# Unit of measurement

Geometric and physical quantities are specified in units of measurement (also size units or physical units ) that have a clear (in practice, well-defined, fixed) value. All other values ​​of the respective size are given as a multiple of the unit. Well-known units of measurement are, for example, meters , seconds , kilowatt hours , Hertz or kilometers per hour .

Units of measure can be defined for all types of quantities, including non-physical quantities, such as currencies or the perceptual quantities of tone or loudness .

## properties

To avoid measured values with very large or very small numbers, prefixes for units of measurement can be used for most units (exceptions e.g. for degrees Celsius or minutes).

Quantities of the dimension number have the unit of measurement 1 (one). This unit is often given additional names ( auxiliary units) for clarity , for example rad or steradian . However, auxiliary units of measure can also be omitted. For proportions of unit 1 are z. B. % (percent), (per mille) or ppm (millionths) commonly used.

## Systems of units

Units can be combined into systems of units such as B. the International System of Units . A system of units has certain basic units from which further units are derived by deriving them.

## Unit symbol

Unit symbols are used to represent the unit names. They are mostly Latin letters or groups of letters, but also Greek letters or other characters. Unit symbols that do not belong to any alphabet were also used for old units of measurement. Unit symbols are not set in italics - not even if the surrounding text is italic. For measurements, there is a space between the number and the unit symbol; a line break separation should be avoided.

Further information on correct use can be found here: Notation of quantities, numerical values ​​and units .

## conversion

The value of a physical quantity is generally the product of a number and a physical unit. In order to represent this value with a different unit (of the same size type), one can transform this product and use known relationships between the units.

Example: A table has a height of 75 cm. It is well known that 1 m = 100 cm. This can be used to shape: 75 cm = 0.75 × 100 cm = 0.75 m.

Often one unit is a multiple of the other (the “multiple” does not have to be an integer), but in some cases the relationship is different. For example, for temperatures in degrees Celsius and in Kelvin:, the two temperature scales have different zero points. ${\ displaystyle \ textstyle t / ^ {\ circ} \ mathrm {C} = T / \ mathrm {K} -273 {,} 15}$

If one unit is a multiple of the other, the conversion can be carried out by multiplying by 1, whereby 1 is written as the quotient of two equal quantities in the two units, so that the first unit is canceled and the second remains.

The conversion from the example above can also be carried out as follows:

${\ displaystyle 1 = {\ frac {1 \, \ mathrm {m}} {100 \, \ mathrm {cm}}}}$
${\ displaystyle 75 \, \ mathrm {cm} = 75 \, \ mathrm {cm} \ cdot 1 = 75 \, \ mathrm {cm} \ cdot {\ frac {1 \, \ mathrm {m}} {100 \ , \ mathrm {cm}}} = {\ frac {75} {100}} \, \ mathrm {m} = 0 {,} 75 \, \ mathrm {m}}$

If a unit is the product or quotient of other units, such conversions can be applied to the latter. When the direct relationship between two entities is not known, but the relationship to a third entity, e.g. B. an SI unit, the conversion can be carried out by concatenating the conversion into the third unit and that of this into the target unit.

Example: 463 feet (ft) per minute (min) are to be converted to knots (kn). It is well known that 1 ft = 0.3048 m, 1 min = 60 s, 1 kn = 1  nm / h , 1 nm = 1852 m, 1 h = 3600 s.

${\ displaystyle 463 \, {\ frac {\ mathrm {ft}} {\ mathrm {min}}} = 463 \, {\ frac {\ mathrm {ft}} {\ mathrm {min}}} \ cdot {\ frac {0 {,} 3048 \, \ mathrm {m}} {1 \, \ mathrm {ft}}} \ cdot {\ frac {1 \, \ mathrm {min}} {60 \, \ mathrm {s} }} \ cdot {\ frac {1 \, \ mathrm {sm}} {1852 \, \ mathrm {m}}} \ cdot {\ frac {3600 \, \ mathrm {s}} {1 \, \ mathrm { h}}} = 4 {,} 572 \, {\ frac {\ mathrm {sm}} {\ mathrm {h}}} = 4 {,} 572 \, \ mathrm {kn}}$

For values ​​of the prefixes for units of measure see this article.

## history

A public measuring standard for the unit of length Elle at the old town hall of Braunschweig

In earlier times, units of measurement were usually defined using material measures that had the corresponding property. This is quite possible, for example. B. for length , volume and mass units , because these can be represented by metal rods, spheres or hollow vessels. Installed in a generally accessible place, for example walled into the facade of the town hall , such a measure made it possible for everyone to calibrate their own measuring devices . Units of measurement used to be very arbitrary and often unrelated to one another, but based on practical aspects such as length dimensions on the human body.

More abstract units of measurement used to have only a subordinate meaning in everyday life. Such units have to be defined using measurement rules that can be reproduced comparatively easily with high accuracy . A distinction must be made between “definition” and “implementation rule”; the appropriate implementation procedures often differ from the procedure specified in the definition. Which method is suitable depends on the accuracy requirements. For example, much more effort can be made to “represent” a unit of measurement as a national standard than for the verification of commercial scales. Depending on the accuracy requirement, embodied dimensions can still be current today.

## Examples

In the International System of Units, the kilogram was defined by the mass of the original kilogram in Paris until 2019 . All masses are given as multiples of this mass. For example, the specification "5.1 kg" meant "5.1 times the mass of the original kilogram in Paris".

The unit meter / second of speed is a unit derived from the base units meter and second in the SI .

Examples of old units: