NIST Guide to the SI, Footnotes

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https://www.nist.gov/pml/special-publication-811/nist-guide-si-footnotes" title="Email" class="nist-social nist-social--envelope-gray"> <span>Email</span> </a> </div> </div> </div> </div>  </div> <div class="nist-block" > <div class="text-with-summary"> <ul> <li><a name="*"></a><strong>*</strong> Executive Order 12770 was published in the Federal Register, Vol. 56, No. 145, p. 35801, July 29, 1991; 15 CFR 1170 was originally published in the Federal Register, Vol. 56, No. 1, p. 160, January 2, 1991, as 15 CFR Part 19, but was redesignated 15 CFR 1170.</li> <li><a name="**"></a><strong>**</strong> See Ref. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#01">[1]</a> or <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#02">[2]</a> for a brief description of the various bodies established by the Meter Convention: The International Bureau of Weights and Measures (BIPM, <em>Bureau International des Poids et Mesures</em>), the International Committee for Weights and Measures (CIPM, <em>Comité International des Poids et Mesures</em> ), and the CGPM. 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. In addition to a complete description of the SI, Refs. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#01">[1]</a> and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#02">[2]</a> also give the various CGPM and CIPM resolutions on which it is based.</li> </ul> <ol> <li><a name="f01"></a>The NIST policy on the use of the SI is set forth in the NIST Administration Manual, Chapter 4, Communications, Subchapter 4.09, NIST Technical Communications Program, Appendix D — Use of Metric Units.</li> <li><a name="f02"></a>According to <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04iso310">Ref. [4: ISO 31-0]</a>, a system of units is coherent with respect to a system of quantities and equations if the system of units is chosen in such a way that the equations between numerical values have exactly the same form (including the numerical factors) as the corresponding equations between the quantities (see Secs. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-chapter-7#711">7.11</a> and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-chapter-7#714">7.14</a>). In such a coherent system, of which the SI is an example, no numerical factor other than the number 1 ever occurs in the expressions for the derived units in terms of the base units.</li> <li><a name="f03"></a>The symbol in parentheses following the name of the unit is its internationally accepted unit symbol, but the octave, phon, and sone have no such unit symbols. For additional information on the neper and bel, see <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#05iec600273">Ref. [5: IEC 60027-3]</a>, and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-chapter-8#87">Sec. 8.7</a> of this <em>Guide.</em></li> <li><a name="f04"></a>This chapter is adapted in part from Refs. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04iso310">[4: ISO 31-0]</a>, and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04iso3111">[4: ISO 31-11]</a>.</li> <li><a name="f05"></a>In addition to Refs. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04">[4]</a> and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#05">[5]</a>, quantity symbols can also be found in ANSI/IEEE Std 280-1985, <em>IEEE Standard Letter Symbols for Quantities Used in Electrical Science and Electrical Engineering</em>. Similarly, in addition to <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04iso3111">Ref. [4: ISO 31-11]</a>, mathematical signs and symbols are also given in ANSI/IEEE Std 260.3-1993, <em>Mathematical Signs and Symbols for Use in Physical Sciences and Technology</em>. Another publication is the book, <em>Symbols, Units, Nomenclature and Fundamental Constants in Physics</em>, 1987 Revision, by E.R. Cohen and P. Giacomo, International Union of Pure and Applied Physics, SUNAMCO Commission [reprinted from Physica, Vol. 146A, Nos. 1-2, p. 1 (November, 1987)]. See also <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#06note3">Ref. [6], Note 3</a>.