diff --git a/wiki/doc/UnitSystem.md b/wiki/doc/UnitSystem.md index bda0845747e094440e25903320c146227aebcbba..1957da1c229229d8578242a0a72521a65826416d 100644 --- a/wiki/doc/UnitSystem.md +++ b/wiki/doc/UnitSystem.md @@ -1,126 +1,130 @@ Description how to build units witht the D-SI format is [here](StructureSIUnits.md). -## SI base units of measurement (platinum units) -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |SI Reference| -|-:|-:|-:|-:|-:| -|\metre|platinum|meter|m|[1, Table 2]| -|\kilogram|platinum|kilogram|kg|[1, Table 2]| -|\second|platinum|second|s|[1, Table 2]| -|\ampere|platinum|ampere|A|[1, Table 2]| -|\kelvin|platinum|kelvin|K|[1, Table 2]| -|\mole|platinum|mole|mol|[1, Table 2]| -|\candela|platinum|candela|cd|[1, Table 2]|" - - -## D-SI additional platinum units of measurement -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |SI Reference| -|-:|-:|-:|-:|-:| -|\one|platinum|one|1|[1, Sec. 2.2.1]| -|\day|platinum|day|d|[1, Table 8]| -|\hour|platinum|hour|h|[1, Table 8]| -|\minute|platinum|minute|min|[1, Table 8]| -|\degree|platinum|degree|°|[1, Table 8]| -|\arcminute|platinum|arcminute|‘|[1, Table 8]| -|\arcsecond|platinum|arcsecond|“|[1, Table 8]|" - - -## SI derived units of measurement -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |SI base unit expression|D-SI base unit expression|SI Reference| -|-:|-:|-:|-:|-:|-:|-:| -|\gram|gold|gram(a|g|10-3 kg|\kilogram|[1, Sec. 3]| -|\radian|gold|radian|rad|m/m|\metre\metre\tothe{-1}|[1, Table 4]| -|\steradian|gold|steradian|sr|m2/m2|\metre\tothe{2}\metre\tothe{-2}|[1, Table 4]| -|\hertz|gold|hertz|Hz|s-1|\second\tothe{-1}|[1, Table 4]| -|\newton|gold|newton|N|m kg s-2|\metre\kilogram\second\tothe{-2}|[1, Table 4]| -|\pascal|gold|pascal|Pa|m-1 kg s-2|\metre\tothe{-1}\kilogram\second\tothe{-2}|[1, Table 4]| -|\joule|gold|joule|J|m2 kg s-2|\metre\tothe{2}\kilogram\second\tothe{-2}|[1, Table 4]| -|\watt|gold|watt|W|m2 kg s-3|\metre\tothe{2}\kilogram\second\tothe{-3}|[1, Table 4]| -|\coulomb|gold|coulomb|C|s A|\second\ampere|[1, Table 4]| -|\volt|gold|volt|V|m2 kg s-3 A-1|\metre\tothe{2}\kilogram\second\tothe{-3}\ampere\tothe{-1}|[1, Table 4]| -|\farad|gold|farad|F|m-2 kg-1 s4 A2|\metre\tothe{-2}\kilogram\tothe{-1}\second\tothe{4}\ampere\tothe{2}|[1, Table 4]| -|\ohm|gold|ohm|Ω|m2 kg s-3 A-2|\metre\tothe{2}\kilogram\second\tothe{-3}\ampere\tothe{-2}|[1, Table 4]| -|\siemens|gold|siemens|S|m-2 kg-1 s3 A2|\metre\tothe{-2}\kilogram\tothe{-1}\second\tothe{3}\ampere\tothe{2}|[1, Table 4]| -|\weber|gold|weber|Wb|m2 kg s-2 A-1|\metre\tothe{2}\kilogram\second\tothe{-2}\ampere\tothe{-1}|[1, Table 4]| -|\tesla|gold|tesla|T|kg s-2 A-1|\kilogram\second\tothe{-2}\ampere\tothe{-1}|[1, Table 4]| -|\henry|gold|henry|H|m2 kg s-2 A-2|\metre\tothe{2}\kilogram\second\tothe{-2}\ampere\tothe{-2}|[1, Table 4]| -|\degreecelsius|gold|degree Celsius|°C|K|\kelvin|[1, Table 4]| -|\lumen|gold|lumen|lm|m2 