ISO 31

ISO 31 (Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrelationships and their presentation. It was revised and replaced by ISO/IEC 80000.

Parts

The standard comes in 14 parts:

Coined words

ISO 31-0 introduced several new words into the English language that are direct spelling-calques from the French. Some of these words have been used in scientific literature.

New phrase Existing phrase Technical meaning
massic <quantity> specific <quantity> a quantity divided by its associated mass
volumic <quantity> [volumic] <quantity> density a quantity divided by its associated volume
areic <quantity> surface <quantity> density a quantity divided by its associated area
lineic <quantity> linear <quantity> density a quantity divided by its associated length

Content

ISO 31-0

This section is an excerpt from ISO 31-0.[edit]

ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It was intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.

ISO 31-1

Its definitions include:

Quantity Unit Remarks
NameSymbolNameSymbolDefinition
angle,
(plane angle)		 α, β, γ, θ, φ radianrad1 rad = 1 m⁄m = 1
degree°1° = π⁄180 rad There is no space between the number and these superscript-style unit symbols. Decimal subdivision of degrees is preferable (i.e., 12.5° instead of 12°30′)
minute′1′ = (1⁄60)°
second″1″ = (1⁄60)′
solid angleΩsteradiansr1 sr = 1 m2⁄m2 = 1
lengthl, L metre m The metre is the length of the path travelled by light in vacuum during a time interval of 1⁄299 792 458 of a second; see speed of light
breadthb
heighth
thicknessd, δ
radiusr, R
diameterd, D
length of path, (linear) displacement vectors, s
distanced, r
cartesian coordinatesx, y, z
radius of curvatureϱ
curvatureϰreciprocal metrem−1
areaAsquare metrem2The units are (1 a = 100 m2) and hectare (1 ha = 100 a) are used for agrarian areas.
volume V cubic metrem3
litreL, l1 L = 1 dm3The capital L is preferred as the small l can be indistinguishable from the number 1 in some fonts.
time, time interval, duration t secondsThe second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom Representations of time of day are defined in ISO 8601.
minutemin1 min = 60 s
hourh1 h = 60 min = 3 600 s
dayd1 d = 24 h = 1 440 min = 86 400 s
angular velocityωradian per secondrad⁄sω=dφ⁄dt
angular accelerationαradian per second squaredrad⁄s2α=dω⁄dt
velocity v (general symbol),
v (velocity vector),
c (propagation speed of waves),
u, v, w (components of a velocity c)		 metre per second m⁄s
kilometre per hour km⁄h
acceleration, acceleration vectora, a metre per second squared m⁄s2 1 g = 9.80665 m⁄s2
acceleration of free fall, acceleration due to gravityg

It includes two annexes:

ISO 31-2

ISO 31-3

Its definitions include (note boldfaced symbols mean quantity is a vector):

Quantity Unit Remarks
NameSymbolNameSymbolDefinition
Force F newton N 1 N = 1 kg·m/s2 Unit named after Isaac Newton
Moment of force, Torque M, 𝝉 N·m 1 N·m = 1 kg·m2/s2 The unit is dimensionally equivalent to the units of energy, the joule; but the joule should not be used as an alternative for the newton metre.
Linear momentum p kg·m/s or N·s
(Linear) impulse J N·s or kg·m/s
Angular momentum L kg·m2/s or N·m·s
Mechanical energy, Work E, W joule J 1 J = 1 kg·m2/s2 = 1 Pa·m3 = 1 W·s Unit named after James Joule. The joule is dimensionally equivalent to the units of torque and moment of force but should be used in preference to the newton metre (N·m).
Power P watt W 1 W = 1 J/s = 1 N·m/s = 1 kg·m2/s3 Unit named after James Watt.
Pressure p pascal Pa 1 Pa = 1 N / m2 = 1 kg/(m·s2) Named after Blaise Pascal.
Normal stress, Shear stress σ,τ pascal Pa 1 Pa = 1 N / m2 = 1 kg/(m·s2) Named after Blaise Pascal.

ISO 31-4

Its definitions include:

Quantity Unit Remarks
NameSymbolNameSymbolDefinition
thermodynamic temperatureT, (Θ)kelvinKThe kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.For practical measurements, the International Temperature Scale of 1990 defines several fixed points and interpolation procedures.
Celsius temperaturet, φdegree Celsius°CThe degree Celsius is a special name for the unit kelvin, for use in stating values of Celsius temperature.t = T − T0, where T0 = 273.15 K
linear expansion coefficientαlreciprocal kelvin, kelvin to the power negative 1K−1αl=1llT

Annex A of ISO 31-4 lists units of heat based on the foot, pound and second and some other units, including the degree Rankine, degree Fahrenheit, British thermal unit and others. Annex B lists conversion factors for three versions of the calorie.

