The Seven Base Units
Since 20 May 2019, every SI unit is defined by fixing the numerical values of seven defining constants (BIPM SI Brochure, 9th edition). The seven base units, and the constant each definition chiefly rests on, are:
The kilogram is the base unit, not the gram
| Quantity | Unit | Symbol | Defined via |
|---|---|---|---|
| time | second | s | caesium-133 hyperfine transition frequency, ΔνCs |
| length | metre | m | speed of light in vacuum, c |
| mass | kilogram | kg | Planck constant, h |
| electric current | ampere | A | elementary charge, e |
| thermodynamic temperature | kelvin | K | Boltzmann constant, k |
| amount of substance | mole | mol | Avogadro constant, NA |
| luminous intensity | candela | cd | luminous efficacy of 540 THz radiation, Kcd |
Derived Units
Every other SI unit is a product or quotient of base units. Some have special names:
- newton (N) — force: the force that accelerates 1 kg at 1 m/s². 1 N = 1 kg·m·s⁻².
- joule (J) — energy: work done by 1 N over 1 m. 1 J = 1 N·m = 1 kg·m²·s⁻².
- watt (W) — power: 1 J per second. 1 W = 1 J/s = 1 kg·m²·s⁻³.
- pascal (Pa) — pressure: 1 N per square metre. 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻².
- volt (V) — electric potential difference: 1 W per ampere. 1 V = 1 W/A = 1 kg·m²·s⁻³·A⁻¹.
The chain matters in practice: once you know power is energy per time, kilowatt-hours follow — 1 kWh = 1,000 W × 3,600 s = 3.6 MJ.
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🌡️Convert °C → KCoherent Units
SI units are coherent: when you combine them in an equation, no extra numerical factor appears. 1 N × 1 m is exactly 1 J; 1 J ÷ 1 s is exactly 1 W; 1 V × 1 A is exactly 1 W. Work entirely in coherent SI units and the arithmetic of a physics formula needs no conversion constants.
Units with a prefix or a non-SI unit break coherence. The kilowatt-hour is accepted for use but is not coherent: combining it with seconds or joules needs the factor 3.6 × 10⁶.
Prefixes
A prefix multiplies a unit by a power of ten and is written directly in front of the symbol with no space. The common ones:
Newest prefixes
| Prefix | Symbol | Factor |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
Writing SI Values Correctly
The BIPM and NIST style rules (BIPM SI Brochure, 9th edition; NIST SP 811, Guide for the Use of the SI) that most often matter:
- Kelvin has no degree sign: 300 K, not 300 °K. Degrees Celsius keep it: 20 °C.
- Leave a space between the number and the symbol: 5 kg, 20 °C, 10 %. Plane-angle degrees are an exception: 30°.
- Symbols are not pluralised and take no full stop: write 5 kg, never "5 kgs" or "5 kg." mid-sentence.
- Case carries meaning: m is metre or milli, M is mega; W is watt; k (kilo) is lower case, K is kelvin. 1 mW and 1 MW differ by a factor of 10⁹.
- Unit names are lower case in running text, even when named after a person (newton, kelvin), while the symbol is capitalised (N, K).