m-2 cd|\metre\tothe{2}\metre\tothe{-2}\candela|[1, Table 4]| -|\lux|gold|lux|lx|m-2 cd|\metre\tothe{-2}\candela|[1, Table 4]| -|\becquerel|gold|becquerel|Bq|s-1|\second\tothe{-1}|[1, Table 4]| -|\sievert|gold|sievert|Sv|m2 s-2|\metre\tothe{2}\second\tothe{-2}|[1, Table 4]| -|\gray|gold|gray|Gy|m2 s-2|\metre\tothe{2}\second\tothe{-2}|[1, Table 4]| -|\katal|gold|katal|kat|s-1 mol|\second\tothe{-1}\mole|[1, Table 4]| -|\bit|gold|bit|bit|1|\one|[1, p. 143]| -|\byte|gold|byte|B|1|\one|[1, p. 143]| -|\ppm|gold|parts per million|ppm|1|\one|[1, Sec. 5.4.7]| -|\percent|gold|percent|%|1|\one|[1, Sec. 5.4.7]|" - - -## Non-SI units of measurement allowed with the SI -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |SI base unit expression|D-SI base unit expression|SI Reference| -|-:|-:|-:|-:|-:|-:|-:| -|\hectare|silver|hectare|ha|m2|\metre\tothe{2}|[1, Table 8]| -|\litre|silver|litre|l|m3|\metre\tothe{3}|[1, Table 8]| -|\tonne|silver|tonne|t|kg|\kilogram|[1, Table 8]| -|\electronvolt|silver|electronvolt|eV|m2 kg s-2|\metre\tothe{2}\kilogram\second\tothe{-2}|[1, Table 8]| -|\dalton|silver|dalton|Da|kg|\kilogram|[1, Table 8]| -|\astronomicalunit|silver|astronomical Unit|au|m|\metre|[1, Table 8]| -|\neper|silver|neper|Np|1|\one|[1, Table 8]| -|\bel|silver|bel|B|1|\one|[1, Table 8]| -|\decibel|silver|decibel(b|dB|1|\one|[1, Table 8]|" +## SI base units of measurement (platinum units) +| D-SI identifier | D-SI medal | SI name | SI symbol | SI reference | +| ---------------:| ----------:| --------:| ---------:| ------------:| +| \metre | platinum | meter | m | [1, Table 2] | +| \kilogram | platinum | kilogram | kg | [1, Table 2] | +| \second | platinum | second | s | [1, Table 2] | +| \ampere | platinum | ampere | A | [1, Table 2] | +| \kelvin | platinum | kelvin | K | [1, Table 2] | +| \mole | platinum | mole | mol | [1, Table 2] | +| \candela | platinum | candela | cd | [1, Table 2] | + + +## D-SI additional platinum units of measurement +| D-SI identifier | D-SI medal | SI name | SI symbol | SI reference | +| ---------------:| ----------:| ---------:| ---------:| ---------------:| +| \one | platinum | one | 1 | [1, Sec. 2.2.1] | +| \day | platinum | day | d | [1, Table 8] | +| \hour | platinum | hour | h | [1, Table 8] | +| \minute | platinum | minute | min | [1, Table 8] | +| \degree | platinum | degree | ° | [1, Table 8] | +| \arcminute | platinum | arcminute | ' | [1, Table 8] | +| \arcsecond | platinum | arcsecond | " | [1, Table 8] | + + +## SI derived units of measurement +|D-SI identifier|D-SI medal|SI name|SI symbol|SI base unit expression|D-SI base unit expression|SI reference| +|--------------:|---------:|------:|--------:|----------------------:|------------------------:|-----------:| +| \gram| gold| gram| g| 10⁻³ kg| \kilogram| [1, Sec. 3]| +| \radian| gold| radian| rad| m/m| \metre\metre\tothe{-1}|[1, Table 