The Metric System of Measurements (Si)

NATIONAt BUREAU MBS OF STANDARDS A 1 1 1 2 345^65 LIBRARY PUBLICATIONS

LC1132 (Supersedes LC1078) THE METRIC SYSTEM OF MEASUREMENTS (SI)

Federal Register Notice of February 26, 1982

April 19,1982

This NBS Letter Circular reproduces the Federal Register notice

that interprets and modifies the International System of Units (SI), the Modernized Metric System, for the United States. This notice

supersedes a similar notice dated October 26, 1977.

Also included is a chart that shows the relationships of all the SI units to which names have been assigned.

May be reproduced freely

U S, DEPARTMENT OF COMMERCE/National Bureau of Standards Washington, D.C, 20234 RELATIONSHIPS OF SI UNITS WITH NAMES This chart shows graphically how the 19 SI derived units with special names listed in Table 2 of the Federal Register Notice, reprinted below, are derived in a coherent manner from the base and supplementary units.

In the first column the symbols of the base and supplementary units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the quantity (measurable attribute) shown below the rectangle. In the third column the sym-

bols of the derived units with special names are shown in solid circles, with the name of the unit shown toward the upper left of the circle, the name of the quantity shown

below the circle, and an expression of the derived unit in terms of other units shown toward the upper right. In the second column are shown those derived units without special names that are used in the derivation of the derived units with special names. In the chart the deriva-

tion of each unit is indicated by arrows bringing in numerator factors (solid lines) and denominator factors

(broken lines).

The degree Celsius, shown on the chart in a broken-

line rectangle, is a special name for the kelvin, for use in expressing Celsius temperatures or temperature intervals.

Where it is used to express temperature intervals, it is equal to the kelvin, as shown on the chart, with the sym-

bol K toward the upper right of the °C circle; where it is used to express Celsius temperatures, the equation below "CELSIUS TEMPERATURE" relates Celsius tem-

perature (t Q q) to thermodynamic temperature (T^)

National Bureau of Standards on Weights and Measures in 1960 and and modification, as published in the interpreted or modified for the United above-cited Federal Register notice of

States by the Secretary of Commerce October 26, 1977. To assist interested Metric System of Measurement; (sec. 4(4), Pub. L. 94-168; sec. 403(a)(3), parties and encourage the proper use of Interpretation and Modification of the Pub. L. 93-380). The Secretary has SI, the entire interpretation and International System of Units for the delegated his authority under these modification, as hereby amended, is United States subsections to the Director of the republished. Accordingly, this notice National Bureau of Standards. supersedes the notice of October 26, 1977. Section 3 of Pub. L. 94-168, the Metric In implementation of this authority, The amendments consist of the Conversion Act of 1975, declares that tables and associated materials were the inclusion in table 2 of the sievert, a policy of the United States shall be published in the Federal Register of to coordinate the special name for the SI derived unit of and plan increasing October 26. 1977 (42 FR 56513-56514), use dose equivalent, the inclusion in table 6 of the metric system in the United setting forth the interpretation and States. of the electronvolt and the unified Section 403 of Pub. L. 93-380, the modification of the International System Education atomic mass unit, and the inclusion in Amendments of 1974, states of Units (hereinafter "SI") for the United the policy table 7 of the rem, a unit of of the United States to States. dose encourage educational agencies and equivalent. The unit “standard institutions to prepare students to use In accordance with recent decisions of atmosphere” is no longer included in the metric system of measurement as the International Committee for Weights table 7. The amendments are indicated part of the regular education program. and Measures of the General by a dagger symbol (f). Under both these acts, the “metric Conference on Weights and Measures, The SI is constructed from seven base system of measurement” is defined as and to refine the earlier interpretation units for independent quantities plus the International System of Units as arid modification, it is deemed two supplementary units for plane angle established by the General Conference appropriate to amend that interpretation and solid angle, listed in table 1. . '

Table 1—SI base and supplementary Table 3 — Examples of SI derived units Certain units that are not part of the units EXPRESSED IN TERMS OF BASE UNITS SI are used so widely that it is impractical to abandon them. The units Quantity Name Symbol Unit Quantity unit SI symbol that are accepted for continued use in

SI base units: the United States with the International length System are listed in table 6. 1 mass k 9 time speed, velocity meter per second m/s electric current ampere A acceleration meter per second m/s 2 Table 6 Units in use with the thermodynamic tempera- kelvm K squared. — ture International System density, mass density kilogram per cubic kg/m 3 meter. cd Name Symbol Value m SI unit J SI supplementary units; specific volume cubic meter per m /kg plane angle kilogram. 2 minute (time) mm 1 mm = 60 s solid angle Sf current density ampere per square A/m meter h day d Id 24 h 86 400 s magnetic field strength . ampere per meter A/m 0 degree (angle) I'M"-/ 180) 'ad * concentration (of mole per cubic meter mol/m Weight'' in common parlance 13 often used to mean ” minute (angle) r sr (i/60)° "mass amount of substance) 2 - 77 / rad luminance candela per square cd/m ( 10 800) 1" meter second '(angle) = (1/60)' = (tt/ 648000) rad * J - 10* 3 3 Units for all other quantities are 1 1 L- 1 dm m 3 t 1 t-10 kg derived from these nine units. In table 2 9 2 hectare (land area) .... ha 1 ha = 10 m 10' 19 are listed 19 SI derived units with telectronvolt eV 1 eV = 1 602 x J. approximately** special names which were derived from 27 Table 4 —Examples of SI derived units tunified atomic U 1 u= 1 660 57 x 10' kg. the base and supplementary units in a EXPRESSED BY MEANS OF SPECIAL NAMES mass unit. approximately** coherent manner, which means, in brief,

