SI Units: The International System of Units
The SI is the modern metric system: seven base units, every other unit built from them, and a set of prefixes for scaling any unit up or down by powers of ten. It is the system of measurement used in science worldwide and in everyday life in almost every country.
The seven base units
Since 2019 each base unit has been fixed by giving an exact value to a constant of nature, rather than by a physical object: the kilogram, for example, is no longer a metal cylinder in a vault near Paris but follows from the Planck constant. That means anyone with the right equipment can realise the units anywhere.
| Quantity | Unit | Symbol | Defined by |
|---|---|---|---|
| time | second | s | caesium-133 hyperfine frequency ΔνCs = 9 192 631 770 Hz |
| length | meter | m | speed of light c = 299 792 458 m/s |
| mass | kilogram | kg | Planck constant h = 6.626 070 15 × 10⁻³⁴ J s |
| electric current | ampere | A | elementary charge e = 1.602 176 634 × 10⁻¹⁹ C |
| thermodynamic temperature | kelvin | K | Boltzmann constant k = 1.380 649 × 10⁻²³ J/K |
| amount of substance | mole | mol | Avogadro constant NA = 6.022 140 76 × 10²³ mol⁻¹ |
| luminous intensity | candela | cd | luminous efficacy Kcd = 683 lm/W at 540 THz |
Derived units
Every other SI unit is a product of powers of the base units. A speed is meters per second, a density kilograms per cubic meter. Twenty-two derived units are common enough to have names and symbols of their own; the newton, for example, is the force that accelerates one kilogram by one meter per second every second.
Derived units with special names
| Quantity | Unit | Symbol | In base units |
|---|---|---|---|
| plane angle | radian | rad | m/m |
| solid angle | steradian | sr | m²/m² |
| frequency | hertz | Hz | s⁻¹ |
| force | newton | N | kg m s⁻² |
| pressure, stress | pascal | Pa | kg m⁻¹ s⁻² |
| energy, work, heat | joule | J | kg m² s⁻² |
| power | watt | W | kg m² s⁻³ |
| electric charge | coulomb | C | A s |
| electric potential difference | volt | V | kg m² s⁻³ A⁻¹ |
| capacitance | farad | F | kg⁻¹ m⁻² s⁴ A² |
| electric resistance | ohm | Ω | kg m² s⁻³ A⁻² |
| electric conductance | siemens | S | kg⁻¹ m⁻² s³ A² |
| magnetic flux | weber | Wb | kg m² s⁻² A⁻¹ |
| magnetic flux density | tesla | T | kg s⁻² A⁻¹ |
| inductance | henry | H | kg m² s⁻² A⁻² |
| Celsius temperature | degree Celsius | °C | K |
| luminous flux | lumen | lm | cd sr |
| illuminance | lux | lx | cd sr m⁻² |
| activity of a radionuclide | becquerel | Bq | s⁻¹ |
| absorbed dose | gray | Gy | m² s⁻² |
| dose equivalent | sievert | Sv | m² s⁻² |
| catalytic activity | katal | kat | mol s⁻¹ |
Some derived units without special names
| Quantity | Unit | Symbol |
|---|---|---|
| area | square meter | m² |
| volume | cubic meter | m³ |
| speed | meter per second | m/s |
| acceleration | meter per second squared | m/s² |
| wavenumber | reciprocal meter | m⁻¹ |
| density | kilogram per cubic meter | kg/m³ |
| surface density | kilogram per square meter | kg/m² |
| specific volume | cubic meter per kilogram | m³/kg |
| current density | ampere per square meter | A/m² |
| magnetic field strength | ampere per meter | A/m |
| amount concentration | mole per cubic meter | mol/m³ |
| luminance | candela per square meter | cd/m² |
SI prefixes
A prefix multiplies a unit by a power of ten: a kilometer is 1 000 meters, a milligram a thousandth of a gram. There are 24 prefixes; ronna, quetta, ronto and quecto were added in 2022 for data storage and for very small quantities in science. Prefixes attach to the gram, not the kilogram (a milligram, never a microkilogram).
| Prefix | Symbol | Factor | Written out |
|---|---|---|---|
| quetta | Q | 10³⁰ | 1 000 000 000 000 000 000 000 000 000 000 |
| ronna | R | 10²⁷ | 1 000 000 000 000 000 000 000 000 000 |
| yotta | Y | 10²⁴ | 1 000 000 000 000 000 000 000 000 |
| zetta | Z | 10²¹ | 1 000 000 000 000 000 000 000 |
| exa | E | 10¹⁸ | 1 000 000 000 000 000 000 |
| peta | P | 10¹⁵ | 1 000 000 000 000 000 |
| tera | T | 10¹² | 1 000 000 000 000 |
| giga | G | 10⁹ | 1 000 000 000 |
| mega | M | 10⁶ | 1 000 000 |
| kilo | k | 10³ | 1 000 |
| hecto | h | 10² | 100 |
| deca | da | 10¹ | 10 |
| deci | d | 10⁻¹ | 0.1 |
| centi | c | 10⁻² | 0.01 |
| milli | m | 10⁻³ | 0.001 |
| micro | µ | 10⁻⁶ | 0.000 001 |
| nano | n | 10⁻⁹ | 0.000 000 001 |
| pico | p | 10⁻¹² | 0.000 000 000 001 |
| femto | f | 10⁻¹⁵ | 0.000 000 000 000 001 |
| atto | a | 10⁻¹⁸ | 0.000 000 000 000 000 001 |
| zepto | z | 10⁻²¹ | 0.000 000 000 000 000 000 001 |
| yocto | y | 10⁻²⁴ | 0.000 000 000 000 000 000 000 001 |
| ronto | r | 10⁻²⁷ | 0.000 000 000 000 000 000 000 000 001 |
| quecto | q | 10⁻³⁰ | 0.000 000 000 000 000 000 000 000 000 001 |
Writing SI units
- Symbols are not abbreviations: no full stop and no plural s (5 kg, not 5 kgs.).
- Leave a space between the number and the symbol (20 °C, 3 m), except for the degree, minute and second of angle (45°).
- Unit names are written in lower case, even when named after a person (newton, pascal), but their symbols take a capital (N, Pa).
- Group long numbers in threes with a thin space, not a comma or point (1 000 000), since the decimal marker may be either.
Converting to and from SI units
Every unit in RK's converters is defined as an exact multiple of an SI unit, so conversions are exact: a foot is 0.3048 m and a pound 0.453 592 37 kg by definition. Use the conversion calculator for everyday units or browse all converters and units.