<i><i>Guide</i></i> for the Use of the International System of Units (SI)

5 Units Outside the SI

Units that are outside the SI, that is, non-SI units, may be divided into three categories:

      —those units that are accepted for use with the SI by the CIPM and hence this Guide;
      —those units that are not accepted for use with the SI by the CIPM, but are temporarily accepted for use with the SI by this Guide; and
      —those units that are not accepted for use with the SI by either the CIPM or this Guide and in the view of this Guide must strictly be avoided.

5.1 Units accepted for use with the SI

      The following four sections discuss in detail the units this Guide accepts for use with the 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 by this Guide, for use with the SI [2, 3]. These units are given in Table 6. The combination of units of this table with SI units to form derived units should be restricted to special cases in order not to lose the advantages of the coherence of SI units. (The use of SI prefixes with the units of Table 6 is discussed in Sec. 6.2.8)

      Additionally, this Guide recognizes that situations on occasion will require the use of time-related units other than those given in Table 6; such as using intervals of time be expressed in weeks, months, or years. In such cases, if a standardized symbol for the unit is not available, the name of the unit should be written out in full. (See Sec. 8.1 for a suggestion regarding the symbol for year and Chapter 9 for the rules and style conventions for spelling unit names.)

Table 6. Non-SI units accepted for use with the SI by the CIPM and this Guide


Name Symbol Value in SI units


minute—time min 1 min = 60 s
hour—time h 1 h = 60 min = 3600 s
day—time d 1 d = 24 h = 86 400s
degree—plane angle(a) ° 1° = (π/180) rad
minute—plane angle(a) 1′ = (1/60)° = (π/10 800) rad
second—plane angle(a) 1″ = (1/60)′ = (π/648 000) rad
hectare(h) ha 1 ha = 1 hm2 = 104m2
liter L(b),1 1 L = 1 dm3 = 10-3m3
metric ton(c) T 1 t = 103kg
neper Np(d,f) [see fotenote (g) regarding the numerical
bel B(e,f) value of logarythmic ratio quantities such
decibel dB(e,f) as the neper, the bel and the decibel]

(a) See also Sec. 7.2.
(b) The alternative symbol for the liter, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter l and the number 1 (see Ref. [1] or [2]). Thus, although both l and L are internationally accepted symbols for the liter, to avoid this risk the symbol to be used in the United States is L (see Refs. [2] and [6]). The script letter is not an approved symbol for the liter.
(c) This is the name to be used for this unit in the United States (see Refs. [2] and [6]); it is also used in some other English-speaking countries. However, this unit is called “tonne” in Ref. [1] and is the name used in many countries.
(d) The statement LA = n Np (where n is a number) is interpreted to mean that ln(A2 / A1) = n. Thus when LA = 1 Np, A2 / A1 = e. The symbol A is used here to denote the amplitude of a sinusoidal signal, and LA is then called the Napierian logarithmic amplitude ratio, or the Napierian amplitude level difference.
(e) The statement LX = m dB = (m / 10) B (where m is a number) is interpreted to mean that lg(X / X0) = m/10. Thus when LX = 1 B, X / X0 = 10, and when LX = 1 dB, X / X0 = 101/10. If X denotes a mean square signal or power-like quantity, LX is called a power level referred to X0. (See Sec. 8.7.)
(f) In using these units it is important that the nature of the quantity be specified, and that any reference value used be specified. These units are not SI units, but they have been accepted by the CIPM for use with the SI. For additional information on the neper and bel, see Ref. [5: IEC 60027-3], and Sec. 8.7 of this Guide.
(g) The numerical values of the neper, bel, and decibel (and hence the relation of the bel and the decibel to the neper) are rarely required. They depend on the way in which the logarithmic quantities are defined.
(h) This unit and its symbol are used to express agrarian area.

5.1.2 Electronvolt, astronomical unit, and unified atomic mass unit

The CIPM, and thus this Guide, accepts for use with the SI the units given in Table 7 [1, 2]. These units are used in specialized fields; their values in SI units must be obtained from experiment and, therefore, are not known exactly. (The use of SI prefixes with the units of Table 7 is discussed in Sec. 6.2.8)

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 Value in SI units

electronvolt eV (a)
astronomical unit ua (b)
unified atomic mass unit u (c)
dalton Da (d)

(a) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum, 1.602 176 487(40) × 10-19 J. This value of 1 eV is the 2006 CODATA recommended value with the standard uncertainty in the last two digits given in parenthesis [19, 20].