ISO 31-5

Some of its definitions are below, with values taken from NIST values of the constants:

NameSymbolDefinitionValue
Speed of light in vacuum c0 299 792 458 m s−1 299 792 458 m s−1
Magnetic constant μ0 4π × 10−7 N A−2 12.566 370 614... × 10−7 N A−2
Electric constant ε0 1μ0c02 8.854 187 817... × 10−12 F m−1
Characteristic impedance of vacuum Z0 μ0 c0 376.730 313 461...Ω

ISO 31-6

The definitions of ISO 31-6, as defined in 1980, included:

Quantity Unit Remarks
NameSymbolNameSymbolDefinition
frequencyf, vhertzHz1 Hz = 1 s−1
circular frequencyωreciprocal second, second to the power of minus ones−1
radian per secondrad/s
wavelengthλmetrem
ångströmÅ1 Å = 10−10 m10 Å = 1 nm
wavenumber, repetencyσreciprocal metre, metre to the power of minus onem−1 The multiple cm−1 is often used.
circular wavenumber, circular repetencyk
velocity (speed) of propagation of electromagnetic waves in vacuoc, c0metre per secondm/s c = (2.99792458 ± 0.000000012) × 108 m/s.
Sometimes c is used for the phase velocity in a medium, in which case c0 is used for the velocity in vacuo.
radiant energyQ, W,
(U, Qe)		jouleJ1 J = 1 kg·m2/s2
radiant energy densityw, (u)joule per cubic metreJ/m3
spectral concentration of radiant energy density (in terms of wavelength), spectral radiant energy density (in terms of wavelength)wλjoule per metre to the fourth powerJ/m4
radiant power, radiant energy fluxP, Φ, (Φe)wattW1 W = 1 J/s
radiant energy fluence rateφ, ψwatt per square metreW/m2
radiant intensityI, (Ie)watt per steradianW/sr

ISO 31-7

Its definitions include:

Quantity Unit Remarks
NameSymbolDefinitionNameSymbol
period,
periodic time		Ttime of one cycleseconds
frequencyf, νf = 1/ThertzHz1 Hz = 1 s−1
loudness levelLNLN = ln(peff/p0)1 kHz where peff is the root-mean-square value of the sound pressure of a pure tone of 1 kHz, which is judged by a normal observer under standardized listening conditions as being as loud as the sound under investigation, and where p0 = 20 μPaphonThe loudness level is 1 phon if 20 log10(peff/p0)1 kHz=1, that is for a pure tone of frequency 1 kHz, 1 phon = 1 dB sound pressure level. This is not a purely physical quantity and unit, as it involves the subjective evaluation by humans.
loudnessNA normal observer's auditory estimate of the ratio between the strength of the sound considered and that of a reference sound having a loudness level of 40 phonssoneA standard relation between loudness in sones and loudness level in phons has been adopted for practical use in ISO 131.

ISO 31-8

Its definitions include:

Quantity Unit Remarks
NameSymbolDefinitionNameSymbol
relative atomic massArRatio of the average mass per atom of an element to 1/12 of the mass of an atom of the nuclide 12C one 1 Formerly called atomic/molecular weight.
Example: Ar(Cl) = 35.453.
Both quantities depend on the nuclidic composition.
relative molecular massMrRatio of the average mass per molecule or specified entity of a substance to 1/12 of the mass of an atom of the nuclide 12C
number of molecules or other elementary entitiesNNumber of molecules or other elementary entities in a systemone1
amount of substancen, (ν)molemolThe mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of 12C. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specific groups of such particles. The definition applies to unbound atoms of 12C, at rest and in their ground state.

Note: In the tables of quantities and their units, the ISO 31-8 standard shows symbols for substances as subscripts (e.g., cB, wB, pB). It also notes that it is generally advisable to put symbols for substances and their states in parentheses on the same line, as in c(H2SO4).

It includes three normative annexes.

Annex A
Names and symbols of the chemical elements

This annex contains a list of elements by atomic number, giving the names and standard symbols of the chemical elements from atomic number 1 (hydrogen, H) to 109 (unnilennium, Une).

The list given in ISO 31-8:1992 was quoted from the 1998 IUPAC "Green Book" Quantities, Units and Symbols in Physical Chemistry and adds in some cases in parentheses the Latin name for information, where the standard symbol has no relation to the English name of the element. Since the 1992 edition of the standard was published, some elements with atomic number above 103 have been discovered and renamed.

Annex B
Symbols for chemical elements and nucleides

Symbols for chemical elements shall be written in roman (upright) type. The symbol is not followed by a full-stop.

Examples:

H He C Ca

Attached subscripts or superscripts specifying a nucleotide or molecule have the following meanings and positions:

Annex C (pH)

pH is defined operationally as follows. For a solution X, first measure the electromotive force EX of the galvanic cell

reference electrode | concentrated solution of KCl | solution X | H2 | Pt

and then also measure the electromotive force ES of a galvanic cell that differs from the above one only by the replacement of the solution X of unknown pH, pH(X), by a solution S of a known standard pH, pH(S). Then obtain the pH of X as

pH(X) = pH(S) + (ES − EX) F / (RT ln 10)

where

F is the Faraday constant;
R is the molar gas constant;
T is the thermodynamic temperature.