’ that they are expressed as products and Quantity Name Unit symbol 3oth L and I are international symbols for liter Because ‘ V can easily be confused with the numeral "1" the symbol quotients of the nine base and "L" is recommended for United States use. dynamic viscosity pascal second Pa ** supplementary units without numerical s The values of these units in terms of SI units are moment of force newton meter Nm obtained experimentally. factors. surface tension newton per meter N/m heat flux density. watt per square W/m 2 their is irradiance meter In those cases where usage heal capacity, joule per kelvm J/K already well established, the use, for a entropy Table 2 —SI derived units with special specific beat joule per kilogram J/(kg K) limited time, of the units in table 7 is names capacrty, specrtic kefvm. accepted, subject to future review. entropy specific energy joule per kilogram J/kg SI unit thermal conductivity watt per meter kelvm W/(m-K) Table 7.—Units in use temporarily with energy density joule per cubic meter J/m 3 Quantity Expression electric field strength volt per meter V/m the International System Name Symbol in terms of electnc charge coulomb per cubic 5 other units C/m density meter. electric flux density coulomb per square C/m 2 frequency .. hertz Hz .... meter 2 lorce newton N kg m/s F/m nautical mile angstrom cune J pressure, stress pascal Pa .. . N/m knot barn roentgen energy, work, joule J Nm bar rad 2 molar energy |Oule per mole J/mol quantity of heat gal 1 trem 3 molar entropy, molar joule per mole kelvm J/(mol K) power, radiant flux watt w . J/s heat capacity 1 electric charge, coulomb . . C As Unit of acceleration. exposure (x and y coulomb per kilogram C/kg quantity of 2 Unit of absorbed dose. rays) 3 electricity. Unit of dose equivalent. absorbed dose rate _ gray per second Gy/s electric potential, volt V W/A potential difference, Metric units, symbols, and terms that electromotive are not in accordance with the foregoing force Interpretation and Modification are no capacitance larad F c/v For use with the SI units there is a set electric resistance ohm n V/A longer accepted for continued use in the conductance s A/V of 16 prefixes (see table 5) to form United States with the International magnetic flux weber Wb VS multiples and submultiples of these System of Units. Accordingly, the magnetic flux density tesla T Wb/m 2 It is important to note that the H Wb/A units. following units and terms listed in the luminous flux _ lumen Im unit a cd sr kilogram is the only SI with table of metric units in section 2 of the prefix. Because double prefixes are not Celsius temperature' degree •c K Act of July 28, 1866 that legalized the table in the Celsius to be used, the prefixes of 5, metric system of weights and measures activity (of a becquerel 8q S' ' case of mass, are to be used with gram radionucbde) in the United States are no longer (symbol and not with kilogram absorbed dose, 9«>y Gy J/kg g) accepted for use in the United States: specific energy (symbol kg). imparted, kerma. myriameter absorbed dose stere index. millier or tdose equivalent, sieved Sv J/kg tonneau dose equivalent Table 5 — SI prefixes quintal index. myriagram Prefix Symbol Factor kilo (for kilogram) 1 In addition to the thermodynamic temperature (symbol T) For more information regarding the expressed in kelvms (see table 1). use is also made of 10*® E Celsius temperature (symbol f) defined by the equation 10 11 P International System of Units, contact 10 12 T Dr. David T. Goldman, National where T0 = 2 73 15 K by definition The unit "degree Cel- 9 10 . G sius" is equal to the unit "kefvin," but "degree Celsius" is a 10 9 M Measurement Laboratory, National special name in place of "kelven" for expressing Celsius 3 temperature A temperature interval or a Celsius temperature 10 kilo „.. k Bureau of Standards, U.S. Department of 2 difference can be expressed in degrees Celsius as well as in 10 h Kelvins. 10' Commerce, Washington, D.C. 20234, 10 1 d telephone (301) 921-3304. 10' 2 centi c # Dated: February 1982. All other SI derived units, such as 10 2, 10' 6 Ambler, those 9 Ernest in tables 3 and 4, are similarly 10' .... derived in a coherent manner from the 10“ 12 Director. 10" 15 f 28 base, supplementary, and special- 10- 19 [FR Doc 82-5150 Filed 2-25-82; 8:45 am) name SI units. BILLING CODE 3510-13-41