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Guide for the Use of the International System of Units (SI)

5 Units Outside the SI

Units that are outside the SI may be divided into three categories:

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 it may be necessary on occasion to use time-related units other than those given in Table 6; in particular, circumstances may require that 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. Units accepted for use with the SI

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 = 86 400 s
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
liter l, L (b) 1 L = 1 dm3 = 10-3 m3
metric ton (c) t 1 t = 103 kg
(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. [2] or [3]). 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. [1] and [8]). The script letter l, 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. [1] and [8]); it is also used in some other English-speaking countries. However, this unit is called "tonne" in Ref. [2] and is the name used in many countries.

5.1.2 Neper, bel, shannon, and the like

There are a few highly specialized units not listed in Table 6 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 neper (Np), bel (B), octave, phon, and sone, and units used in information technology, including the baud  (Bd), bit (bit), erlang (E), hartley (Hart), and shannon (Sh). (Footnote 4) 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. [6]) or of IEC (Ref. [7]).

5.1.3 Electronvolt and unified atomic mass unit

The CIPM, and thus this Guide, also finds it necessary to accept for use with the SI the two units given in Table 7 [2,3]. 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.)

Note:   In some fields the unified atomic mass unit is called the dalton, symbol Da; however, this name and symbol are not accepted by the CGPM, CIPM, ISO, or IEC for use with the SI. Similarly, 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.

Table 7. Units accepted for use with the SI whose values in SI units are obtained experimentally
Name Symbol Definition
electronvolt eV (a)
unified atomic mass unit u (b)
(a) The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum; 1 eV = 1.602 177 33 � 10-19 J with a combined standard uncertainty of 0.000 000 49 � 10-19 J [20, 21].

(b) The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide 12C; 1 u = 1.660 540 2 � 10-27 kg with a combined standard uncertainty of 0.000 001 0 � 10-27 kg [20, 21].

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 or so-called natural units. The use of these units with the SI is, in the view of this Guide, permissible when it is necessary for the most effective communication of information. In such cases, the specific natural units that are used must be identified. This requirement applies even to the system of units customarily called "atomic units" used in theoretical atomic physics and chemistry, inasmuch as there are several different systems that have the appellation "atomic units. "Examples of physical quantities used as natural units are given in Table 8.

This Guide also takes the position that while theoretical results intended primarily for other theorists may be left in natural units, if they are also intended for experimentalists, they must also be given in acceptable units. NIST measurement results must always be given in such units first.

Table 8. Examples of physical quantities sometimes used as natural units
Kind of quantity Physical quantity used as a unit Symbol
action Planck constant divided by 2π h bar
electric charge elementary charge e
energy Hartree energy Eh
length Bohr radius a0
length Compton wavelength (electron) λC
magnetic flux magnetic flux quantum Φ0
magnetic moment   Bohr magneton �B
magnetic moment   nuclear magneton �N
mass electron rest mass me
mass proton rest mass mp
speed speed of electromagnetic waves in vacuum   c

5.2 Units temporarily accepted for use with the SI

Because of existing practice in certain fields or countries, in 1978 the CIPM considered that it was permissible for the units given in Table 9 to continue to be used with the SI until the CIPM considers that their use is no longer necessary [2,3]. However, these units must not be introduced where they are not presently used. Further, this Guide strongly discourages the continued use of these units by NIST authors except for the nautical mile, knot, are, and hectare; and except for the curie, roentgen, rad, and rem until the year 2000 (the cessation date suggested by the Committee for Interagency Radiation Research and Policy Coordination or CIRRPC, a United States Government interagency group). (Footnote 5)

Table 9. Units temporarily accepted for use with the SI
Name (a)   Symbol   Value in SI units
nautical mile - 1 nautical mile = 1852 m
knot - 1 nautical mile per hour = (1852/3600) m/s
ångström Å 1 Å = 0.1 nm = 10-10 m
are (b) a 1 a = 1 dam2 = 102 m2
hectare (b) ha 1 ha = 1 hm2 = 104 m2
barn b 1 b = 100 fm2 = 10-28 m2
bar bar 1 bar= 0.1 MPa = 100 kPa = 1000 hPa= 105 Pa
gal Gal 1 Gal = 1 cm/s2 = 10-2 m/s2
curie Ci 1 Ci = 3.7 � 1010 Bq
roentgen R 1 R = 2.58 � 10-4 C/kg
rad rad (c) 1 rad = 1 cGy = 10-2 Gy
rem rem 1 rem = 1 cSv = 10-2 Sv
(a) See Sec. 5.2 for the position of this Guide regarding the continued use of these units.

(b) This unit and its symbol are used to express agrarian areas.

(c) 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. 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 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)
Name Symbol Value in SI units
erg erg 1 erg = 10-7 J
dyne dyn 1 dyn = 10-5 N
poise (a) P 1P = 1 dyn � s/cm2 = 0.1 Pa � s
stokes (b) St 1St = 1 cm2/s = 10-4 m2/s
gauss (c) Gs, G 1 Gs corresponds to 10-4 T
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
(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 unit of the SI, which has four dimensions when only mechanical and electric quantities are considered.

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 (�m). Table 11 gives a few examples of some of these other unacceptable units.

Table 11. Examples of other unacceptable units
Name Symbol Value in SI units
fermi fermi 1 fermi = 1 fm = 10-15 m
metric 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 � 1 � = 1 �m = 10-6 m
calorie (various) calth (thermochemical)   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 �g = 10-9 kg
lambda (volume) λ 1 λ = 1 �L = 10-6 L = 10-9 m3

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

Consistent with accepted practice [2,3], this Guide uses the term "units of the SI" to mean the SI units, that is, the SI base units, SI derived units, and SI supplementary 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 units of the SI plus (a) those units accepted for use with the SI (see Table 6 and Table 7 and Sec. 5.1.1, Sec. 5.1.2, and Sec. 5.1.3); (b) those units temporarily accepted for use with the SI (see Table 9 and Sec. 5.2); and (c) appropriate multiples and submultiples of such accepted and temporarily accepted units. Because natural and atomic units are not widely recognized for use with the SI, they are not included in the term. However, such units may be used to the extent discussed in Sec. 5.1.4.
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