Units
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Go to the Geometrized Units page.
The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System (SI) of units, the modern form of the metric system. The SI has been or is in the process of being adopted throughout the world.
In trade, weights and measures is often a subject of governmental regulation, to ensure fairness and transparency. The Bureau international des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI). Metrology is the science for developing national and internationally accepted units of weights and measures.
In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures developed long ago for commercial purposes.
Science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measure can aid researchers in problem solving (see, for example, dimensional analysis).
SI Units
The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are seven base units: Each of these base units represents, at least in principle, different kinds of physical quantities. From these seven base units, several other units are derived. In addition to the SI units, there is also a set of non-SI units accepted for use with SI which includes some commonly used units such as the litre.
| Name | Symbol | Quantity |
|---|---|---|
| metre | m | length |
| kilogram | kg | mass |
| second | s | time |
| ampere | A | electric current |
| kelvin | K | thermodynamic temperature |
| candela | cd | luminous intensity |
| mole | mol | amount of substance |
A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.
| Multiples | Name | deca- | hecto- | kilo- | mega- | giga- | tera- | peta- | exa- | zetta- | yotta- | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Symbol | da | h | k | M | G | T | P | E | Z | Y | ||
| Factor | 100 | 101 | 102 | 103 | 106 | 109 | 1012 | 1015 | 1018 | 1021 | 1024 | |
| Subdivisions | Name | deci- | centi- | milli- | micro- | nano- | pico- | femto- | atto- | zepto- | yocto- | |
| Symbol | d | c | m | µ | n | p | f | a | z | y | ||
| Factor | 100 | 10−1 | 10−2 | 10−3 | 10−6 | 10−9 | 10−12 | 10−15 | 10−18 | 10−21 | 10−24 | |
US Customary Units
| Unit | Divisions | SI Equivalent |
|---|---|---|
| Exact relationships shown in boldface | ||
| International | ||
| 1 inch (in) | 25.4 mm | |
| 1 foot (ft) | 12 in | 0.3048 m |
| 1 yard (yd) | 3 ft | 0.9144 m |
| 1 mile (mi) | 5,280 ft or 1,760 yd | 1.609344 km |
| Survey | ||
| 1 link (li) | 33/50 ft | 0.201168 m |
| 1 foot (survey) | 1200/3937 m | 0.3048006 m |
| 1 rod (rd) | 25 li | 5.029210 m |
| 1 chain (ch) | 4 rd | 20.1168 m |
| 1 furlong (fg) | 10 ch | 201.168 m |
| 1 mile (survey) | 80 ch | 1.609347 km |
The United States Customary System of units of measurement (also called the English, Imperial or American) is the primary and most commonly used system of measurement in the United States. In some cases SI (International System of Units—the modern metric system) are used in the United States alongside US customary units.
English units, in a global context, are the historical system of units which originated in England. There are many points of difference between the present-day nonmetric English units (Imperial units) and the United States customary units. These differences are detailed in a comparison of the two systems.
The system for measuring length in the United States customary system is based on the inch, foot, yard, and mile, which are the only four customary length measurements in everyday use. However, for each of these units there exist two slightly different definitions, yielding two different systems of measure: international measure, and U.S. survey measure. The relationships between the different units within each measure is the same, but each measure has a slightly different definition.
