國際單位制（，簡稱），源於公制（又稱米制），是世界上最普遍採用的標準度量衡單位系統。國際單位制以七個基本單位為基礎，由此建立起一系列相互換算關係明確的「一致單位」。另有二十個基於十進制的詞頭，當加在單位名稱或符號前的時候，可用於表達該單位的倍數或分數。
國際單位制從1948年開始建立，於1960年正式公佈。它建基於米-千克-秒制（MKS），而非任何形式的厘米-克-秒制（CGS）。國際單位制的設計意圖是，先定義詞頭和單位名稱，但單位本身的定義則會隨著度量科技的進步、精準度的提高，根據國際協議來演變。例如，分別於2011年、2014年舉辦的第24、25屆國際度量衡大會討論了有關重新定義公斤的提案。[1]
隨著科學的發展，厘米-克-秒制中出現了不少新的單位，而各學科之間在單位使用的問題上也沒有良好的協調。因此在1875年，多個國際組織協定《米制公約》，創立了國際度量衡大會，目的是訂下新度量衡系統的定義，並在國際上建立一套書寫和表達計量的標準。
國際單位制已受大部分發達國家所採納，但在英語國家當中，國際單位制並沒有受到全面的使用。
![前奧匈帝國與意大利邊境上（今蓬泰巴）的石碑以「Myriameter」標示距離。這一單位等於10公里，在19世紀中歐曾經使用過，但現已被淘汰。[2][3]](/winstonyin/zhwiki/blob/master/Alter Grenzstein Pontebba 01.jpg "前奧匈帝國與意大利邊境上（今蓬泰巴）的石碑以「Myriameter」標示距離。這一單位等於10公里，在19世紀中歐曾經使用過，但現已被淘汰。[2][3]")
1875年，法國根據《米制公約》把維護公斤和米定義原器的責任轉交給國際組織。1921年，公約適用範圍擴大至所有物理量，包括最早於1893年定義的各種電單位。
1948年，學者們開始將公制重新制訂為一套「實用單位制」，經過逾十年的發展後，終於在1960年公佈「國際單位制」。1954年第10屆國際度量衡大會把電流、溫度及發光強度定為基本物理量，使基本物理量增加至六個。相對應的基本單位有米、公斤、秒、安培、開爾文和坎德拉。1971年，國際單位制再添一個基本物理量──以摩爾來表示物質的量。
1791年，法國科學院的一個委員會受國民議會和路易十六的委派，開始建立一套統一的、基於理性的度量衡系統，這將成為公制。[4]成員包括「現代化學之父」安東萬-羅倫·德·拉瓦節及數學家皮耶爾-西蒙·拉普拉斯和阿德里安-馬里·勒壤得。[5] Public response included resistance, apathy, and sometimes ridicule.[6]委員會在設計長度、體積和質量的相互關係時所遵從的原則，和1668年英國神職人員約翰·威爾金斯在《論正真的文字和哲學語言》（）中所提倡的一致。[7][8]他們也根據最早於1670年由法國神職人員提出的方法，利用地球的子午線作為長度的定義基礎。[9][10]1791年3月30日，國民議會採納了委員會的新度量衡系統，並批准在敦刻爾克和巴塞羅那之間進行勘察，以確立子午線的長度。1792年7月11日，委員會提出將長度、面積、容積和質量的單位名稱分別定為metre（公尺）、are（公畝）、litre（公升）和grave（公斤的舊名），而這些單位的倍數和分數則用以十進制為基礎的詞頭來表示，如centi表示一百分之一，kilo表示一千倍等等。[11]
1795年4月7日法律（芽月18日法）訂下了gramme（克）和kilogramme（千克），分別取代先前的gravet（準確來說是milligrave）和grave。在皮埃爾·梅尚和的子午線勘察結束後，米和公斤的標準原器於1799年6月22日正式交由法國國家檔案館（）保管。同年12月10日，即拿破崙的霧月政變之後的一個月，霜月19日法正式通過，法國將全面採用公制。[17][18]
19世紀上半葉，不同基本單位有不同的常用倍數詞頭：法國和德國部分地區常用myriametre（1萬米）量度距離，但在量度質量時卻用kilogramme（1千克），而非myriagramme（1萬克）。[2]
1832年，德國數學家卡爾·弗里德里希·高斯在威廉·韋伯的協助下，得出了地球磁場的強度，並以毫米、克和秒所組成的單位寫出。秒因此從實際上成為了一個基本單位。[12]此前，科學家只是以相對值來比較各地的地磁場強度，但高斯把磁鐵在磁力底下的扭矩與物體在引力底下的扭矩視為等同，所以能夠為磁場強度設下一個建立在質量、長度和時間上量綱。[19]
1860年代，詹姆斯·克拉克·馬克士威及威廉·湯姆森（開爾文男爵）等科學家在英國科學促進協會的主持下，在高斯的基礎上做了進一步的規範，建立起一套由基本單位和導出單位所組成的一致單位制。利用一致性原則，他們成功定義了一組厘米-克-秒制單位，包括：爾格表達能量、達因表達力、微巴表達壓力、泊表達剪切黏度、斯托克斯表達運動黏度等等。[15]
法國的度量衡改革啟發了計量學上的國際合作計劃，多國最終於1875年簽署《米制公約》。[5]公約最初只規定了米和公斤的標準：作為定義標準的共有30件米原器及40件公斤原器，材料均為含90%鉑和10%銥的合金，由英國莊信萬豐公司製造，1889年被國際度量衡大會採用。原器中隨機各選出一件分別做國際米原器和國際公斤原器，從此取代早前由法國國家檔案館保管的米和公斤原器。公約的每個簽署國都可擁有一個餘下的原器，做該國的定義標準。[20]
- 國際度量衡大會（）：每四至六年舉辦一次，由各成員國代表組成，目的是討論國際度量衡委員會有關國際單位制新發展的報告；
- 國際度量衡委員會（）：委員為八名有威望的科學家，由國際度量衡大會選出，每年在國際度量衡局召開會議，並對國際度量衡大會提出行政上和技術上的建議；
