SI Units and Prefixes

Every base unit now hangs off a constant

A unit needs a reference that anyone can get to. For most of the history of the metric system that reference was an object: a bar for the metre, a cylinder for the kilogram. Objects get scratched, contaminated or lost, and there is only ever one of them, so the world’s measurements end up depending on the condition of a single artefact in a single vault.

Since 2019 each base unit is fixed instead by a constant, which a good enough laboratory can reproduce from nothing. The metre follows from the speed of light, the kilogram from the Planck constant, the ampere from the elementary charge, the kelvin from the Boltzmann constant, and the mole from the Avogadro constant at exactly 6.02214076 × 10²³ entities. The second is the oldest of the current definitions, set in 1967 as 9,192,631,770 periods of the caesium-133 hyperfine transition. The candela is the outlier, weighted by human perception, which is why it belongs to photometry and lighting rather than to most physics calculations.

The prefixes that get misread

Prefix symbols are case-sensitive, and several of them collide with unit symbols. These are the ones worth a second look:

• k against K. Lower case k is kilo. Capital K is the kelvin, so kB and KB are different things.
• m doing two jobs. m is milli as a prefix and the metre as a unit. The notation is the only thing separating mm, a millimetre, from m·m, a square metre: a prefix is joined to its unit, while a product of units takes a centred dot or a space.
• µ against u. The micro symbol is the Greek mu. Where that cannot be typed the accepted substitute is u, which is why ug on a label means µg.
• M against m. Mega is 10⁶ and milli is 10⁻³, nine orders of magnitude apart on one keystroke.
• da is two characters. Deca has the only two-letter prefix symbol, so it cannot be split the way single-letter symbols can.

A prefix also binds to its unit before any exponent applies. 1 km² means (10³ m)², so 10⁶ m², not 10³ m². Prefixes never stack either: there is no millimicrometre, only a nanometre.

Four of these prefixes are newer than most printed tables

Ronna, quetta, ronto and quecto were adopted by the General Conference on Weights and Measures in November 2022, taking the range out to 10³⁰ and in to 10⁻³⁰. Any chart produced before then stops at yotta and yocto, which is usually why a reader cannot find Q, R, q or r in the reference already on the wall.

Most of the range sees little use. Hecto survives almost entirely in the hectopascal, which weather reports use because one hPa is one millibar, and deci survives in the decibel and the decimetre. Nothing in the table can go stale, since every prefix is a defined power of ten and every base unit is fixed by a defining constant. The kelvin is worth one last note: it is written K, never with a degree sign and never as degrees kelvin, and because a kelvin and a degree Celsius are the same size, a temperature difference needs no conversion between them.