Essentials of the SI
Introduction
This is a brief summary of the SI, the modern metric system of measurement. Long the language universally used in science, the SI has become the dominant language of international commerce and trade. These "essentials" are adapted from NIST Special Publication 811 (SP 811), prepared by B. N. Taylor and entitled Guide for the Use of the International System of Units (SI), and NIST Special Publication 330 (SP 330), edited by B. N. Taylor and entitled The International System of Units (SI). Users requiring more detailed information may access SP 811 and SP 330 online from the Bibliography, or order SP 811 for postal delivery. Information regarding the adoption and maintenance of the SI may be found in the section International aspects of the SI.
Some useful definitions
A quantity in the general sense is a property ascribed to phenomena, bodies, or substances that can be quantified for, or assigned to, a particular phenomenon, body, or substance. Examples are mass and electric charge.
A quantity in the particular sense is a quantifiable or assignable property ascribed to a particular phenomenon, body, or substance. Examples are the mass of the moon and the electric charge of the proton.
A physical quantity is a quantity that can be used in the mathematical equations of science and technology.
A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.
The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed. 
For example, the value of the height hW of the
| The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.
For detailed information on the SI base units, see Definitions of the SI base units and their Historical context. SI derived units Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted. Table 2. Examples of SI derived units | |||||||||||||||||||||||||||||||||||||||
| | ||
| Derived quantity | Name | Symbol |
| area | square meter | m2 |
| volume | cubic meter | m3 |
| speed, velocity | meter per second | m/s |
| acceleration | meter per second squared | m/s2 |
| wave number | reciprocal meter | m-1 |
| mass density | kilogram per cubic meter | kg/m3 |
| specific volume | cubic meter per kilogram | m3/kg |
| current density | ampere per square meter | A/m2 |
| magnetic field strength | ampere per meter | A/m |
| amount-of-substance concentration | mole per cubic meter | mol/m3 |
| luminance | candela per square meter | cd/m2 |
| mass fraction | kilogram per kilogram, which may be represented by the number 1 | kg/kg = 1 |
| | ||
Table 3. SI derived units with special names and symbols
For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in Table 3.
Table 3. SI derived units with special names and symbols SI derived unit Derived quantity Name Symbol Expression Expression plane angle radian (a) rad - m·m-1 = 1 (b) solid angle steradian (a) sr (c) - m2·m-2 = 1 (b) frequency hertz Hz - s-1 force newton N - m·kg·s-2 pressure, stress pascal Pa N/m2 m-1·kg·s-2 energy, work, quantity of heat joule J N·m m2·kg·s-2 power, radiant flux watt W J/s m2·kg·s-3 electric charge, quantity of electricity coulomb C - s·A electric potential difference, volt V W/A m2·kg·s-3·A-1 capacitance farad F C/V m-2·kg-1·s4·A2 electric resistance ohm V/A m2·kg·s-3·A-2 electric conductance siemens S A/V m-2·kg-1·s3·A2 magnetic flux weber Wb V·s m2·kg·s-2·A-1 magnetic flux density tesla T Wb/m2 kg·s-2·A-1 inductance henry H Wb/A m2·kg·s-2·A-2 Celsius temperature degree Celsius °C - K luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd activity (of a radionuclide) becquerel Bq - s-1 absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2 dose equivalent (d) sievert Sv J/kg m2·s-2 catalytic activity katal kat s-1·mol (a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
in terms of
other SI units
in terms of
SI base units
electromotive force 
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.
For a graphical illustration of how the 22 derived units with special names and symbols given in Table 3 are related to the seven SI base units, see relationships among SI units.
Note on degree Celsius. The derived unit in Table 3 with the special name degree Celsius and special symbol °C deserves comment. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation
t= T- T0.
The unit of Celsius temperature is the degree Celsius, symbol °C. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by
t/°C = T/K - 273.15.
It follows from the definition of t that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numerical value of a given temperature difference or temperature interval whose value is expressed in the unit degree Celsius (°C) is equal to the numerical value of the same difference or interval when its value is expressed in the unit kelvin (K). Thus, temperature differences or temperature intervals may be expressed in either the degree Celsius or the kelvin using the same numerical value. For example, the Celsius temperature difference 
t and the thermodynamic temperature difference T between the melting point of gallium and the triple point of water may be written as t = T = 29.7546 K.