- 國際度量衡局（）：位於法國塞夫爾的一所國際計量學中心，負責保管國際公斤原器，為國際度量衡大會和國際度量衡委員會提供計量服務，亦是它們的秘書處和會議舉辦的場地。其最初的作用是定期將各國的米和公斤原器與國際公斤原器進行比較。
《米制公約》[23]以及國際度量衡大會名義下的所有官方文件都是以法語書寫的。[22]
19世紀後期至20世紀初期，人們採用了一系列不一致的單位制，在質量上有的用克，有的用公斤；在長度上有的用厘米，有的用米。例如有：表達功率的「Pferdestärke」（公制馬力）、[26]表達滲透性的達西[27]及表達氣壓和血壓的毫米汞柱。這些廣泛使用的單位之中，有的用到了標準重力。
到了第二次世界大戰尾聲，全球各地仍然使用著各種不同的單位制，有的是公制的另類版本，有的則是基於所謂的「習慣單位」，如美制單位。1948年，在國際純粹與應用物理學聯合會及法國政府代表的參與下，第9屆國際度量衡大會委派國際度量衡委員會對科學界、技術界和教育界的計量需求進行一項調查，並為一種單一整合、能供遵守《米制公約》的世界各國使用的單位制提出建議。[28]
根據此項調查的結論，1954年第10屆國際度量衡大會決定，這個國際性的單位制應以六個基本單位為基礎，能夠用於測量溫度、可見光輻射、機械及電磁物理量。建議中的六個基本單位分別為：米、公斤、秒、安培、開爾文和坎德拉。1960年第11屆國際度量衡大會正式將這一單位制命名為「國際單位制」（），簡稱SI。[22][29]國際度量衡局也曾把國際單位制稱為「現代公制」。[22]1971年第14屆國際度量衡大會將摩爾納入為第七個基本單位。[30]
國際物理量系統（）是以以下七個基本物理量為基礎的系統：長度、質量、時間、電流、熱力學溫度、物質的量和發光強度。其他物理量，如面積、壓力及電阻，都可以根據明確、不相互矛盾的公式從這些基本物理量推導得出。國際物理量系統所定義的，是國際單位制單位所量度的物理量。[31]ISO/IEC 80000國際標準對國際物理量系統做了定義，定義於2009年經ISO 80000-1進一步完善。[32]
《手冊》是由國際度量衡委員會屬下的單位顧問委員會所編寫。單位顧問委員會的主席由國際度量衡委員會提名，但成員來自於國際度量衡大會及委員會以外的國際組織。[34]
《國際單位制手冊》所用的「物理量」、「單位」、「因次」等名詞，都出自由計量學聯合導則委員會（JCGM）出版的《國際計量詞彙》。該委員會是一個由八個國際標準組織組成的工作小組，由國際度量衡局局長擔任會長。[35]用於定義國際單位制的物理量和公式，統稱為「國際物理量系統」，列於ISO/IEC 80000物理量與單位國際標準。
國際單位制的組成部分為：一組基本單位、一組有特殊名稱的導出單位以及一組十進制倍數詞頭。根據《國際單位制手冊》，「SI單位」囊括以上三個部分，而「一致SI單位」則只包含基本和導出單位。[22]
國際單位制以一組基本單位為基礎，所有其他單位都是用基本單位建立起來的。馬克士威最初提出一致單位制的概念時，列出了三個可用的基本單位：質量、長度及時間單位。之後，吉奧爾吉提倡加入電的基本單位。理論上，電流、電勢、電阻、電荷等物理量的單位都可以做基本單位，當選定其中一個做基本單位後，其餘的電單位都可以通過物理定律從基本單位推導得出；國際單位制最終選擇了使用電流。後期又加入了三個分別量度物質的量、溫度及發光強度的基本單位。
| 單位名稱 | 單位符號 | 物理量 | 定義（部分）[n 38] | 因次符號 |
|---|---|---|---|---|
| 米 | m | 長度 | L | |
| 公斤[n 39] | kg | 質量 | M | |
| 秒 | s | 時間 | T | |
| 安培 | A | 電流 | I | |
| 開爾文 | K | 熱力學溫度 | Θ | |
| 摩爾 | mol | 物質的量 | N | |
| 坎德拉 | cd | 發光強度 | J | |
|
國際單位制導出單位是基本單位在乘冪、乘積或相除後產生的單位，如此形成的導出單位可以有無限多個。[22][33]每個導出單位都與一個導出物理量相對應，例如，速度是建立在時間和長度上的物理量，在國際單位制中所對應的導出單位是「米每秒」（符號為m/s）。導出單位的因次可以用基本單位的因次組合來表達。
一致單位是指定義中係數均為1的導出單位，也就是定義中不會出現像標準重力或是水的密度之類的常數。例如，牛頓的定義是，使1公斤的質量產生1米每二次方秒的加速度需要的力。因為國際單位制中質量及加速度的單位分別是kg及m⋅s−2，而且力是質量和加速度之積（），所以力的單位牛頓即為kg⋅m⋅s−2。除了基本單位的積和冪以外，牛頓的定義不含其他數值，因此屬於一致單位。
為方便使用，一些導出單位也有專用的名稱及符號。[14]這些導出單位還可以進一步用來定義更多的導出單位，其專用名也可以用來表達新的導出單位。如上文所述，力的國際單位制導出單位是kg⋅m⋅s−2，其專用名為牛頓（N）；壓強的單位是帕斯卡（Pa），可定義為「牛頓每平方米」（N/m2）。[43]
| 名稱 | 符號 | 物理量 | 以其他SI單位表達 | 以基本單位表達 |
|---|---|---|---|---|
| 弧度 | rad | 角 | m·m−1 | |
| 球面度 | sr | 立體角 | m2·m−2 | |
| 赫茲 | Hz | 頻率 | s−1 | |
| 牛頓 | N | 力、重量 | kg·m·s−2 | |
| 帕斯卡 | Pa | 壓強、應力 | N/m2 | kg·m−1·s−2 |