Defined this way, pH is a quantity of dimension 1, that is it has no unit. Values pH(S) for a range of standard solutions S are listed in Definitions of pH scales, standard reference values, measurement of pH, and related terminology. Pure Appl. Chem. (1985), 57, pp 531–542, where further details can be found.

pH has no fundamental meaning; its official definition is a practical one. However, in the restricted range of dilute aqueous solutions having amount-of-substance concentrations less than 0.1 mol/L, and being neither strongly alkaline nor strongly acidic (2 < pH < 12), the definition is such that

pH = −log10[c(H+) y1 / (1 mol/L)] ± 0.02

where c(H+) denotes the amount-of-substance concentration of hydrogen ion H+ and y1 denotes the activity coefficient of a typical uni-univalent electrolyte in the solution.

ISO 31-9

ISO 31-10

Its definitions include:

Quantity Unit Remarks
NameSymbolDefinitionNameSymbolDefinition
activity A Expectation value of the number of spontaneous nuclear transitions from a particular energy state occurring in an amount of radionuclide in a small time interval, divided by that time interval becquerelBq1 Bq = 1/sThe becquerel is a special name for second to the power minus one, to be used as the SI unit of activity.
curie:
1 Ci = 3.7×1010 Bq (exactly)
absorbed dose D For any ionizing radiation, the mean energy imparted to an element of irradiated matter divided by the mass of this element grayGy1 Gy = 1 J/kgThe gray is a special name for joule per kilogram, to be used as the SI unit for absorbed dose.
rad:
1 rad = 0.01 Gy
dose equivalent H Product of D, Q and N, at the point of interest in tissue, where D is the absorbed dose, Q is the quality factor and N is the product of any other modifying factors
H = D · Q · N
For Q and N, see CIPM, 1984, Recommendation 1 and ICRU Report 33 (1980) 		sievertSv1 Sv = 1 J/kgThe sievert is a special name for joule per kilogram, to be used as the SI unit for dose equivalent.
rem:
1 rem = 0.01 Sv

ISO 31-11

It included definitions for symbols for mathematical logic, set theory, arithmetic and complex numbers, functions and special functions and values, matrices, vectors, and tensors, coordinate systems, and miscellaneous mathematical relations.

ISO 31-12

ISO 31-13

Replacement

A second international standard on quantities and units is IEC 60027. The ISO 31 and IEC 60027 standards were revised by the two organizations in collaboration to integrate both standards into a joint standard ISO/IEC 80000 ISO/IEC 80000 - Quantities and Units, in which the quantities and equations used with SI are to be referred as the International System of Quantities (ISQ). ISO/IEC 80000 supersedes both ISO 31 (and part of IEC 60027), as follows:

See also

Notes

  1. ↑ This is the text of the note in the standard ISO 31-6 as published in 1980. At the time, the metre was not defined in terms of the speed of light. Today, the speed of light is defined as exactly 299,792,458 m/s.
  1. ↑ "ISO 31-0:1992 Quantities and units — Part 0: General principles". International Organization for Standardization. Retrieved 8 May 2021.
  2. ↑ NIST SP811(§8.9)
  3. ↑ Mills, I. (1993). Quantities, units and symbols in physical chemistry/prepared for publication by Ian Mills...[et al.]. Oxford; Boston: Blackwell Science; Boca Raton, Fla.: CRC Press [distributor].
  4. ↑ Taylor, B. (1995). Guide for the use of the International System of Units (SI): the metric system. DIANE Publishing.
  5. ↑ Dietrich, P. M.; Streeck, C.; Glamsch, S.; Ehlert, C.; Lippitz, A.; Nutsch, A.; Beckhoff, B.; W. E. S., Unger (2015). "Quantification of silane molecules on oxidized silicon: are there options for a traceable and absolute determination?". Analytical Chemistry. 87 (19): 10117–10124. Bibcode:2015AnaCh..8710117D. doi:10.1021/acs.analchem.5b02846. PMID 26334589.
  6. ↑ Sertlek, H. Ö.; Slabbekoorn, H.; Ten Cate, C.; Ainslie, M. A. (2019). "Source specific sound mapping: Spatial, temporal and spectral distribution of sound in the Dutch North Sea". Environmental Pollution. 247: 1143–1157. Bibcode:2019EPoll.247.1143S. doi:10.1016/j.envpol.2019.01.119. PMID 30823343.
  7. ↑ "Fundamental Physical Constants from NIST". physics.nist.gov. Retrieved 14 June 2025.
  8. ↑ International Standard ISO 31/6: Quantities and units of light and related electromagnetic radiations (PDF) (Second ed.). International Organization for Standardization. 1980-12-15. Retrieved 2024-02-11 – via iTeh.
  9. ↑ Thompson, Ambler; Taylor, Barry M (March 2008). Guide for the Use of the International System of Units (SI) — NIST Special Publication 811, 2008 Edition — Second Printing (PDF). Gaithersburg, MD, USA: NIST.
  10. ↑ Tolga, G. O. K. (2016). The importance of symbols and units in natural science. The Eurasia Proceedings of Educational and Social Sciences, 4, 165-167.
  11. ↑ (, )

References