Guide for the Use of SI Units

1 Page 1 NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor Guide for the Use of the International System of Units (SI) SI m A K cd mol kg s Open at page → 3 Page 3 NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technol... Open at page → 4 Page 4 National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 20... Open at page → 5 Page 5 Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measur... Open at page → 6 Page 6 Guide for the Use of the International System of Units (SI) It is quite natural for NIST to publish documents on the use of the SI. First, NIST coordinates the Federal Government policy on the conversion to the SI by Fed... Open at page → 7 Page 7 Guide for the Use of the International System of Units (SI) v Check List for Reviewing Manuscripts The following check list is intended to help NIST authors review the conformity of their manuscripts with proper SI usage... Open at page → 8 Page 8 Guide for the Use of the International System of Units (SI) vi (9) ? Values of quantities are expressed in acceptable units using Arabic numerals and the symbols for the units. (See Sec. 7.6.) m = 5 kg but not: m = five... Open at page → 9 Page 9 Guide for the Use of the International System of Units (SI) vii Contents Preface............................................................................................................................................... Open at page → 10 Page 10 Guide for the Use of the International System of Units (SI) viii 6.2 Rules and style conventions for SI prefixes........................................................................... 13 6.2.1 Typeface and spacing ..... Open at page → 11 Page 11 Guide for the Use of the International System of Units (SI) ix 9 Rules and Style Conventions for Spelling Unit Names..................................................................... 31 9.1 Capitalization................ Open at page → 12 Page 12 Guide for the Use of the International System of Units (SI) x Appendix C. Comments on the References of Appendix D—Bibliography ....................................... 70 C.1 Defining document for the SI: BIPM SI Brochur... Open at page → 13 Page 13 Guide for the Use of the International System of Units (SI) 1 1 Introduction 1.1 Purpose of Guide The International System of Units was established in 1960 by the 11th General Conference on Weights and Measures (CGPM— se... Open at page → 14 Page 14 Guide for the Use of the International System of Units (SI) 2 2 NIST Policy on the Use of the SI In accordance with various Federal Acts, the Code of Federal Regulations, and Executive Order 12770 (see Preface), it is NI... Open at page → 15 Page 15 Guide for the Use of the International System of Units (SI) 3 3 Other Sources of Information on the SI 3.1 Publications Appendix C briefly describes a number of publications that deal with the SI and related topics; cita... Open at page → 16 Page 16 Guide for the Use of the International System of Units (SI) 4 4.1 SI base units Table 1 gives the seven base quantities, assumed to be mutually independent, on which the SI is founded, and the names and symbols of their... Open at page → 17 Page 17 Guide for the Use of the International System of Units (SI) 5 Table 3. The 22 SI coherent derived units with special names and symbols. SI coherent derived unit (a) Special name Special symbol Expression in terms of othe... Open at page → 18 Page 18 Guide for the Use of the International System of Units (SI) 6 where T 0 = 273.15 K by definition. To express Celsius temperature, the unit degree Celsius, symbol ºC, which is equal in magnitude to the unit kelvin, is use... Open at page → 19 Page 19 Guide for the Use of the International System of Units (SI) 7 Tables 3 and 4 also show that the values of several different quantities are expressed in the same SI unit. For example, the joule per kelvin (J/K) is the SI... Open at page → 20 Page 20 Guide for the Use of the International System of Units (SI) 5.1.1 Hour, degree, liter, and the like Certain units that are not part of the SI are essential and used so widely that they are accepted by the CIPM, and thus... Open at page → 21 Page 21 Guide for the Use of the International System of Units (SI) 9 Table 7. Non-SI Units accepted for use with the