| 焦耳 | J | 能量、功、熱量 | N·m | kg·m2·s−2 |
| 瓦特 | W | 功率、輻射通量 | J/s | kg·m2·s−3 |
| 庫侖 | C | 電荷 | s·A | |
| 伏特 | V | 電壓（電勢差）、電動勢 | W/A | kg·m2·s−3·A−1 |
| 法拉 | F | 電容 | C/V | kg−1·m−2·s4·A2 |
| 歐姆 | Ω | 電阻、阻抗、電抗 | V/A | kg·m2·s−3·A−2 |
| 西門子 | S | 電阻 | A/V | kg−1·m−2·s3·A2 |
| 單位 | Wb | 磁通量 | V·s | kg·m2·s−2·A−1 |
| 特斯拉 | T | 磁通量密度（磁場） | Wb/m2 | kg·s−2·A−1 |
| 亨利 | H | 電感 | Wb/A | kg·m2·s−2·A−2 |
| 攝氏度 | °C | 溫度（相對於273.15 K） | K | |
| 流明 | lm | 光通量 | cd·sr | cd |
| 勒克斯 | lx | 照度 | lm/m2 | m−2·cd |
| 貝克勒爾 | Bq | 放射性活度 | s−1 | |
| 戈瑞 | Gy | 致電離輻射的吸收劑量 | J/kg | m2·s−2 |
| 西弗 | Sv | 致電離輻射等效劑量 | J/kg | m2·s−2 |
| 開特 | kat | 催化活度 | mol·s−1 | |
|
在基本和導出單位名稱之前加上詞頭，可表達該單位的倍數和分數。詞頭所代表的倍數都是10的整數冪，在倍數高於100或低於時則都是1000的整數冪。例如，詞頭kilo（千）表示一千倍，milli（毫）表示千分之一，也就是說，1000毫米（millimetre）為之1-{米}-（metre，又作-{公尺}-），1000米為之1-{千米}-（kilometre，又作-{公里}-），如此類推。這些詞頭不能夠結合使用，即百萬分之一米可寫作微米（micrometre），但不可寫作毫毫米（millimillimetre）。在對公斤（kilogramme）加上詞頭時，以克（gramme）作為「基本」單位，因此百萬分之一公斤寫作毫克（milligramme），而非微公斤（microkilogram）。每個詞頭均有一個區分大小寫的符號，使用時加在單位符號之前。[22][44]
| 倍數 | 詞頭名稱 | deca | hecto | kilo | mega | giga | tera | peta | exa | zetta | yotta | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 詞頭符號 | da | h | k | M | G | T | P | E | Z | Y | ||
| 中文（中國大陸） | -{十}- | -{百}- | -{千}- | -{兆}- | -{吉（咖）}- | -{太（拉）}- | -{拍（它）}- | -{艾（可萨）}- | -{泽（它）}- | -{尧（它）}- | ||
| 中文（台灣） | -{十}- | -{百}- | -{千}- | -{百萬}- | -{吉}- | -{兆}- | -{拍}- | -{艾}- | -{皆}- | -{佑}- | ||
| 係數 | 100 | 101 | 102 | 103 | 106 | 109 | 1012 | 1015 | 1018 | 1021 | 1024 | |
| 分數 | 詞頭名稱 | deci | centi | milli | micro | nano | pico | femto | atto | zepto | yocto | |
| 詞頭符號 | d | c | m | μ | n | p | f | a | z | y | ||
| 中文（中國大陸） | -{分}- | -{厘}- | -{毫}- | -{微}- | -{纳（诺）}- | -{皮（可）}- | -{飞（母托）}- | -{阿（托）}- | -{仄（普托）}- | -{幺（科托）}- | ||
| 中文（台灣） | -{分}- | -{厘}- | -{毫}- | -{微}- | -{奈}- | -{皮}- | -{飛}- | -{阿}- | -{介}- | -{攸}- | ||
| 係數 | 100 | 10−1 | 10−2 | 10−3 | 10−6 | 10−9 | 10−12 | 10−15 | 10−18 | 10−21 | 10−24 | |
雖然國際單位制本身已足以表達任何物理量，但在科技界和商界等的出版物中仍會出現許多非國際單位制單位，而這些單位的使用很可能會持續很長一段時間。也有一些單位由於深深地植根在歷史和個別文化當中，所以將會在可見的未來繼續使用下去。國際度量衡委員會承認亦認可這種做法，並頒佈了一份「可以與SI並用的非SI單位」清單，其分類如下：[22][44]
- 可以與SI並用的非SI單位（表6）：
- 一些時間、角度及非SI的舊公制單位都有較長的使用歷史。大部分社會都利用太陽日以及從太陽日細分出來的非十進制時間段作為量度時間的基礎；與英呎和磅不同的是，這些時間單位無論在哪裡測量都是相同的。弧度是一個圓周的，雖然有數學上的好處，但不便於導航。與時間單位相似，用於導航的角度單位在世界各地的使用比較統一。公噸、公升和公頃是國際度量衡大會在1879年採用的，今天保留為可與SI並用的單位，有各自的專用符號。已收錄的單位有
- 在SI下的數值須經實驗得出的非SI單位（表7）：
