# System of units

A system of **units** , previously a **system of measurement** , is a collection of units of measurement in which exactly one unit is assigned to each type of size . In Germany, the International System of Units (SI, for systême international) is generally used. Other systems of units are the CGS system or the Anglo-American measurement system .

## meaning

Physical quantities can only ever be specified as a multiple of a unit of measurement (short: unit). This is the equation for the relationship between place , time and speed with non-accelerated movement

where is the unit of length, the unit of speed and the unit of time. is a real constant of proportionality that depends on the choice of units.

The constants can be summarized and obtained by transforming this equation

With

- .

For example, if the location is given in meters (m), the time in seconds (s) and the speed in multiples of the vacuum speed of light ( ), then is and the constant is

So if you have, for example, a speed of 0.5 c and a time of 2 s, the equation results

- a conclusive result.

Since it is impractical to include such a constant in every equation, it makes sense to choose units so that many constants become 1. As *defined* one (thus m / s according to the above example, the unit of velocity in meter / second ), and thus the constant is found to be in the above equation , then what the familiar equation

results.

The constant in this equation says something about the system of units used. Many natural constants are in truth "unit system constants". The Boltzmann constant is nothing more than a conversion factor between energy and temperature (which is why the temperature is often given in units of energy). So it actually says nothing about nature , only something about the temperature scale used.

## variants

While it makes little sense to define a system of units in which it does not apply, for reasons of visualization, different ways of writing size equations have become established especially for the physical quantities of electrodynamics . This is the first Maxwell equation in a vacuum in SI units

in Gaussian cgs units

and in Heaviside-Lorentz units (also called rationalized cgs)

From the point of view of the SI, these spellings differ only in that the constant is arbitrarily set equal to a number in the two CGS systems . This has the consequence that the electric current strength loses the character of a basic quantity in these unit systems; in addition, units of measurement and dimensions are ambiguous: a size value such as B. 2.0 cm can then be the measure of a length, but also z. B. also that of the capacitance of a capacitor.

Some important systems of units are:

- SI unit system (and its predecessor MKS system and MKSA system )
- Technical measurement system
- CGS system of units
- Gaussian system of units
- Heaviside-Lorentz unit system
- Geometric units (in relativity theory )
- Natural units (in high energy physics )
- Atomic units (in atomic physics )
- various systems of astronomical units
- Planck units

## See also

## Individual evidence

- ↑ Practical course in physics , Wilhelm Walcher, Teubner Verlag.

## Web links

- Spectrum Akademischer Verlag (Hrsg.): Units systems - Lexicon of physics . Heidelberg 1998 ( Spektrum.de [accessed November 4, 2016]).
- Articles on the math planet about systems of units