SI derived units
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| SI derived units | |
|---|---|
| Name | SI derived units |
| Standard | International System of Units (SI) |
| Category | Units of measurement |
| Derived from | SI base units |
| Established | 1960 |
SI derived units
SI derived units are units of measurement obtained algebraically from the seven SI base units: the metre, kilogram, second, ampere, kelvin, mole, and candela. They provide standardized measures for a wide range of physical quantities used in research, engineering, trade, and teaching across nations and institutions such as the International Bureau of Weights and Measures, the International Organization for Standardization, and national metrology institutes like the National Institute of Standards and Technology and the National Physical Laboratory (United Kingdom). Derived units facilitate interoperability between disciplines represented by organizations such as the International Union of Pure and Applied Chemistry, the International Union of Pure and Applied Physics, and industry consortia including the IEEE.
Definition and relationship to SI base units
Derived units are defined by algebraic combinations of the seven SI base units established by the General Conference on Weights and Measures and codified by the Metre Convention. For example, the unit of force is expressed as kilogram metre per second squared (kg·m·s−2) and given a special name by international resolution. National and international standards bodies, including the European Committee for Standardization and the International Electrotechnical Commission, treat derived units as coherent when they are formed without numerical factors from base units. The coherence ensures traceability to primary realizations maintained by laboratories like the Physikalisch-Technische Bundesanstalt and the Laboratoire national de métrologie et d'essais. Legal metrology frameworks in jurisdictions such as the United States, United Kingdom, France, and Germany adopt SI derived units for regulatory compliance.
List of SI derived units with special names
A subset of derived units has been assigned special names and symbols by international agreement; these include units for force, pressure, energy, power, electric charge, voltage, capacitance, resistance, conductance, magnetic flux, magnetic flux density, inductance, luminous flux, and frequency. Examples with internationally recognized names include the newton, pascal, joule, watt, coulomb, volt, farad, ohm, siemens, weber, tesla, henry, lumen, and hertz. Bodies that adopted or recommended these names include the International Committee for Weights and Measures, the International Astronomical Union, and standardizing organizations such as the International Federation of Clinical Chemistry and Laboratory Medicine. Historical adopters and promulgators include the Conseil International des Poids et Mesures and national academies like the Royal Society and the Académie des sciences (France). The list is used by regulatory agencies such as the Food and Drug Administration, the European Medicines Agency, and industrial standards developers including ASTM International.
Coherent derived units and combinations
Coherent derived units arise when derived quantities are expressed only in terms of base units, without additional numerical factors, forming algebraic combinations that preserve dimensional consistency. Coherent combinations underpin equations used in frameworks like Maxwell's equations, Newton's laws of motion, and the Navier–Stokes equations, and are essential in modeling performed at institutions such as the CERN and observatories like the European Southern Observatory. Coherence facilitates unit conversion algorithms used in software developed by entities such as the Open Geospatial Consortium and scientific computing projects hosted by organizations like the European Space Agency and the National Aeronautics and Space Administration. When non-coherent units (for example, minute or hectare) are used they are convertible to coherent SI derived forms via exact factors.
Rules for unit symbols and nomenclature
The symbols and names of SI derived units follow precise rules set out by the International Bureau of Weights and Measures and adopted by standards organizations including the International Organization for Standardization and the International Electrotechnical Commission. Unit symbols are printed in roman type and are case-sensitive; prefixes such as kilo, mega, milli, micro, nano and pico have standardized symbols. National guidelines from the National Research Council (Canada), the Standards Council of Canada, and professional societies such as the Royal Society of Chemistry and the American Chemical Society reinforce consistent usage in publications like journals of the American Physical Society and textbooks used at universities including University of Oxford and Massachusetts Institute of Technology. Proper nomenclature avoids ambiguity in international treaties, technical standards, and patent filings adjudicated by courts and agencies worldwide.
History and revisions of derived units
The evolution of SI derived units has been shaped by scientific advances and international agreements dating from the 19th century metrology work of the International Commission of Weights and Measures through the 20th century adoption of the SI system at the 11th General Conference on Weights and Measures in 1960. Major revisions and clarifications have been promulgated by successive meetings of the General Conference on Weights and Measures and technical committees from the International Committee for Weights and Measures. Changes include the addition of special names, refinements to definitions (including the 2019 redefinition of base units linked to fundamental constants) and harmonization with electrical standards developed by laboratories like the National Institute of Standards and Technology and the Physikalisch-Technische Bundesanstalt. Historical debates involved scientific bodies such as the Royal Society and professional groups including the International Union of Pure and Applied Chemistry.
Usage in science, industry, and education
SI derived units are ubiquitous across experimental research at institutions such as the Max Planck Society, computational modeling at centers like the Lawrence Berkeley National Laboratory, industrial metrology in firms including Siemens and General Electric, and quality systems implemented under standards like ISO 9001. They are taught in curricula at universities and schools accredited by organizations such as the European Higher Education Area and are required in scholarly publications of societies like the American Physical Society and the Institute of Electrical and Electronics Engineers. Adoption by international projects—ranging from the Human Genome Project to multinational engineering initiatives—ensures interoperability, traceability, and reproducibility in measurement across borders.