- 物理學家很多時候會使用和某些自然現象有關的測量單位，這些單位往往和國際單位制單位的大小相差許多個數量級。《國際單位制手冊》列出了一些最常用的自然單位以及它們的符號和標準數值，但必須通過實驗才能得出這些單位在國際單位制下的數值。
- 電子伏特（eV）及道爾頓/原子質量單位（Da或u）。
- 其他非SI單位（表8）：
- 一些單位雖然沒有得到國際度量衡大會的正式認可，但仍廣泛應用在醫療和導航等眾多領域中。國際度量衡委員會為確保在國際上的一致性，也在《手冊》中列出此類單位，但建議在使用時先作定義。
- 與CGS和CGS高斯單位制相關的非SI單位（表9）
1879年，國際度量衡委員會公佈了有關書寫長度、面積、體積和質量之符號的建議書。物理學家曾經以μ表示微米、λ表示微升、γ表示微克，但自從1900年前後，他們開始分別改用μm、μL和μg。1935年，距《米制公約》修訂已有十多年，國際度量衡委員會終於正式採用這項提案，建議在所有單位前加上μ來代表的倍數。[45]
1948年，第9屆國際度量衡大會通過了首份有關米制符號書寫格式的建議書，為今天使用的規則奠定了基礎。[46]這些規則之後又經過國際標準化組織（ISO）及國際電工委員會（IEC）的增訂，現已囊括單位符號和名稱、詞頭符號和名稱、物理量符號的書寫方式以及物理量數值的表達方式。[22]ISO和IEC所發佈的有關SI符號表達方式的規則，都與《國際單位制手冊》中的規則一致。[47]，ISO和IEC正在將各自有關物理量及單位的標準整合成單一套標準，最終將成為ISO/IEC 80000標準。有關印刷物理量及單位的標準收錄在ISO 80000-1:2009中。[48]
在一些歐洲語言中，國際單位制單位名稱可視為普通名詞：如在英文和法文中，單位名稱都以小寫字母開頭（牛頓「newton」、赫茲「hertz」、帕斯卡「pascal」等等），儘管相應的單位符號可能以大寫字母開頭。[49][50]由於德文中的普通名詞均以大寫字母開頭，因此單位名稱也不例外。[51]單位名稱的拼寫則由各語言的官方組織決定（法文有法蘭西學術院，德文有德語正寫法協會等等）。國際單位制單位在英式和美式英文中的拼寫並不相同：英式英文（亦包括澳洲、加拿大、紐西蘭等）使用「deca-」（10倍數詞頭）、「metre」（米）和「litre」（升），美式英文則分別用「deka-」、「meter」和「liter」。[52]
同樣，在形成單位名稱的眾數時，也須遵守該語言自身的語法。以英文為例，亨利「henry」會變成「henries」。[53][44]不過，勒克斯「lux」、赫茲「hertz」和西門子「siemens」都有不規則眾數──它們在單數和眾數下都有相同的拼法。波蘭文的眾數規則更為複雜：以米、公斤、秒為例，當數量為1時寫「metr」、「kilogram」、「sekunda」，數量個位數為2、3、4且十位數不是1時寫「metry」、「kilogramy」、「sekundy」，數量為其他整數（包括0）時寫「metrów」、「kilogramów」、「sekund」，數量為非整數（如0.67、2.45等）時寫「metra」、「kilograma」、「sekundy」。[54]
在英文中，若須表達單位之間相乘，可用連字號或空格（牛頓米寫作「newton-metre」或「newton metre」），並通過改變最後者來形成整個複合單位的眾數（10 newton-metres）。數字與單位符號之間建議加入一個空格（一個25公斤的球體「a 25 kg sphere」）。把單位名稱用作形容詞時，同樣根據英文語法加入一個連字號（一個25公斤的球體「a 25-kilogram sphere」）。[55]
中文中的國際單位制單位名稱及詞頭都以漢字書寫，而單位符號則用國際通用的拉丁或希臘字母書寫。在中華民國（台灣）和中華人民共和國（香港及澳門除外）的法律管轄範圍內，國際單位制單位及詞頭的譯名分別由《法定度量衡單位及其所用之倍數、分數之名稱、定義及代號》[56]及《中华人民共和国法定计量单位》[57]所規定。在基本單位中，兩岸名稱相同的有-{米}-（又稱-{公尺}-）、-{千克}-（又稱-{公斤}-）、秒和安培，在台灣/大陸譯名不同的則有-{克耳文/开尔文}-、-{莫耳/摩尔}-和-{燭光/坎德拉}-；在倍數詞頭中，兩岸相同的有微、毫、厘、分、十、百、千，不同的則有-{奈/纳诺}-、-{百萬/兆}-、-{兆/太拉}-等等，其中「兆」一字在台灣和大陸分別表示1012和106。在中國大陸，多於一個漢字的單位名稱或詞頭亦可簡寫成單個漢字，如-{纳诺}-寫作-{纳}-、-{坎德拉}-寫作-{坎}-等。
19世紀中國在引進度量衡單位時，沿襲日文，創造出一系列多音節漢字（計量用漢字），如「瓩」（讀千瓦）、「糎」（讀厘米）、「嗧」（讀加侖）等等。這些漢字今已被淘汰，改用單音節漢字。[58]
日本在明治時期期間創造了一系列國字（日製漢字）來表示公制單位。三個基本單位取原有漢字：米、升、瓦（即克），再結合六個詞頭漢字：千、百、十、分、厘、毛，從而組成共18個新的獨立漢字，如七個長度單位：粁、粨、籵、米、粉、糎和粍。這些漢字都是借字，其讀音取自英文，如「粁」取「kilometre」之音，讀「キロメートル」。不過這些漢字在日本已被淘汰，改用直接表音的片假名，如「キロメートル」。單位及詞頭符號則用拉丁或希臘字母書寫，如「km」。今天仍在通用的漢字單位名稱有「平米」（即平方米）等。