The special names and symbols of the 22 SI derived units with special names and symbols given in Table 3 may themselves be included in the names and symbols of other SI derived units, as shown in Table 4.
Table 4. Examples of SI derived units whose names and symbols include SI derived units with special names and symbols
Derived quantity Name Symbol dynamic viscosity pascal second Pa·s moment of force newton meter N·m surface tension newton per meter N/m angular velocity radian per second rad/s angular acceleration radian per second squared rad/s2 heat flux density, irradiance watt per square meter W/m2 heat capacity, entropy joule per kelvin J/K specific heat capacity, specific entropy joule per kilogram kelvin J/(kg·K) specific energy joule per kilogram J/kg thermal conductivity watt per meter kelvin W/(m·K) energy density joule per cubic meter J/m3 electric field strength volt per meter V/m electric charge density coulomb per cubic meter C/m3 electric flux density coulomb per square meter C/m2 permittivity farad per meter F/m permeability henry per meter H/m molar energy joule per mole J/mol molar entropy, molar heat capacity joule per mole kelvin J/(mol·K) exposure (x and coulomb per kilogram C/kg absorbed dose rate gray per second Gy/s radiant intensity watt per steradian W/sr radiance watt per square meter steradian W/(m2·sr) catalytic (activity) concentration katal per cubic meter kat/m3
rays)
Units outside the SI
Certain units are not part of the International System of Units, that is, they are outside the SI, but are important and widely used. Consistent with the recommendations of the International Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures), the units in this category that are accepted for use with the SI are given in Table 6.
Table 6. Units outside the SI that are accepted for use with the SI
Units outside the SI Certain units are not part of the International System of Units, that is, they are outside the SI, but are important and widely used. Consistent with the recommendations of the International Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures), the units in this category that are accepted for use with the SI are given in Table 6. Table 6. Units outside the SI that are accepted for use with the SI Name Symbol Value in SI units minute (time) min 1 min = 60 s hour h 1 h = 60 min = 3600 s day d 1 d = 24 h = 86 400 s degree (angle) ° 1° = ( minute (angle) 1 second (angle) 1 liter L metric ton (a) t 1 t = neper Np 1 Np = 1 bel (b) B 1 B = (1/2) ln 10 Np (c) electronvolt (d) eV 1 eV = 1.602 18 x 10-19 J, approximately unified atomic mass unit (e) u 1 u = 1.660 54 x 10- astronomical unit (f) ua 1 ua = 1.495 98 x (a) In many countries, this unit is called "tonne.''
/180) rad 
= (1/60)° = (/10 800) rad = (1/60) = (/648 000) rad
(b) The bel is most commonly used with the SI prefix deci: 1 dB = 0.1 B.
(c) Although the neper is coherent with SI units and is accepted by the CIPM, it has not been adopted by the General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures) and is thus not an SI unit.
(d) The electronvolt is the kinetic energy acquired by an electron passing through a potential difference of 1 V in vacuum. The value must be obtained by experiment, and is therefore not known exactly.
(e) The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide
(f) The astronomical unit is a unit of length. Its value is such that, when used to describe the motion of bodies in the solar system, the heliocentric gravitation constant is (0.017 202 098 95)2 ua3·d-2. The value must be obtained by experiment, and is therefore not known exactly.
(a) In many countries, this unit is called "tonne.''
(b) The bel is most commonly used with the SI prefix deci: 1 dB = 0.1 B.
(c) Although the neper is coherent with SI units and is accepted by the CIPM, it has not been adopted by the General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures) and is thus not an SI unit.
(d) The electronvolt is the kinetic energy acquired by an electron passing through a potential difference of 1 V in vacuum. The value must be obtained by experiment, and is therefore not known exactly.