</li> <li><a name="f06"></a>This appendix is essentially the same as Appendix B of the 1995 Edition. That appendix was significantly revised version of Appendix C of the 1991 Edition, which was reprinted from ANSI/IEEE Std 268-1982, <em>American National Standard Metric Practice</em>, ©1982 by the Institute of Electrical and Electronics Engineers, Inc., with the permission of the IEEE. The origin of this material is E.A. Mechtly, <em>The International System of Units — Physical Constants and Conversion Factors</em>, NASA SP-7012, Second Revision, National Aeronautics and Space Administration (U.S. Government Printing Office, Washington, DC, 1973).</li> <li><a name="f07"></a>For remarks on U.S. survey foot, see <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b#B6">Sec. B.6</a>.</li> <li><a name="f08"></a>One technical atmosphere equals one kilogram-force per square centimeter (1 at = 1 kgf/cm<sup>2</sup>).</li> <li><a name="f09"></a>The Fifth International Conference on the Properties of Steam (London, July 1956) defined the International Table calorie as 4.1868 J. Therefore, the exact conversion factor for the International Table Btu is 1.055 055 852 62 kJ. Note that the notation for International Table used in this listing is subscript "IT." Similarily, the notation for thermochemical is subscript "th." Further, the thermochemical Btu, Btu<sub>th</sub>, is based on the thermochemical calorie, cal<sub>th</sub>, where cal<sub>th</sub> = 4.184 J exactly.</li> <li><a name="f10"></a>The small calorie or gram calorie approximates the energy needed to increase the temperature of 1 gram of water by 1 C. Subscripts <sub>"IT"</sub> and <sub>"th"</sub> refer to International Table and thermochemical calories, respectively; see <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-footnotes#09">footnote 9</a>.</li> <li><a name="f11"></a>The kilogram calorie or "large calorie" is an obsolete term used for the kilocalorie, which is the calorie used to express the energy content of foods. However, in practice, the prefix "kilo" is usually omitted.</li> <li><a name="f12"></a>Conversion factors for mercury manometer pressure units are calculated using the standard value for the acceleration of gravity and the density of mercury at the stated temperature. Additional digits are not justified because the definitions of the units do not take into account the compressibility of mercury or the change in density caused by the revised practical temperature scale, ITS-90. Similar comments also apply to water manometer pressure units. Conversion factors for conventional mercury and water manometer pressure units are based on <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-d#04iso800003">Ref. [4: ISO 80000-3]</a>.</li> <li><a name="f13"></a>The exact conversion factor is 1.638 706 4 E-05.</li> <li><a name="f14"></a>The darcy is a unit for expressing the permeability of porous solids, not area.</li> <li><a name="f15"></a>The centigrade temperature scale is obsolete; the degree centigrade is only approximately equal to the degree Celsius.</li> <li><a name="f16"></a>This is a unit for the quantity second moment of area, which is sometimes called the "moment of section" or "area moment of inertia" of a plane section about a specified axis.</li> <li><a name="f17"></a>The exact conversion factor is 10<sup>4</sup>/π.</li> <li><a name="f18"></a>This conversion factor is based on 1 d = 86 400 s; and 1 Julian century = 36 525 d. (See <em>The Astronomical Almanac for the Year 1995</em>, page K6, U.S. Government Printing Office, Washington, DC, 1994).</li> <li><a name="f19"></a>In 1964 the General Conference on Weights and Measures reestablished the name "liter" as a special name for the cubic decimeter. Between 1901 and 1964 the liter was slightly larger (1.000 028 dm<sup>3</sup>); when one uses high-accuracy volume data of that time, this fact must be kept in mind.</li> <li><a name="f20"></a>The value of this unit, 1 nautical mile = 1852 m, was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name "International nautical mile."</li> <li><a name="f21"></a>See <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b#B5">Sec. B.5</a>.</li> <li><a name="f22"></a>The exact conversion factor is 4.535 923 7 E-01. All units in Secs. <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b8">B.8</a> and <a href="https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b9">B.9</a> that contain the pound refer to the avoirdupois pound.