Although the writing of unit names is language-specific, the writing of unit symbols and the values of quantities is consistent across all languages and therefore the SI Brochure has specific rules in respect of writing them.[22] The guideline produced by the National Institute of Standards and Technology (NIST)[59] clarifies language-specific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure.[53]
General rules for writing SI units and quantities apply to text that is either handwritten or produced using an automated process:
- The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, , 22 K. This rule explicitly includes the percent sign (%)[22] and the symbol for degrees of temperature (°C).[22] Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space.
- Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence.
- A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., k in km, M in MPa, G in GHz). Compound prefixes are not allowed.
- Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-breaking space; e.g., N·m or N m.
- Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m·s−1, or . Only one solidus should be used; e.g., kg/(m·s2) and kg·m−1·s−2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
The lowercase letters (neither "metres" nor "seconds" were named after people), the space between the value and the units, and the superscript "2" to denote "squared".
- The first letter of symbols for units derived from the name of a person is written in upper case; otherwise, they are written in lower case. E.g., the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", but the symbol for mole is written "mol". Thus, "T" is the symbol for tesla, a measure of magnetic field strength, and "t" the symbol for tonne, a measure of mass. Since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. The American NIST recommends that within the United States "L" be used rather than "l".
- Symbols of units do not have a plural form; e.g., 25 kg, not 25 .
- Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities; the former is the typical power requirement of a hearing aid (1 milliwatt or 0.001 watts), and the latter the typical power requirement of a suburban train (1 megawatt or watts).
- The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European countries.[60]
- Spaces should be used as a thousands separator () in contrast to commas or periods (1,000,000 or 1.000.000) to reduce confusion resulting from the variation between these forms in different countries.
- Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators.
- Since the value of "billion" and "trillion" can vary from language to language, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. No alternative is suggested in the SI Brochure.
Further rulesare specified in respect of production of text using printing presses, word processors, typewriters and the like.
- Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.
- In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix–unit combinations, or unit–exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and letter-like symbols sub-ranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode symbols. The cursive ℓ, a letter-like symbol, has been used in a number of countries in addition to China and Japan as a symbol for the litre, but this is not currently recommended by any standards body.
- In print, the space used as a thousands separator (commonly called a thin space) is typically narrower than that used between words.
![Silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative standard uncertainty of or less, held by Achim Leistner.[61]](/winstonyin/zhwiki/blob/master/Silicon sphere for Avogadro project.jpg "Silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative standard uncertainty of or less, held by Achim Leistner.[61]")
The published mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit."[22] In the current (2016 ) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en pratique shall be developed for determining the value of each unit. In particular:
- At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than and at least one of these values should be better than . Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.[63][64]
- When the kelvin is being determined, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in and that these values be corroborated by other measurements.[65]
The preamble to the Metre Convention read "Desiring the international uniformity and precision in standards of weight and measure, have resolved to conclude a convention ...".[23] Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself and clarification of how to use units of measure that are not part of SI, but are still nevertheless used on a worldwide basis.
Since 1960 the CGPM has made a number of changes to SI. These include:
- The 13th CGPM (1967) renamed the "degree Kelvin" (symbol °K) to the "kelvin" (symbol K)[22]
- The 14th CGPM (1971) added the mole (symbol mol) to the list of base units.[66]
- The 14th GCPM (1971) added the pascal (symbol Pa) for pressure and the siemens (symbol S) for electrical conductance to the list of named derived units.[22]
- The 15th CGPM (1975) added the becquerel (symbol Bq) for "activity referred to a radionuclide" and the gray (symbol Gy) for ionizing radiation to the list of named derived units[22]
- In order to distinguish between "absorbed dose" and "dose equivalent", the 16th CGPM (1979) added the sievert (symbol Sv) to the list of named derived units as the unit of dose equivalent.[22]
- The 16th CGPM (1979) clarified that in a break with convention either the letter "L" or the letter "l" may be used as a symbol for the litre.[22]
- The 21st CGPM (1999) added the katal (symbol kat) for catalytic activity to the list of named derived units.[22]
- In its original form (1960), the SI defined prefixes for values ranging from pico- (symbol p) having a value of 10−12 to tera- (symbol T) having a value of 1012. The list was extended at the 12th CGPM (1964),[22] at the 15th CGPM (1975)[22] and at the 19th CGPM (1991)[22] to give the current range of prefixes.
Although, in theory, SI can be used for any physical measurement, it is recognised that some non-SI units still appear in the scientific, technical and commercial literature, and will continue to be used for many years to come. In addition, certain other units are so deeply embedded in the history and culture of the human race that they will continue to be used for the foreseeable future.[67] The CIPM has catalogued such units and included them in the SI Brochure so that they can be used consistently.
The first such group comprises the units of time and of angles and certain legacy non-SI metric units. Most of mankind has used the day and its subdivisions as a basis of time with the result that the second, minute, hour and day, unlike the foot or the pound, were the same regardless of where it was being measured. The second has been catalogued as an SI unit, its multiples as units of measure that may be used alongside the SI. The measurement of angles has likewise had a long history of consistent use – the radian, being of a revolution, has mathematical niceties, but it is cumbersome for navigation, hence the retention of the degree, minute and second of arc. The tonne, litre and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols.
Physicists often use units of measure that are based on natural phenomena such as the speed of light, the mass of a proton (approximately one dalton), the charge of an electron and the like. These too have been catalogued in the SI Brochure with consistent symbols, but with the caveat that their physical values need to be measured.
In the interests of standardising health-related units of measure used in the nuclear industry, the 12th CGPM (1964) accepted the continued use of the curie (symbol Ci) as a non-SI unit of activity for radionuclides;[22] the becquerel, sievert and gray were adopted in later years. Similarly, the millimetre of mercury (symbol mmHg) was retained for measuring blood pressure.[22]
SI has become the world's most widely used system of measurement, used in both everyday commerce and science.[69][70] The change to SI had little effect on everyday life in countries that used the metric system – the metre, kilogram, litre and second remained unchanged as did the way in which they were used – most of the changes only affected measurements in the workplace.[71] The CGPM has a role of recommending changes, but no formal role in the enforcement of such changes—another inter-governmental organisation, the International Organization of Legal Metrology (OIML) provides a forum for harmonisation of national standards and legislation in respect of metrology.