(e) The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide
(f) The astronomical unit is a unit of length. Its value is such that, when used to describe the motion of bodies in the solar system, the heliocentric gravitation constant is (0.017 202 098 95)2 ua3·d-2. The value must be obtained by experiment, and is therefore not known exactly.
|
| The liter in Table 6 deserves comment. This unit and its symbol l were adopted by the CIPM in 1879. The alternative symbol for the liter, L, was adopted by the CGPM in Other units outside the SI that are currently accepted for use with the SI by NIST are given in Table 7. These units, which are subject to future review, should be defined in relation to the SI in every document in which they are used; their continued use is not encouraged. The CIPM currently accepts the use of all of the units given in Table 7 with the SI except for the curie, roentgen, rad, and rem. Because of the continued wide use of these units in the Table 7. Other units outside the SI that are currently accepted for use with the SI, subject to further review |
| Table 7. Other units outside the SI that are currently accepted for use with the SI, subject to further review | ||
| Name | Symbol | Value in SI units |
| nautical mile | | 1 nautical mile = |
| knot | | 1 nautical mile per hour = (1852/3600) m/s |
| are | a | |
| hectare | ha | |
| bar | bar | 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa |
| ångström | Å | 1 Å = 0.1 nm = 10- |
| barn | b | 1 b = 100 fm2 = 10- |
| curie | Ci | 1 Ci = 3.7 x 1010 Bq |
| roentgen | R | 1 R = 2.58 x 10-4 C/kg |
| rad | rad | 1 rad = 1 cGy = 10-2 Gy |
| rem | rem | 1 rem = 1 cSv = 10-2 Sv |
| | ||
Background
The following definitions of the SI base units are taken from NIST Special Publication 330 (SP 330), The International System of Units (SI). See the Bibliography for a description of SP 330 and other NIST publications on the SI, and online access.
Definitions of the SI base units
| International aspects of the SI The International System of Units, universally abbreviated SI (from the French Le Système International d'Unités), is the modern metric system of measurement. The SI was established in 1960 by the 11th General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures). The CGPM is the international authority that ensures wide dissemination of the SI and modifies the SI as necessary to reflect the latest advances in science and technology. The CGPM is an intergovernmental treaty organization created by a diplomatic treaty called the Meter Convention (Convention du Mètre, often called the Treaty of the Meter in the The Meter Convention also created the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures) and the International Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures). The BIPM, which is located in Sèvres, a suburb of Paris, France, and which has the task of ensuring worldwide unification of physical measurements, operates under the exclusive supervision of the CIPM, which itself comes under the authority of the CGPM. The CGPM consists of delegates from all the Member States of the Meter Convention and currently meets every four years (the 22nd CGPM took place in October, 2003). The CIPM consists of eighteen members, each belonging to a different Suggested modifications to the SI are submitted to the CGPM by the CIPM for formal adoption. The CIPM may also on its own authority pass clarifying resolutions and recommendations regarding the SI (these resolutions and recommendations usually deal with matters of interpretation and usage). To assist it in its broad spectrum of technical activities, the CIPM has set up a number of Consultative Committees (Comités Consultatifs). These committees provide the CIPM with information on matters that it refers to them for study and advice. Each Consultative Committee, the Chairman of which is normally a member of the CIPM, is composed of delegates from national metrology institutes such as NIST, specialized institutes, and other international organizations, as well as individual members. The Consultative Committee for Units (CCU, Comité Consultatif des Unités), which was set up in 1964 and which replaced the Commission for the System of Units set up by the CIPM in 1954, advises the CIPM on matters dealing with the SI. In particular, the CCU helps to draft the BIPM SI Brochure, of which NIST Special Publication 330 (SP 330) is the The current Dr. Barry N. Taylor NIST, Bldg. 225, Rm. B161 Telephone: 301-975-4220 Fax: 301-975-4578 email: barry.taylor@nist.gov The Metric System Additional information | ||||
| Bibliography: links, citations and online publications
BIPM, International Bureau of Weights and Measures ANSI, American National Standards Institute ISO, International Organization for Standardization
Information on the SI within this reference is primarily based on three NIST publications, which are available in electronic (acrobat pdf) format. (If you do not have this software, you may wish to obtain it free from Adobe.) Guide to the SI, with a focus on usage and unit conversions: This publication, abbreviated SP 811, has been prepared by NIST to provide assistance in the use of the SI. The topics covered by SP 811 include:
|
| |||
|
| Guide to the SI, with a focus on history: This publication, abbreviated SP 330, is the Guide to the SI, with a legal focus: This notice restates the interpretation of the SI for the Diagram of SI unit relationships:
History of the SI, with a focus on the BIPM This publication, abbreviated SP 420, gives the history of the first century (1875-1975) of the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures), including the history of the Convention du Mètre (Meter Convention) and the SI. It is out of print, and not available online. Weights and measurements in the United States, with a focus on history:
|
No comments:
Post a Comment