4]| +| \steradian| gold|steradian| sr| m²/m²| \metre\tothe{2}\metre\tothe{-2}|[1, Table 4]| +| \hertz| gold| hertz| Hz| s⁻¹| \second\tothe{-1}|[1, Table 4]| +| \newton| gold| newton| N| m kg s⁻²| \metre\kilogram\second\tothe{-2}|[1, Table 4]| +| \pascal| gold| pascal| Pa| m⁻¹ kg s⁻²|\metre\tothe{-1}\kilogram\second\tothe{-2}|[1, Table 4]| +| \joule| gold| joule| J| m² kg s⁻²| \metre\tothe{2}\kilogram\second\tothe{-2}|[1, Table 4]| +| \watt| gold| watt| W| m² kg s⁻³| \metre\tothe{2}\kilogram\second\tothe{-3}|[1, Table 4]| +|\coulomb|gold|coulomb| C| s A| \second\ampere|[1, Table 4]| +| \volt|gold| volt| V| m² kg s⁻³ A⁻¹| \metre\tothe{2}\kilogram\second\tothe{-3}\ampere\tothe{-1}|[1, Table 4]| +| \farad|gold| farad| F|m⁻² kg⁻¹ s⁴ A²|\metre\tothe{-2}\kilogram\tothe{-1}\second\tothe{4}\ampere\tothe{2}|[1, Table 4]| +| \ohm|gold| ohm| Ω| m² kg s⁻³ A⁻²| \metre\tothe{2}\kilogram\second\tothe{-3}\ampere\tothe{-2}|[1, Table 4]| +|\siemens|gold|siemens| S|m⁻² kg⁻¹ s³ A²|\metre\tothe{-2}\kilogram\tothe{-1}\second\tothe{3}\ampere\tothe{2}|[1, Table 4]| +| \weber|gold| weber| Wb| m² kg s⁻² A⁻¹| \metre\tothe{2}\kilogram\second\tothe{-2}\ampere\tothe{-1}|[1, Table 4]| +| \tesla|gold| tesla| T| kg s⁻² A⁻¹| \kilogram\second\tothe{-2}\ampere\tothe{-1}|[1, Table 4]| +| \henry|gold| henry| H| m² kg s⁻² A⁻²| \metre\tothe{2}\kilogram\second\tothe{-2}\ampere\tothe{-2}|[1, Table 4]| +|\degreecelsius|gold| degree Celsius| °C| K| \kelvin|[1, Table 4]| +| \lumen|gold| lumen| lm|m2 m⁻² cd|\metre\tothe{2}\metre\tothe{-2}\candela|[1, Table 4]| +| \lux|gold| lux| lx| m⁻² cd| \metre\tothe{-2}\candela|[1, Table 4]| +| \becquerel|gold| becquerel| Bq| s⁻¹| \second\tothe{-1}|[1, Table 4]| +| \sievert|gold| sievert| Sv| m² s⁻²| \metre\tothe{2}\second\tothe{-2}|[1, Table 4]| +| \gray|gold| gray| Gy| m² s⁻²| \metre\tothe{2}\second\tothe{-2}|[1, Table 4]| +| \katal|gold| katal|kat| s⁻¹ mol| \second\tothe{-1}\mole|[1, Table 4]| +| \bit|gold| bit|bit| 1| \one| [1, p. 143]| +| \byte|gold| byte| B| 1| \one| [1, p. 143]| +| \ppm|gold|parts per million|ppm| 1| \one|[1, Sec. 5.4.7]| +| \percent|gold| percent| %| 1| \one|[1, Sec. 5.4.7]| + + +## Non-SI units of measurement allowed with the SI +|D-SI identifier|D-SI medal| SI name|SI symbol|SI base unit expression| D-SI base unit expression|SI reference| +|--------------:|---------:|-------:|--------:|----------------------:|--------------------------:|-----------:| +| \hectare|silver| hectare|ha| m²| \metre\tothe{2}|[1, Table 8]| +| \litre|silver| litre| l| m³| \metre\tothe{3}|[1, Table 8]| +| \tonne|silver| tonne| t| kg| \kilogram|[1, Table 8]| +| \electronvolt|silver| electronvolt|eV|m² kg s⁻²|\metre\tothe{2}\kilogram\second\tothe{-2}|[1, Table 8]| +| \dalton|silver| dalton|Da| kg| \kilogram|[1, Table 8]| +|\astronomicalunit|silver|astronomical unit|au| m| \metre|[1, Table 8]| +| \neper|silver| neper|Np| 1| \one|[1, Table 8]| +| \bel|silver| bel| B| 