Measurement of any quantity involves comparison with a precisely defined unit value. This is necessary for a measurement to mean the same thing in different places and to different people.

Standard units of measure need to be identified and defined as accurately as possible. The system that is used in the scientific community is called Système International d’Unités, abbreviated to SI.

All of the SI units used in scientific measurements can be calculated from just seven fundamental units.

Quantity measured | Unit | Symbol | Definition |
---|---|---|---|

Length | metre | m | The distance travelled by light in a vacuum in 1/299,792,458 s. |

Mass | kilogram | kg | The mass of the international prototype kilogram (IPK) preserved at Sèvres in France. |

Time | second | s | The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the |

Thermodynamic temperature | kelvin | K | The kelvin is 1/273.16 of the thermodynamic temperature of the triple point of water. To calculate degrees Celsius, subtract 273.15. In other words, °C = K − 273.15. |

Amount of substance | mole | mol | The mole is the amount of substance that contains as many chemical units as there are atoms in 0.012 kg of carbon-12. |

Electric current | ampere | A | The ampere is the current in two very long parallel wires 1 m apart that gives rise to a magnetic force per unit length of 2 x 10 |

Luminous intensity | candela | Cd | The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10 |

## Length

The speed of light, represented by the symbol ‘c’, is a physical constant established to be exactly 299,792,458 m s^{-1}. The ‘metre’ is defined using this constant.

Distance covered in 1/299,792,458 second is exactly 1 metre.

## Mass

The international prototype kilogram (IPK) is made of a platinum/iridium alloy. It is cylindrical in shape, the height and diameter having the same dimensions – 39.17 mm. The IPK is kept at the International Bureau of Weights and Measures (BIPM) in Sèvres on the outskirts of Paris.

## Time

Caesium atomic clocks operate by exposing caesium atoms to microwaves until they start to vibrate at one of their resonant frequencies. By measuring this frequency, which is an unchanging property of matter, a time measure can be established. One second is defined as the time taken to complete 9,192,631,770 oscillations of the caesium 133 atom exposed to suitable microwave stimulation. Caesium clocks are very stable, and accuracies of 1 second in 1.4 million years have been reported.

## Temperature

The three phases of water are solid ice, liquid water and gaseous water vapour. They can only exist together in equilibrium at a temperature of 0.01°C or 273.16 K and a pressure of 611.73 Pa. This point is known as the ‘triple point’ of water and is an unchanging property of water.

H | H | H |

The unit of thermodynamic temperature, known as the kelvin, is defined as 1/273.16 of the thermodynamic temperature of the triple point of water. To calculate degrees Celsius, subtract 273.15. In other words, °C = K − 273.15.

## Amount of substance

A mole is the amount of substance that contains as many chemical units (atoms, molecules or other particles) as there are atoms in exactly 12 grams of carbon-12 (i.e. 6.023 X 10^{23}).

## Electric current

The ampere is the current in two very long parallel wires 1 m apart that gives rise to a magnetic force per unit length of 2 x 10^{-7} N/m.

## Luminous intensity

A common candle emits light with a luminous intensity of roughly 1 candela. The SI definition for the candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10^{12} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

In other words, if a light source emits 1 candela of luminous intensity uniformly across a solid angle of 1 steradian, the total luminous flux emitted into that angle is 1 lumen (lm). This unit of measurement is called lux (lx = lm/m^{2}) and is the amount of total light in lumens divided by the area being illuminated.

To convert candela into lux, divide the candela value by the square of the distance in metres from the light source to the illuminated surface. For example, a 100 watt light bulb has a luminous intensity of about 1,700 lumens. At a distance of 3 metres directly below the bulb, the total lux is 1,700/3^{2} = 189 lux.

#### Nature of science

The aim of science is to explain phenomena by using empirical evidence. Data collection often involves measurement, and standard units of measure need to be identified and defined as accurately as possible to enable consistency and comparison.

#### Useful links

The Measurement Standards Laboratory of New Zealand has prepared PDF translation of the BIPM’s Concise Summary of the SI in te reo Māori that can be downloaded here.

BIPM is the intergovernmental organisation through which Member States act together on matters related to measurement science and measurement standards.

This informative and fun animation How big is a mole? (Not the animal, the other one.) teaches students about the concept of the mole in chemistry.