SI by the CIPM and this Guide, whose values in SI units are obtained experimentally Name Symbol Definition and... Open at page → 22 Page 22 Guide for the Use of the International System of Units (SI) 10 5.2 Other Non-SI units accepted for use with the SI Because of established practice in certain fields or countries, in 1978 the CIPM considered that it was p... Open at page → 23 Page 23 Guide for the Use of the International System of Units (SI) 11 Table 10. Examples of CGS units with special names (not accepted for use w ith the SI by this Guide ) Name Symbol Value in SI units erg dyne poise (a) stokes... Open at page → 24 Page 24 Guide for the Use of the International System of Units (SI) 12 6 Rules and Style Conventions for Printing and Using Units 6.1 Rules and style conventions for unit symbols The following eight sections give rules and style... Open at page → 25 Page 25 Guide for the Use of the International System of Units (SI) avoid possible confusion; for this same reason, only one of these two allowed forms should be used in any given manuscript. 6.1.6 Unit symbols obtained by divis... Open at page → 26 Page 26 Guide for the Use of the International System of Units (SI) 14 6.2.2 Capitalization The prefix symbols Y (yotta), Z (zetta), E (exa), P (peta), T (tera), G (giga), an d M (mega) are printed in upper-case letters while al... Open at page → 27 Page 27 Guide for the Use of the International System of Units (SI) 15 unit symbol for gram, and the names of such multiples and submultiples are formed by attaching SI prefix names to the name “gram.” Example: 10 −6 kg = 1 mg (... Open at page → 28 Page 28 Guide for the Use of the International System of Units (SI) 16 2. An alternative way of writing c /(m/s) is {c} m/s, meaning the numerical value of c when c is expressed in the unit m/s. 7.2 Space between numerical value... Open at page → 29 Page 29 Guide for the Use of the International System of Units (SI) 17 Note: V is a quantity symbol for potential difference. 7.5 Unacceptability of mixing information with units When one gives the value of a quantity, any infor... Open at page → 30 Page 30 Guide for the Use of the International System of Units (SI) 18 as “the reading lamp was designed to take two 60-watt light bulbs,” or “the rocket journeyed uneventfully across 380 000 kilometers of space,” or “they bough... Open at page → 31 Page 31 Guide for the Use of the International System of Units (SI) 19 — the practice in a particular field of science or technology. A digit is significant if it is required to express the numerical value of a quantity. In the... Open at page → 32 Page 32 Guide for the Use of the International System of Units (SI) 20 the symbol % and the number by which it is multiplied [4: ISO 31-0]. Further, in keeping with Sec. 7.6, the symbol % should be used, not the name “percent.”... Open at page → 33 Page 33 Guide for the Use of the International System of Units (SI) 21 the relative expanded uncertainty of the resistance R is U r = 3 ppm Because the names of numbers 10 9 and larger are not uniform worldwide, it is best that... Open at page → 34 Page 34 Guide for the Use of the International System of Units (SI) Eg/eV = 1.425 − 1.337x + 0.270x 2 , 0 ≤ x ≤ 0.15, where x is an appropriately defined amount-of-substance fraction (see Sec. 8.6.2). k /(S / cm) = 0.065 135 + 1... Open at page → 35 Page 35 Guide for the Use of the International System of Units (SI) 23 A derived quantity of dimension one, which is sometimes called a “dimensionless quantity,” is one for which all of the dimensional exponents are zero: dim Q... Open at page → 36 Page 36 Guide for the Use of the International System of Units (SI) 24 Inasmuch as NIST is a scientific and technical organization, the word “weight” used in the everyday sense (that is, to mean mass) should appear only occasion... Open at page → 37 Page 37 Guide for the Use of the International System of Units (SI) 25 8.6 Amount of substance, concentration, molality, and the like The following section discusses amount of substance, and the subsequent nine sections, which a... Open at page → 38 Page 38 Guide for the Use of the International System of Units (SI) Table 12. Summary description of nine quantities that are quotients involving amount of substance, volume, or mass (a) Quantity in numerator Amount of Substance... Open at page → 39 Page 39 Guide for the Use of the International System of Units (SI) 27 2. For a mixture, this term is often called “mean molar volume.” 