How units work
Seven agreements hold up every measurement on Earth.
Pick your depth. Same facts at every level — only the detail changes.
A unit is an agreed-upon amount — so when two people say "three metres," they mean exactly the same thing. That's all a unit is: a promise everyone keeps. The whole world agreed on seven basic ones, and every other unit is built by combining them, like words built from letters.
The metric system steps by tens (a kilometre is 1,000 metres) because tens are easy to compute with; older systems stepped by twelves and sixteens because those divide evenly into halves, thirds, and quarters at the market stall. Both were rational choices for their time. The traps live between systems: a US gallon and an imperial gallon differ by 20%, and a food "Calorie" is secretly a thousand calories. Every US customary unit is officially defined as an exact metric amount underneath — an inch has been exactly 25.4 mm since 1959.
The SI has seven base units — second, metre, kilogram, ampere, kelvin, mole, candela — and every other unit is a product of their powers: a newton is kg·m/s², a joule is N·m, a watt is J/s. That structure gives you dimensional analysis, the quiet superpower: track the units through a calculation and they must cancel to the units of the answer. If they don't, the answer is wrong before you check a single digit.
Since the 2019 redefinition, every SI base unit is fixed by pinning a constant of nature to an exact value: the second by the cesium transition frequency, the metre by the speed of light, the kilogram by the Planck constant, the ampere by the elementary charge, the kelvin by the Boltzmann constant, the mole by the Avogadro number, the candela by a fixed luminous efficacy. Nothing physical to lose, scratch, or drift — the kilogram was the last artifact, a platinum-iridium cylinder that had measurably diverged from its own copies before it was retired. Definitions are exact; realizations of them in any lab still carry measurement uncertainty — that distinction is the whole discipline of metrology.
The seven base units — everything else is built from these
The multiplier system — one set of prefixes, every unit
Instead of inventing a new unit for every size, the SI bolts a prefix onto an existing one. Learn six prefixes once and they work everywhere — on metres, grams, watts, and bytes alike.
giga- G × 10⁹
GB — a billion bytes
mega- M × 10⁶
MW — a million watts
kilo- k × 10³
km — a thousand metres
milli- m × 10⁻³
mm — a thousandth of a metre
micro- µ × 10⁻⁶
µg — a millionth of a gram
nano- n × 10⁻⁹
nm — how chip features are sized
The superpower — if the units don't cancel, the answer is wrong
Units aren't decoration on a number — they multiply and divide with it. Drive 120 km in 2 h and the units divide too: 120 km ÷ 2 h = 60 km/h. The famous failures are unit failures: NASA's Mars Climate Orbiter burned up in 1999 because one team wrote thruster figures in pound-seconds and another read them as newton-seconds. Checking that units cancel is the cheapest error-detection system ever invented — and it costs nothing but attention.