Measure · since 20 May 2019
The SI: seven constants
The International System of Units is built on seven constants of nature whose values are fixed by definition. Every unit, from the metre to the volt, follows from them. No unit depends on a physical object any more.
The defining constants
Exact by definition: these numbers will never be revised.
| Symbol | Constant | Exact value | Fixes |
|---|---|---|---|
| ΔνCs | hyperfine transition frequency of caesium-133 | 9 192 631 770 Hz | s |
| c | speed of light in vacuum | 299 792 458 m/s | m |
| h | Planck constant | 6.626 070 15 × 10⁻³⁴ J s | kg |
| e | elementary charge | 1.602 176 634 × 10⁻¹⁹ C | A |
| k | Boltzmann constant | 1.380 649 × 10⁻²³ J/K | K |
| NA | Avogadro constant | 6.022 140 76 × 10²³ mol⁻¹ | mol |
| Kcd | luminous efficacy of 540 THz radiation | 683 lm/W | cd |
Source: The International System of Units (SI), 9th edition (2019), with later updates.
The seven base units
| Symbol | Unit | How it is fixed now | Then |
|---|---|---|---|
| s | second time | Fixed by taking the caesium frequency ΔνCs to be exactly 9 192 631 770 Hz. | Defined from the caesium atom since 1967; before that, as a fraction of the year 1900, and earlier of the mean solar day. |
| m | metre length | The distance light travels in vacuum in 1/299 792 458 of a second, because c is fixed. | Since 1983. Before: a wavelength of krypton-86 light (1960), and before that a platinum-iridium bar in Sèvres (1889). |
| kg | kilogram mass | Fixed by taking the Planck constant h to be exactly 6.626 070 15 × 10⁻³⁴ J s, with the metre and second. | Since 2019. From 1889 to 2019 it was the mass of one metal cylinder, the International Prototype, kept near Paris. |
| A | ampere electric current | Fixed by taking the elementary charge e to be exactly 1.602 176 634 × 10⁻¹⁹ C: one ampere is that many charges per second, inverted. | Since 2019. Before: the current giving a set force between two long parallel wires (1948). |
| K | kelvin thermodynamic temperature | Fixed by taking the Boltzmann constant k to be exactly 1.380 649 × 10⁻²³ J/K. | Since 2019. From 1954 to 2019: 1/273.16 of the temperature of the triple point of water. |
| mol | mole amount of substance | Exactly 6.022 140 76 × 10²³ specified entities (atoms, molecules, ions…). | Since 2019. Before: as many entities as atoms in 12 g of carbon-12. |
| cd | candela luminous intensity | Fixed by taking the luminous efficacy of green light at 540 × 10¹² Hz to be exactly 683 lm/W. | Since 1979, restated in 2019. Earlier definitions used a glowing platinum surface and, before that, candles. |
Why constants instead of objects
An object can be damaged, lost or slowly change: the old kilogram cylinder and its copies drifted apart by tens of micrograms. A constant of nature is the same in every laboratory, so anyone with the right apparatus can realise the unit without travelling to Paris.