# Base units

We include all seven of the base units at the core of the SI. They are so called because each one introduces an independent physical quantity not contained in any other unit in the system. The formal definitions are given along with a lay person’s guide as to what they measure (note that the formal definitions may be simplified for clarity).

## SI base units

 Unit name Symbol What it measures and its definition metre m Length or distance The metre is a unit of distance and is the basis for measuring length, area and volume. The metre was originally derived from one ten millionth of the distance from Earth’s pole to the equator but has been refined(1) several times to link it to more stable physical constants. It is now defined in terms of the distance travelled at the speed of light during a precisely defined fraction of a second. The metre is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s−1, where the second is defined in terms of the caesium frequency ΔνCs. The effect of this definition is that one metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second. kilogram kg Mass In ordinary language, the kilogram measures what most regard as weight. Strictly speaking, mass is the amount of matter in an object, whereas weight is to do with the pull of gravity (how heavy it is). It was originally just 1000 grams where 1 gram was the mass of 1 cubic centimetre of water (making the kilogram equal to the mass of 1 litre of water). The kilogram is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of c and ΔνCs. second s Time The second is the familiar unit of time that we count with our watches and clocks. It is defined by the natural beats of a highly stable caesium atomic clock. The second is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1. ampere A Electric current The ampere is the familiar ‘amp’ that we associate with things like fuses and electric cable. It is the fundamental base unit for electricity and magnetism. The ampere is defined in terms of the amount of electric charge on one electron. The ampere is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10−19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ΔνCs. kelvin K Thermodynamic temperature The kelvin measures temperature in the way we normally understand it, i.e. how hot something is. It is closely linked to the Celsius scale except that zero kelvin (0 K) is when there is no heat at all (absolute zero). 0 K = -273.15 °C). The kelvin is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10−23 when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs. mole mol Amount of substance Used in chemistry and physics, it represents a fixed number of “elementary entities” of a substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. candela cd Luminous intensity The candela is the SI unit of luminous intensity in a given direction. Essentially, this measures the ‘brightness’ of radiation. It is defined in terms of the intensity of a very pure yellow-green light source with a strength measured by its power spread over a cone shaped beam. The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.

(1) Note that although the definition has changed, the actual length of the metre has not. The revised definition represents a very precise statement of the length of the original prototype that was used as the master reference for the measurement of distance world-wide. We now know it to be slightly in error in respect of the true figure of the Earth (inevitably so with the huge advancements in technology since the eighteenth century) but that is of no practical consequence. Nevertheless, the fact that the Earth’s circumference is very close to 40 000 km is still handy when using globes or world maps.

## SI redefinition

Prior to the definitions adopted in 2018, the SI was defined through seven base units from which the derived units were constructed as products of powers of the base units. Defining the SI by fixing the numerical values of seven defining constants has the effect that this distinction is no longer needed, since all units, base as well as derived units, can be constructed directly from the defining constants. Nevertheless, the concept of base units and derived units is maintained because it is useful and historically well established.