</li> <li><a name="f23"></a>If the local value of the acceleration of free fall is taken as <em>g</em><sub>n</sub> = 9.806 65 m/s<sup>2</sup> (the standard value), the exact conversion factor is 4.448 221 615 260 5 E+00.</li> <li><a name="f24"></a>The therm (EC) is legally defined in the Council Directive of 20 December 1979, Council of the European Communities (now the European Union, EU). The therm (U.S.) is legally defined in the Federal Register of July 27, 1968. Although the therm (EC), which is based on the International Table Btu, is frequently used by engineers in the United States, the therm (U.S.) is the legal unit used by the U.S. natural gas industry.</li> <li><a name="f25"></a>Defined (not measured) value.</li> <li><a name="f26"></a>The American National Standards Institute, Inc. (11 West 42nd Street, New York, NY 10036) is a private sector organization that serves as a standards coordinating body, accredits standards developers that follow procedures sanctioned by ANSI, designates as American National Standards those standards submitted for and receiving approval, serves as the United States Member Body of the International Organization for Standardization (ISO), and functions as the administrator of the United States National Committee for the International Electrotechnical Commission (IEC).</li> </ol> </div> </div> <div class="nist-block" >  <div data-elastic-exclude="" class="nist-tags"> <a href="/topic-terms/metrology" hreflang="en">Metrology</a></div>  </div> </div> </div> </div> <div class="grid-container"> <div class="nist-page__region nist-page__region--content-bottom" > <div class="nist-block" > <div class="text-italic font-sans-2xs"> Created January 29, 2016, Updated February 17, 2022 </div> </div> </div> </div> </section> <nav role="navigation" aria-labelledby="book-label-445651" class="nist-booknav"> <ul> <li class="nist-booknav__item nist-booknav__item--prev"> <a href="/pml/special-publication-811/nist-guide-si-appendix-d-bibliography" rel="prev" title="Go to previous page" class="nist-booknav__link"><b>‹</b> NIST Guide to the SI, Appendix D: Bibliography</a> </li> <li class="nist-booknav__item nist-booknav__item--next"> <a href="/pml/special-publication-811/nist-guide-si-version-history" rel="next" title="Go to next page" class="nist-booknav__link">NIST Guide to the SI, Version History <b>›</b></a> </li> </ul> </nav> </div> <div data-elastic-exclude>  <footer class="nist-footer padding-bottom-4"> <div class="grid-container nist-footer__info"> <div class="grid-row"> <div class="tablet:grid-col-6"> <div class="nist-footer__logo"> <a href="/" title="National Institute of Standards and Technology" rel="home"> <img class="nist-footer__logo-img" src="/libraries/nist-component-library/dist/img/logo/NIST-Logo-Brand-White.svg" alt="National Institute of Standards and Technology logo" width="300px" height="42px" /> </a> </div> <div class="nist-footer__contact"> <h3 class="nist-footer__contact-heading">HEADQUARTERS</h3> <address> 100 Bureau Drive<br> Gaithersburg, MD 20899<br> <a href="tel:301-975-2000">301-975-2000</a> </address> <p> <a href="mailto:do-webmaster@nist.gov">Webmaster</a> | <a href="https://www.nist.gov/about-nist/contact-us">Contact Us</a> | <a href="https://www.nist.gov/visit">Our Other Offices</a> </p> </div> </div> <div class="tablet:grid-col-6"> <div class="nist-footer__social-links"> <a class="nist-social nist-social--x-white" href=" https://x.com/NIST"> <span>X.com</span> </a> <a class="nist-social nist-social--facebook-white" href=" https://www.facebook.com/NIST"> <span>Facebook</span> </a> <a class="nist-social nist-social--linkedin-white" href=" https://www.linkedin.com/company/nist"> <span>LinkedIn</span> </a> <a class="nist-social nist-social--instagram-white" href=" https://www.instagram.com/nist/"> <span>Instagram</span> </a> <a class="nist-social nist-social--youtube-white" href=" https://www.youtube.com/NIST"> <span>YouTube</span> </a> <a class="nist-social nist-social--giphy-white" href=" https://giphy.com/nist"> <span>Giphy</span> </a> <a class="nist-social nist-social--rss-white" href=" https://www.nist.gov/news-events/nist-rss-feeds"> <span>RSS Feed</span> </a> <a class="nist-social nist-social--envelope-white" href=" https://public.govdelivery.com/accounts/USNIST/subscriber/new"> <span>Mailing List</span> </a> </div> <div class="nist-footer__feedback"> How are we doing? 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