3. The amagat should not be used to express molar volumes or reciprocal molar volumes. (One... Open at page → 40 Page 40 Guide for the Use of the International System of Units (SI) * Am,A * Bm,B B Vx Vx ∑ = ϕ where x A, xB, xC, . . . are the amount-of-substance fractions of A, B, C, . . ., . . . are the molar volumes of the pure substances... Open at page → 41 Page 41 Guide for the Use of the International System of Units (SI) prefixes to them, such as the millineper, symbol mNp (1 mNp = 0.001 Np), and the decibel, symbol dB (1 dB = 0.1 B). Level-of-a-field-quantity is defined by the... Open at page → 42 Page 42 Guide for the Use of the International System of Units (SI) 30 the quantity whose level is being reported, for example, electric field strength E or sound pressure p, and x ref is the value of the reference quantity, for... Open at page → 43 Page 43 Guide for the Use of the International System of Units (SI) 31 Note: Parentheses around a word means that the word is often omitted. (c) The adjective areic is used to modify the name of a quantity, or the terms surface... Open at page → 44 Page 44 Guide for the Use of the International System of Units (SI) 32 Example: pascal second or pascal-second 9.5 Spelling unit names obtained by division When the name of a derived unit formed from other units by division is s... Open at page → 45 Page 45 Guide for the Use of the International System of Units (SI) 33 10.1 Kinds of symbols Letter symbols are of three principal kinds: (a) symbols for quantities, (b) symbols for units, and (c) symbols for descriptive terms.... Open at page → 46 Page 46 Guide for the Use of the International System of Units (SI) 34 understandability of NIST typed and typeset scientific and technical publications is facilitated if symbols are in the correct typeface. The typeface in whic... Open at page → 47 Page 47 Guide for the Use of the International System of Units (SI) A ·B = C (vectors) T (tensors) (matrices) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2111 2221aa aa A Symbols used as subscripts and superscripts are italic if they represent quantities or... Open at page → 48 Page 48 Guide for the Use of the International System of Units (SI) 36 Table 13. Greek alphabet in roman and italic type Greek Letter Name Roman Italic alpha Α α Α α beta Β β Β β gamma Γ γ Γ γ delta Δ δ Δ δ epsilon Ε ε Ε ε zeta... Open at page → 49 Page 49 Guide for the Use of the International System of Units (SI) State of ionization: Ba ++ Co(NO 2)6 − − −. or or [Co(NO 2)6] 3 − −3 62 )NO(Co Electronic excited state: Ne*, CO* Nuclear excited state: 15 N* or 15 N m 10.5 Pr... Open at page → 50 Page 50 Guide for the Use of the International System of Units (SI) 38 Notes: 1. When the comma is used as the decimal marker, the preferred sign fo r the multiplication of numbers is the half-high dot. However, even when the co... Open at page → 51 Page 51 Guide for the Use of the International System of Units (SI) 39 Appendix A. Definitions of the SI Base Units A.1 Introduction The following definitions of the SI base units are taken from Refs. [1, 2]; it should be noted... Open at page → 52 Page 52 Guide for the Use of the International System of Units (SI) 40 Appendix B. Conversion Factors 6 B.1 Introduction Sections B.8 and B.9 give factors for converting values of quantities expressed in various units— predomina... Open at page → 53 Page 53 Guide for the Use of the International System of Units (SI) 41 Notes: 1. Guidance on rounding converted numerical values of quantities is given in Sec. B.7.2. 