(b)The astronomical unit is approximately equal to the mean Earth-Sun distance. It is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.017 202 098 95 radians per day (known as the Gaussian constant). The value and standard uncertainty of the astronomical unit, ua, is 1.495 978 706 91(6) × 1011 m. This is cited from the IERS Conventions 2003 (D.D. McCarthy and G. Petit eds., IERS Technical Note 32, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2004, 12). The value of the astronomical unit in meters comes from the JPL ephemerides DE403 (Standish E.M., Report of the IAU WGAS Sub-Group on Numerical Standards, Highlights of Astronomy, Appenzeller ed., Dordrecht: Kluwer Academic Publishers, 1995, 180-184).

(c)The unified atomic mass unit is equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state, 1.660 538 782(83) × 10-27 kg. This value of 1 u is the 2006 CODATA recommended value with the standard uncertainty in the last two digits given in parenthesis [18, 19].

(d)The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state. The dalton is often combined with SI prefixes, for example to express the masses of large molecules in kilodaltons, kDa, or megadaltons, MDa.

Note: The abbreviation, AMU is not an acceptable unit symbol for the unified atomic mass unit. The only allowed name is “unified atomic mass unit” and the only allowed symbol is u.

5.1.3 Units from International Standards

    There are a few highly specialized units that are given by the International Organization for Standardization (ISO) or the International Electrotechnical Commission (IEC) and which in the view of this Guide are also acceptable for use with the SI. They include the octave, phon, and sone, and units used in information technology, including the baud (Bd), bit (bit), erlang (E), hartley (Hart), and shannon (Sh)3. It is the position of this Guide that the only such additional units NIST authors may use with the SI are those given in either the International Standards on quantities and units of ISO (Ref. [4]) or of IEC (Ref. [5]).

5.1.4 Natural and atomic units

    In some cases, particularly in basic science, the values of quantities are expressed in terms of fundamental constants of nature. The two most important of these unit systems are the natural unit (n.u.) system used in high energy or particle physics, and the atomic unit (a.u.) system used in atomic physics and quantum chemistry. The use of these units with the SI is not formally accepted by the CIPM, but the CIPM recognizes their existence and importance. Therefore, this Guide formally accepts their use when it is necessary for effective communication. In such cases, the specific unit system used must be identified. Examples of physical quantities used as units are given in Table 8.

Table 8. Examples of physical quantities sometimes used as units


Kind of quantity Physical quantity used as a unit Symbol

speed speed of light in vacuum (n.u.) c
action Planck constant divided by 2π (n.u.) h
mass electron rest mass (n.u. and a.u.) me
electric charge elementary charge (a.u.) e
length Bohr radius (a.u.) a0
energy Hartree energy (a.u.) Eh
time ratio of action to energy (a.u.) h/ Eh

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 permissible for the following units given in Table 9, nautical mile, knot, angstrom, are, barn, bar, and millimeter of mercury to continue to be used with the SI. However, these units must not be introduced in fields where they are not presently used. Further, this Guide strongly discourages the continued use of these units by NIST authors except when absolutely necessary. If these units are used by NIST authors the values of relevant quantities shall be given in terms of SI units first followed by these non-SI units in parentheses.

The curie, roentgen, rad, and rem have been added to the NIST 330 [2] and Table 9 of this Guide, since they are in wide use in the United States, especially in regulatory documents dealing with health and safety. Nevertheless, this Guide strongly discourages the continued use of the curie, roentgen, rad, and rem and recommends that SI units should be used by NIST authors only if necessary. If these units are used by NIST authors the values of relevant quantities shall be given in terms of SI units first followed by these outdated non-SI units in parentheses.