1| \one|[1, Table 8]| +| \decibel|silver| decibel|dB| 1| \one|[1, Table 8]| ## SI prefixes decimal -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |Multiplyer|SI Reference| -|-:|-:|-:|-:|-:|-:| -|\deca|gold|deca(a|da|10|[1, Table 7]| -|\hecto|gold|hecto(a|h|100|[1, Table 7]| -|\kilo|gold|kilo(a,b|k|1000|[1, Table 7]| -|\mega|gold|mega(a|M|1000000|[1, Table 7]| -|\giga|gold|giga(a|G|1000000000|[1, Table 7]| -|\tera|gold|tera(a|T|1000000000000|[1, Table 7]| -|\peta|gold|peta(a|P|1000000000000000|[1, Table 7]| -|\exa|gold|exa(a|E|1000000000000000000|[1, Table 7]| -|\zetta|gold|zetta(a|Z|1000000000000000000000|[1, Table 7]| -|\yotta|gold|yotta(a|Y|1000000000000000000000000|[1, Table 7]| -|\ronna|gold|ronna|R|1000000000000000000000000000|[2, Resolution 3]| -|\quetta|gold|quetta|Q|1000000000000000000000000000000|[2, Resolution 3]| -|\deci|gold|deci(a ,b|d|0.1|[1, Table 7]| -|\centi|gold|centi(a|c|0.01|[1, Table 7]| -|\milli|gold|milli(a|m|0.001|[1, Table 7]| -|\micro|gold|micro(a|μ|0.000001|[1, Table 7]| -|\nano|gold|nano(a|n|0.000000001|[1, Table 7]| -|\pico|gold|pico(a|p|0.000000000001|[1, Table 7]| -|\femto|gold|femto(a|f|0.000000000000001|[1, Table 7]| -|\atto|gold|atto(a|a|0.000000000000000001|[1, Table 7]| -|\zepto|gold|zepto(a|z|0.000000000000000000001|[1, Table 7]| -|\yocto|gold|yocto(a|y|0.000000000000000000000001|[1, Table 7]| -|\ronto|gold|ronto|r|0.000000000000000000000000001|[2, Resolution 3]| -|\quecto|gold|quecto|q|0.000000000000000000000000000001|[2, Resolution 3]|" +| D-SI identifier | D-SI medal | SI name | SI symbol | Multiplier | SI reference | +| ---------------:| ----------:| -------:| ---------:| --------------------------------:| -----------------:| +| \deca | gold | deca | da | 10 | [1, Table 7] | +| \hecto | gold | hecto | h | 100 | [1, Table 7] | +| \kilo | gold | kilo | k | 1000 | [1, Table 7] | +| \mega | gold | mega | M | 1000000 | [1, Table 7] | +| \giga | gold | giga | G | 1000000000 | [1, Table 7] | +| \tera | gold | tera | T | 1000000000000 | [1, Table 7] | +| \peta | gold | peta | P | 1000000000000000 | [1, Table 7] | +| \exa | gold | exa | E | 1000000000000000000 | [1, Table 7] | +| \zetta | gold | zetta | Z | 1000000000000000000000 | [1, Table 7] | +| \yotta | gold | yotta | Y | 1000000000000000000000000 | [1, Table 7] | +| \ronna | gold | ronna | R | 1000000000000000000000000000 | [2, Resolution 3] | +| \quetta | gold | quetta | Q | 1000000000000000000000000000000 | [2, Resolution 3] | +| \deci | gold | deci | d | 0.1 | [1, Table 7] | +| \centi | gold | centi | c | 0.01 | [1, Table 7] | +| \milli | gold | milli | m | 0.001 | [1, Table 7] | +| \micro | gold | micro | μ | 0.000001 | [1, Table 7] | +| \nano | gold | nano | n | 0.000000001 | [1, Table 7] | +| \pico | gold | pico | p | 0.000000000001 | [1, Table 7] | +| \femto | gold | femto | f | 0.000000000000001 | [1, Table 7] | +| \atto | gold | atto | a | 