Both the degree and rate of adoption of SI varied from country to country—countries that had not adopted the metric system by 1960 and subsequently adopted SI did so directly as part of their metrication programs while others migrated from the CGS system of units to SI. In 1960, the world's largest economy was that of the United States, followed by the United Kingdom, West Germany, France, Japan, China and India.[72] The United States and the United Kingdom were non-metric, France and Germany had been using the metric system for about a century, and China had been using the metric system for 35 years, while India and Japan had adopted the metric system within the preceding five years. Other non-metric countries were those where the United Kingdom or the United States had considerable influence.[73] These differences are brought out in the examples below:
Even though the use of metric units was legalised for trade in the UK in 1864, the UK had signed the Metre Convention in 1884 and the UK Parliament had defined the yard and the pound in terms of the metre and the kilogram in 1897, the UK continued to use the imperial system of measure[74] and to export the imperial system of units to the Empire. In 1932, the system of Imperial Preference was set up at the Ottawa Conference. Although Ireland left the Commonwealth in 1948 and South Africa in 1961,[75] both continued their close economic ties with the Commonwealth.[76]
By 1980 all apart from the United Kingdom, Canada and Ireland had effectively completed their programs. In the United Kingdom the breakdown of voluntary metrication in the mid-1970s[80] coincided with the United Kingdom's obligations as part of the EEC to adopt the metric system, resulting in legislation to force metrication in certain areas and the Eurosceptic movement adopting an anti-metrication stance and the United Kingdom seeking a number of derogations from the relevant EEC directives. Once the metrication of most consumer goods was completed in 2000, aspects of British life, especially in government, commerce and industry used SI.[80] Although imperial units are widely encountered in unregulated areas such as the press and everyday speech, SI or units approved for use alongside SI are used in most areas where units of measure are regulated. High-profile exceptions include the sale of draught beer, the sale of milk in returnable containers, and United Kingdom road signs. Irish road signs (road distances and speeds) were converted to metric units during the first decade of the 21st century;[81] otherwise, the situation in Ireland is similar to that in the United Kingdom.[82]
Canada has adopted it for most purposes, but imperial units are still legally permitted and remain in common use throughout a few sectors of Canadian society, particularly in the buildings, trades and railways sectors.[83][84]
In 1960, all the largest industrialised nations that had an established history of using the metric system were members of the European Economic Community (EEC).
In 1972, in order to harmonise units of measure as part of a programme to facilitate trade between member states, the EEC issued directive 71/354/EEC.[85] This directive catalogued units of measure that could be used for "economic, public health, public safety and administrative purposes" and also provided instructions for a transition from the existing units of measure that were in use. The directive replicated the CGPM SI recommendations and in addition pre-empted some of the additions whose use had been recommended by the CIPM in 1969, but had not been ratified by the CGPM. The directive also catalogued units of measure whose status would be reviewed by the end of 1977 (mainly coherent CGS units of measure) and also catalogued units of measure that were to be phased out by the end of 1977, including the use of obsolete names for the sale of timber such as the stere, the use of units of force and pressure that made use of the acceleration due to gravity, the use of non-coherent units of power such as the Pferdestärke (PS), the use of the calorie as a measure of energy and the stilb as a measure of luminance. The directive was silent in respect of units that were specific to one or two countries including the pond, pfund, livre (Dutch, German and French synonyms for 500 g), thereby effectively prohibiting their use as well.
When the directive was revisited during 1977, some of the older units that were being reviewed (such as millimetre of mercury for blood pressure) were retained but others were phased out, thereby broadly aligning the allowable units with SI. The directive was however overhauled to accommodate British and Irish interests in retaining the imperial system in certain circumstances.[86] It was reissued as directive 80/181/EEC. During subsequent revisions, the directive has reflected changes in the definition of SI. The directive also formalised the use of supplementary units, which in 1979 were permitted for a period of ten years. The cut-off date for the use of supplementary units was extended a number of times and in 2009 was extended indefinitely.[87]
India was one of the last countries to start a metrication programme before the advent of SI. When it became independent in 1947, both imperial and native units of measure were in use. Its metrication programme started in 1956 with the passing of the Standards of Weights and Measures Act. Part of the act fixed the value of the seer (a legacy unit of mass) to 0.9331 kg exactly; elsewhere the Act declared that from 1960 all non-metric units of measure were to be illegal.[88]