Table 9. Other non-SI units accepted for use with the SI either by the CIPM and this Guide (indicated by*), or by this Guide (indicated by**)

 
Name Symbol Value in SI units

nautical mile* 1 nautical mile = 1852 m
knot* 1 nautical mile per hour = (1852/3600)m/s
ångström* Å Å = 0.1 nm = 10-10 m
barn* b 1 b = 100 fm2 = 10-28 m2
bar* bar 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa
millimeter of mercury* mmHg 1 mmHg ˜ 133.322 Pa
curie** Ci 1 Ci = 3.7 x 1010 Bq
roentgen ** R 1 R = 2.58 x 10-4 C/kg
rad** rad(a) 1 rad=1 cGy=10-2 Gy
rem ** rem 1 rem = 1 cSv = 10-2 Sv

     (a) When there is risk of confusion with the symbol for the radian, rd may be used as the symbol for rad.

5.3 Units not accepted for use with the SI

     The following two sections briefly discuss units not accepted for use with the SI.

5.3.1 CGS units

     Table 10 gives examples of centimeter-gram-second (CGS) units having special names. These units are not accepted for use with the SI by this Guide. Further, no other units of the various CGS systems of units, which includes the CGS Electrostatic (ESU), CGS Electromagnetic (EMU), and CGS Gaussian systems, are accepted for use with the SI by this Guide except such units as the centimeter, gram, and second that are also defined in the SI.

Table 10. Examples of CGS units with special names (not accepted for use with the SI by this Guide)

 
Name Symbol Value in SI units

erg erg 1 erg = 10-7 J
dyne dyn 1 dyn = 10-5 N
poise(a) P 1 P = 1 dyn · s/cm2 = 0.1 Pa · s
stokes(b) St 1 St = 1cm2/s = 10-4 m2/s
gauss(c) Gs,G 1 Gs corresponds to 10-4T
oersted(c) Oe 1 Oe corresponds to (1000/4π) A/m
maxwell(c) Mx 1 Mx corresponds to 10-8 Wb
stilb sb 1 sb = 1 cd/cm2 = 104 cd/m2
phot ph 1 ph = 104 lx
gal(d) Gal 1 Gal = 1 cm s -2 = 10-2 m s-2

  (a) The poise (P) is the CGS unit for viscosity (also called dynamic viscosity). The SI unit is the pascal second (Pa · s).
  (b) The stokes (St) is the CGS unit for kinematic viscosity. The SI unit is the meter squared per second (m2/s).
  (c) This unit is part of the so-called electromagnetic three-dimensional CGS system and cannot strictly speaking be compared to the corresponding SI unit, which has four dimensions when only mechanical and electric.
  (d)The gal is employed in geodesy and geophysics to express acceleration due to gravity.

5.3.2 Other unacceptable units

There are many units besides CGS units that are outside the SI and not accepted for use with it, including, of course, all of the U.S. customary (that is, inch-pound) units. In the view of this Guide such units must strictly be avoided and SI units, their multiples or submultiples, or those units accepted or temporarily accepted for use with the SI (including their appropriate multiples and submultiples), must be used instead. This restriction also applies to the use of unaccepted special names for SI units or special names for multiples or submultiples of SI units, such as mho for siemens (S) and micron for micrometer(µm). Table 11 gives a few examples of some of these other unacceptable units.

Table 11. Example of other unacceptable units

 
Name Symbol Value in SI units

fermi fermi 1 fermi = 1 fm = 10-15m
photometric carat metric carat 1 metric carat = 200 mg = 2 × 10-4 kg
torr Torr 1 Torr = (101 325/760) Pa
standard atmosphere atm 1 atm = 101 325 Pa
kilogram-force kgf 1 kgf = 9.806 65 N
micron µ 1 m = 1 µm = 10-6 m
calorie (various) calth(thermalchemical) 1 calth = 4.184 J
x unit xu 1 xu ˜ 0.1002 pm = 1.002 × 10-13 m
stere st 1 st = 1 m3
gamma γ 1 γ = 1 nT = 10-9 T
gamma(mass) γ 1 γ = 1 µmg = 10-9 kg
lambda(volume) λ 1 λ = 1 µL = 10-6 L = 10-9 m3

5.4 The terms "SI units" and "acceptable units"

     Consistent with accepted practice [1, 2], this Guide uses either the term “SI units” or “units of the SI” to mean the SI base units and SI coherent derived units, and multiples and submultiples of these units formed by using the SI prefixes. The term “acceptable units,” which is introduced in this Guide for convenience, is used to mean the SI units plus (a) those non-SI units accepted for use with the SI (see Tables 6 - 9); and (b) appropriate multiples and submultiples of such accepted non-SI units.


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