0.000000000000000001 | [1, Table 7] | +| \zepto | gold | zepto | z | 0.000000000000000000001 | [1, Table 7] | +| \yocto | gold | yocto | y | 0.000000000000000000000001 | [1, Table 7] | +| \ronto | gold | ronto | r | 0.000000000000000000000000001 | [2, Resolution 3] | +| \quecto | gold | quecto | q | 0.000000000000000000000000000001 | [2, Resolution 3] | ## SI prefixes binary -|D-SI Identifyer|D-SI Medal|SI name|SI symbol |Multiplyer|SI Reference| -|-:|-:|-:|-:|-:|-:| -|\kibi|gold|kibi|Ki |1024|[1, p. 143]| -|\mebi|gold|mebi|Mi|1048576|[1, p. 143]| -|\gibi|gold|gibi|Gi|1073741824|[1, p. 143]| -|\tebi|gold|tebi|Ti|1099511627776|[1, p. 143]| -|\pebi|gold|pebi|Pi|1125899906842624|[1, p. 143]| -|\exbi|gold|exbi|Ei|1152921504606846976|[1, p. 143]| -|\zebi|gold|zebi |Zi|1180591620717411303424|[1, p. 143]| -|\yobi|gold|yobi |Yi|1208925819614629174706176|[1, p. 143]|" - +| D-SI identifier | D-SI medal | SI name | SI symbol | Multiplier | SI reference | +| ---------------:| ----------:| -------:| ---------:| -------------------------:| ------------:| +| \kibi | gold | kibi | Ki | 1024 | [1, p. 143] | +| \mebi | gold | mebi | Mi | 1048576 | [1, p. 143] | +| \gibi | gold | gibi | Gi | 1073741824 | [1, p. 143] | +| \tebi | gold | tebi | Ti | 1099511627776 | [1, p. 143] | +| \pebi | gold | pebi | Pi | 1125899906842624 | [1, p. 143] | +| \exbi | gold | exbi | Ei | 1152921504606846976 | [1, p. 143] | +| \zebi | gold | zebi | Zi | 1180591620717411303424 | [1, p. 143] | +| \yobi | gold | yobi | Yi | 1208925819614629174706176 | [1, p. 143] | + +## Operators for combining units +| D-SI identifier | Description | Examples | D-SI medal | +| ---------------:| ---------------------------------------------------------------:| ----------------------------------:| ----------:| +| | Multiplication: simply append one unit to another | \metre\metre | platinum | +| \tothe{n} | Exponent: following a unit where n is an integer or (+-)0.5 | \metre\tothe{2}, \volt\tothe{-0.5} | platinum | +| \per | Division: All units on the left side of the operator devided by all units on its right side | \metre\per\metre | silver | ### References +[1] BIPM: 9th edition SI brochure (english): https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf +[2] BIPM: List of Resolutions for the 27th meeting of the General Conference on Weights and Measures 2022: https://www.bipm.org/documents/20126/77765681/Resolutions-2022.pdf/281f3160-fc56-3e63-dbf7-77b76500990f#page=22 -[1] BIPM: 9th edition SI brochure (englisch): https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf - -[2] BIPM: List of Resolutions for the 27th meeting of the General Conference on Weights and Measures 2022 - -[**Home**](wiki/d-si-online-guide.md) +[**Home**](wiki/d-si-online-guide.md) <a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br />This documentation is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.