Four years after the Indian Government announced its metrication programme, SI was published. The result was that the initial metrication programme was a conversion to the CGS system of units and the subsequent adoption of SI has been haphazard. Fifty years later, many of the country's schoolbooks still use CGS or imperial units.[89] Originally the Indian Government had planned to replace all units of measure with metric units by 1960. In 1976 a new Weights and Measures Act replaced the 1956 Act which, amongst other things, required that all weighing devices be approved before being released onto the market place. However, in 2012, it was reported that traditional units were still encountered in small manufacturing establishments and in the marketplace alongside CGS, SI and imperial measures, particularly in the poorer areas.[90]
![Banana market stall in Kerala, India – the trader is using hexagonal weights – a shape that is consistent with metric weights, both in India[91] and internationally[68]](/winstonyin/zhwiki/blob/master/Half Bananas for Sale at Market - Trivandrum - Kerala - India.jpg "Banana market stall in Kerala, India – the trader is using hexagonal weights – a shape that is consistent with metric weights, both in India[91] and internationally[68]")
On 10 February 1964, the National Bureau of Standards (now the National Institute of Standards and Technology) issued a statement that it was to use SI except where this would have an obvious detrimental effect. In 1968 Congress authorised the U.S. Metric Study the emphasis of which was to examine the feasibility of adopting SI.[96] The first volume was delivered in 1970.[97] The study recommended that the United States adopt the International System of units,[98] and in 1975 Congress passed the Metric Conversion Act of 1975, which established a national policy of coordinating and planning for the increased use of the metric measurement system in the United States.[99] Metrication was voluntary and to be coordinated by the United States Metric Board (USMB).[100]
Efforts during the Ford and Carter administrations to force metrication were seized on by many newspaper editorialists as being dictatorial.[5] Public response included resistance, apathy, and sometimes ridicule.[101] The underlying reasons for this response include a relative uniformity of weights and measures (though, notably, US liquid measure differed by about 20% from British Imperial measure, which was adopted throughout the British Empire in 1824) inherited from the United Kingdom in 1776, a homogeneous economy and the influence of business groups and populists in Congress caused the country to look at the short-term costs associated with the change-over, particularly those that would be borne by the consumer rather than long-term benefits of efficiency and international trade. The Metrication Board was disbanded under President Ronald Reagan's direction in 1982.[5]
The 1988 Omnibus Foreign Trade and Competitiveness Act removed international trade barriers and amended the Metric Conversion Act of 1975, designating the metric system as "the Preferred system of weights and measures for United States trade and commerce". The legislation stated that the federal government has a responsibility to assist industry, especially small business, as it voluntarily converts to the metric system of measurement.[102] Exceptions were made for the highway and construction industries; the Department of Transportation planned to require metric units by 2000, but this plan was cancelled by the 1998 highway bill TEA21.[103] However, the US military uses the metric system widely, partly because of the need to work with armed services from other nations.[104] Although overall responsibility for labelling requirements of consumer goods lies with Congress and is therefore covered by federal law, details of labelling requirements for certain commodities are controlled by state law or by other authorities such as the Food and Drug Administration, Environmental Protection Agency and Alcohol and Tobacco Tax and Trade Bureau.[105] The federal Fair Packaging and Labeling Act (FPLA), originally passed in 1964, was amended in 1992 to require consumer goods directly under its jurisdiction to be labelled in both customary and metric units. Some industries are engaged in efforts to amend this law to allow manufacturers to use only metric labelling.[106] The National Conference on Weights and Measures has developed the Uniform Packaging and Labeling Regulations (UPLR) which provides a standard approach to those sections of packaging law that are under state control. Acceptance of the UPLR varies from state to state – fourteen states accept it by merely citing it in their legislation.[107]
Meanwhile, in 1999 the UPLR was amended to permit metric-only labelling and automatically became law in those states that accept UPLR "as is". By 1 January 2009, 48 out of 50 states permit metric-only labelling, either through UPLR or through their own legislation.[105] the use of metric (and therefore SI) units in the United States does not follow any pattern. Dual-unit labelling on consumer goods is mandatory. Some consumer goods such as soft drinks are sold in metric quantities, but milk is sold in customary units. The engineering industry is equally split. The automotive industry is largely metric,[108] but aircraft such as the Boeing 787 Dreamliner were designed using customary units.[109]
自從1960年重新定義米之後，公斤便一直是唯一一個依賴某件人造物體來定義的國際單位制基本單位：全球各地的公斤標準都須定期與位於法國塞夫爾的國際公斤原器進行比較。[110]
2007年第23屆國際度量衡大會建議國際度量衡委員會進一步研究，如何通過固定物理常數的數值來定義基本單位，從而代替現用的國際公斤原器，並使國際單位制的宗旨從「單位之定義」轉移至「物理常數之定義」。[111][112]
2010年，單位顧問委員會在英國召開的會議通過了《國際單位制手冊》的修訂草案，同年呈交至國際度量衡委員會。[113][114]此項草案建議：
- 除光速以外，為四個物理常數──普朗克常數、基本電荷、波茲曼常數及阿佛加德羅常數──定義固定精確數值。
- 淘汰國際公斤原器。
- 修訂公斤、安培、開爾文及摩爾的現用定義。
- 所有基本單位的定義措辭改為更加精簡，並須反映出著重點從「單位之定義」轉移至「物理常數之定義」。
在2011年第24屆大會上，國際度量衡委員會從原則上贊成對定義進行必要的修訂，並重申修訂前必須達到的各項條件。[116]2014年第25屆大會召開時，第23屆大會所設下的條件仍未滿足，因此大會再次建議在確立物理常數固定值方面做進一步工作。[117]
國際單位制重新定義的提案預計將於2018年第26屆大會上通過採納。[118]科學技術數據委員會基本常數任務組已宣佈將於該次大會上公佈的數值的提交限期。[119]