousand. The decimal set counts in powers of 1,000. The binary set, written with an extra i as in KiB and MiB, counts in powers of 1,024, which is 2 to the power 10, the power of two closest to 1,000. UnitUtils treats them as distinct units, so 1 kB and 1 KiB never collapse into the same number.

The consequence is that the binary unit is always the larger of the pair, and the difference compounds: 2.4% at kilo, 4.9% at mega, 7.4% at giga and 9.95% at tera. A manufacturer quoting decimal sizes and an operating system reporting binary sizes will therefore disagree more about a large drive than a small one.

Why a 1 TB drive shows about 931 GB

Drive capacities are sold in decimal bytes, so a drive labelled 1 TB holds 1,000,000,000,000 bytes. Many operating systems report free space in binary units while still labelling the column GB. The arithmetic behind the number on screen is then 1,000,000,000,000 ÷ 1,073,741,824 = 931.32 GiB. Nothing is missing: the gap is the difference between 1,000 and 1,024, compounded across the four prefix steps from kilo to tera.

Internet speeds into download times

Take a line advertised at 100 megabits per second. Divide by 8 to reach bytes: 100 ÷ 8 = 12.5 megabytes per second. A 1.5 GB file is 1,500 MB, so at that full rate it takes 1,500 ÷ 12.5 = 120 seconds, which is exactly two minutes.

Real transfers take longer, because an advertised speed is the capacity of the line rather than the rate the file transfer gets. The same arithmetic is useful in reverse: to move a 100 MB file in under ten seconds you need at least 100 ÷ 10 = 10 MB/s, which is 10 × 8 = 80 Mbit/s before any overhead.

Converting by hand

Every data conversion is one multiplication and one division: multiply by the number of bits in the unit you have, then divide by the number of bits in the unit you want. Both numbers are whole, so the arithmetic is exact. To turn 5 MB into kibibytes, multiply out to bytes, 5 × 1,000,000 = 5,000,000, then divide by the bytes in a kibibyte, 5,000,000 ÷ 1,024 = 4,882.8125 KiB.

Report only the digits you trust. The note on precision sets out how many significant digits the UnitUtils converters show before rounding and when very large or very small values are written in exponent form.