2. If the value of a quantity is expressed in a unit of the c... Open at page → 54 Page 54 Guide for the Use of the International System of Units (SI) 42 FORCE DIVIDED BY AREA Thermal Resistance (see PRESSURE) Thermal Resistivity LENGTH POWER LIGHT PRESSURE or STRESS (FORCE MASS and MOMENT OF INERTIA DIVIDED B... Open at page → 55 Page 55 Guide for the Use of the International System of Units (SI) 43 1 ft = (1200/3937) m 1 ft = 0.3048 m 1 ft = 0.999 998 ft 1 rd, pole, or perch = 16 ½ ft 40 rd = 1 fur = 660 ft 8 fur = 1 U.S. survey mile (also called “statu... Open at page → 56 Page 56 Guide for the Use of the International System of Units (SI) 44 The final result, l = 11.0 m, is based on the following reasoning: The numerical value “36” has two significant digits, and thus a relative maximum possible... Open at page → 57 Page 57 Guide for the Use of the International System of Units (SI) 45 B.8 Factors for units listed alphabetically Caution: The units listed in column 1 are in general not to be used in NIST publications, with the exception of t... Open at page → 58 Page 58 Guide for the Use of the International System of Units (SI) 46 To convert from to Multiply by British thermal unit th inch per second square foot degree Fahrenheit [Btu th·in/(s·ft 2 ·ºF)] .................................. Open at page → 59 Page 59 Guide for the Use of the International System of Units (SI) 47 To convert from to Multiply by British thermal unit th per square foot second [Btu th / (ft 2 · s)] .............................................. watt per s... Open at page → 60 Page 60 Guide for the Use of the International System of Units (SI) 48 To convert from to Multiply by circular mil .......................................................... square millimeter (mm 2 ) ...................... 5.067... Open at page → 61 Page 61 Guide for the Use of the International System of Units (SI) 49 To convert from to Multiply by degree Rankine (temperature interval) (ºR) ......... kelvin (K) ............................................. 5.555 556 E−01 d... Open at page → 62 Page 62 Guide for the Use of the International System of Units (SI) 50 To convert from to Multiply by gal (Gal) ............................................................... meter per second squared (m / s 2 ) ................... Open at page → 63 Page 63 Guide for the Use of the International System of Units (SI) 51 To convert from to Multiply by inch per second squared (in / s 2 ) .......................... meter per second squared (m / s 2 ) ................. 2.54 E−02... Open at page → 64 Page 64 Guide for the Use of the International System of Units (SI) 52 To convert from to Multiply by mil (angle) ........................................................... radian (rad) ............................................ Open at page → 65 Page 65 Guide for the Use of the International System of Units (SI) 53 To convert from to Multiply by ounce (avoirdupois) per square inch (oz / in 2 ) ..... kilogram per square meter (kg / m 2 ) .... 4.394 185 E+01 ounce (avoird... Open at page → 66 Page 66 Guide for the Use of the International System of Units (SI) 54 To convert from to Multiply by pound-force second per square foot (lbf · s/ft 2 ) ..................................................... pascal second (Pa · s... Open at page → 67 Page 67 Guide for the Use of the International System of Units (SI) 55 To convert from to Multiply by square foot per second (ft 2 / s) ............................. square meter per second (m 2 / s) .......... 9.290 304 E−02 sq... Open at page → 68 Page 68 Guide for the Use of the International System of Units (SI) 56 To convert from to Multiply by watt per square inch (W / in 2 ) .............................. watt per square meter (W / m 2 ) ............ 1.550 003 E+03 w... Open at page → 69 Page 69 Guide for the Use of the International System of Units (SI) 57 B.9 Factors for units listed by kind of quantity or field of science Caution: The units listed in column 1 are in general not to be used in NIST publications... Open at page → 70 Page 70 Guide for the Use of the International System of Units (SI) 58 To convert from to Multiply by abohm .................................................................. ohm (Ω ) ............................................... Open at page → 71 Page 71 Guide for the Use of the International System of Units (SI) 59 To convert from to Multiply by foot pound-force (ft · lbf) ..................................... joule (J) .................................................... Open at page → 72 Page 72 Guide for the Use of the International System of Units (SI) 60 To convert from to Multiply by Coefficient of Heat Transfer British thermal unit IT per hour square foot degree Fahrenheit [Btu IT / (h · ft 2 · ºF)] .......... Open at page → 73 Page 73 Guide for the Use of the International System of Units (SI) 61 To convert from to Multiply by Heat Capacity and Entropy British thermal unit IT per degree Fahrenheit (Btu IT / ºF) ........................................... Open at page → 74 Page 74 Guide for the Use of the International System of Units (SI) 62 To convert from to Multiply by Thermal Diffusivity square foot per hour (ft 2 / h) ................................ square meter per second (m 2 / s) .......... Open at page → 75 Page 75 Guide for the Use of the International System of Units (SI) 63 To convert from to Multiply by mile, nautical 20 .................................................... meter (m) ................................................ Open at page → 76 Page 76 Guide for the Use of the International System of Units (SI) 64 To convert from to Multiply by MASS DENSITY (see MASS DIVIDED BY VOLUME) MASS DIVIDED BY AREA ounce (avoirdupois) per square foot (oz / ft 2 ) ...... kilogra... Open at page → 77 Page 77 Guide for the Use of the International System of Units (SI) 65 To convert from to Multiply by kilogram-force meter (kgf · m) ............................ newton meter (N · m).............................. 9.806 65 E+00 o... Open at page → 78 Page 78 Guide for the Use of the International System of Units (SI) 66 To convert from to Multiply by inch of mercury (32 ºF) 12 ..................................... pascal (Pa) .............................................. 3.... Open at page → 79 Page 79 Guide for the Use of the International System of Units (SI) 67 To convert from to Multiply by TEMPERATURE INTERVAL degree Celsius (ºC) .............................................. kelvin (K) .............................. Open at page → 80 Page 80 Guide for the Use of the International System of Units (SI) 68 To convert from to Multiply by VISCOSITY, KINEMATIC centistokes (cSt) .................................................. meter squared per second (m 2 / s) .... Open at page → 81 Page 81 Guide for the Use of the International System of Units (SI) 69 To convert from to Multiply by VOLUME DIVIDED BY TIME (includes FLOW) cubic foot per minute (ft 3 / min) .......................... cubic meter per second (m... Open at page → 82 Page 82 Guide for the Use of the International System of Units (SI) 70 Appendix C. Comments on the References of Appendix D— Bibliography C.1 Defining document for the SI: BIPM SI Brochure The defining document for the Internati... Open at page → 83 Page 83 Guide for the Use of the International System of Units (SI) 71 Institute (ANSI) standard. 26 It is based on the International System of Units as interpreted for use in the United States (see Secs. C.1 and C.2), and has b... Open at page → 84 Page 84 Guide for the Use of the International System of Units (SI) 72 A Federal Register Notice of July 28, 1998, [16] declares that there are now only two classes of units in the International System of Units: base units and d... Open at page → 85 Page 85 Guide for the Use of the International System of Units (SI) 73 Appendix D. Bibliography [1] Le Systéme International d’Unités (SI), The International System of Units (SI), 8th Edition (Bur. Intl. Poids et Mesures, Sèvres... Open at page → 86 Page 86 Guide for the Use of the International System of Units (SI) 74 Note: ISO 31-0:1992— ISO 31-13:1992 and ISO 1000:1992 are reprinted in the ISO Standards Handbook Quantities and units (International Organization for Standa... Open at page → 87 Page 87 Guide for the Use of the International System of Units (SI) 75 [12] Federal Register, Vol. 33, No. 146, p. 10755, July 27, 1968. [13] Federal Register, Vol. 55, No. 245, p. 52242, December 20, 1990. [14] Federal Register... Open at page → 88 Page 88 Guide for the Use of the International System of Units (SI) 76 This page intentionally left blank. Open at page → 89 Page 89 SI COHERENT DERIVED UNITS WI TH SPECIAL NAMES AND SYMBOLS (Explanation of Graphic on Back Cover) Derived units are defined as products of powers of the base units. When the product of powers includes no numerical factor... Open at page → 90 Page 90 ACCELERATION VELOCITY AREA VOLUME ABSORBED DOSE DOSE EQUIVALENT PRESSURE, STRESS FORCE ENERGY,WORK, QUANTITY OF HEAT VOLTAGE, ELECTROMOTIVE FORCE CAPACITANCE ELECTRIC CHARGE ACTIVITY (OF A RADIONUCLIDE) CONDUCTANCERESIST... Open at page →