Thestandard atomic weight of achemical element (symbolA_r°(E) for element "E") is theweighted arithmetic mean of therelative isotopic masses of allisotopes of that elementweighted by each isotope's abundance onEarth. For example, isotope⁶³Cu (A_r = 62.929) constitutes 69% of thecopper on Earth, the rest being⁶⁵Cu (A_r = 64.927), so

${\displaystyle A_{\text{r}}\text{°}{(}_{\text{29}}\text{Cu})=0.69\times 62.929+0.31\times 64.927=\mathrm{63.55.}}$

Relative isotopic mass isdimensionless, and so is the weighted average. It can be converted into a measure of mass (withdimensionM) by multiplying it with the atomic mass constantdalton.

Among various variants of the notion ofatomic weight (A_r, also known asrelative atomic mass) used by scientists, the standard atomic weight(A_r°) is the most common and practical. The standard atomic weight of each chemical element is determined and published by theCommission on Isotopic Abundances and Atomic Weights (CIAAW) of theInternational Union of Pure and Applied Chemistry (IUPAC) based on natural, stable,terrestrial sources of the element. The definition specifies the use of samples from many representative sources from the Earth, so that the value can widely be used as the atomic weight for substances as they are encountered in reality—for example, in pharmaceuticals and scientific research. Non-standardized atomic weights of an element are specific to sources and samples, such as the atomic weight of carbon in a particular bone from a particular archaeological site. Standard atomic weight averages such values to therange of atomic weights that a chemist might expect to derive from many random samples from Earth. This range is the rationale for theinterval notation given for some standard atomic weight values.

Of the 118 known chemical elements, 84 have this Earth-environment based value, all but 4 of which have stable isotopes. Typically, such a value is, for example helium:A_r°(He) =4.002602(2). The "(2)" indicates the uncertainty in the last digit shown, to read4.002602±0.000002. IUPAC also publishesabridged values, rounded to five significant figures. For helium,A_{r, abridged}°(He) =4.0026.

For fourteen elements the samples diverge on this value, because their sample sources have had a different decay history. For example, thallium (Tl) in sedimentary rocks has a different isotopic composition than in igneous rocks and volcanic gases. For these elements, the standard atomic weight is noted as an interval:A_r°(Tl) =[204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes aconventional value. For thallium,A_{r, conventional}°(Tl) =204.38.

Thestandard atomic weight is a special value of the relative atomic mass. It is defined as the "recommended values" of relative atomic masses of sourcesin the local environment of theEarth's crust andatmosphere as determined by theIUPAC Commission on Atomic Weights and Isotopic Abundances (CIAAW).^[2] In general, values from different sources are subject to natural variation due to a different radioactive history of sources. Thus, standard atomic weights are an expectation range of atomic weights from a range of samples or sources. By limiting the sources to terrestrial origin only, the CIAAW-determined values have less variance, and are a more precise value for relative atomic masses (atomic weights) actually found and used in worldly materials.

TheCIAAW-published values are used and sometimes lawfully required in mass calculations. The values have an uncertainty (noted in brackets), or are an expectation interval (see example in illustration immediately above). This uncertainty reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement (which is much smaller with quality instruments).^[3]

Although there is an attempt to cover the range of variability on Earth with standard atomic weight figures, there are known cases of mineral samples which contain elements with atomic weights that are outliers from the standard atomic weight range.^[2]

Forsynthetic elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore, for synthetic elements thetotal nucleon count of the most stable isotope (i.e., the isotope with the longest half-life) is listed in brackets, in place of the standard atomic weight.

When the term "atomic weight" is used in chemistry, usually it is the more specific standard atomic weight that is implied. It is standard atomic weights that are used in periodic tables and many standard references in ordinary terrestrial chemistry.

Lithium represents a unique case where the natural abundances of the isotopes have in some cases been found to have been perturbed by human isotopic separation activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources, such as rivers.^{[citation needed][dubious –discuss]}

An example of why "conventional terrestrial sources" must be specified in giving standard atomic weight values is the element argon. Between locations in theSolar System, the atomic weight of argon varies as much as 10%, due to extreme variance in isotopic composition. Where the major source of argon is the decay of⁴⁰
K in rocks,⁴⁰
Ar will be the dominant isotope. Such locations include the planets Mercury and Mars, and the moon Titan. On Earth, the ratios of the three isotopes³⁶Ar : ³⁸Ar : ⁴⁰Ar are approximately 5 : 1 : 1600, giving terrestrial argon a standard atomic weight of 39.948(1).

However, such is not the case in the rest of the universe. Argon produced directly, bystellar nucleosynthesis, is dominated by thealpha-process nuclide³⁶
Ar. Correspondingly, solar argon contains 84.6%³⁶
Ar (according tosolar wind measurements),^[4] and the ratio of the three isotopes³⁶Ar : ³⁸Ar : ⁴⁰Ar in the atmospheres of the outer planets is 8400 : 1600 : 1.^[5] The atomic weight of argon in the Sun and most of the universe, therefore, would be only approximately 36.3.^[6]

Famously, the published atomic weight value comes with an uncertainty. This uncertainty (and related: precision) follows from its definition, the source being "terrestrial and stable". Systematic causes for uncertainty are:

1. Measurement limits. As always, the physical measurement is never finite. There is always more detail to be found and read. This applies to everysingle, pure isotope found. For example, today the mass of the main natural fluorine isotope (fluorine-19) can be measured to the accuracy of eleven decimal places:18.998403163(6). But a still more precise measurement system could become available, producing more decimals.
2. Imperfect mixtures of isotopes. In the samples taken and measured themix (relative abundance) of those isotopes may vary. For example, copper. Whilein general its two isotopes make out 69.15% and 30.85% each of all copper found, the naturalsample being measured can have had an incomplete 'stirring' and so the percentages are different. The precision is improved by measuring more samples of course, but there remains this cause of uncertainty. (Example: lead samples vary so much, it can not be noted more precise than four figures:207.2)
3. Earthly sources with a different history. Asource is the greater area being researched, for example 'ocean water' or 'volcanic rock' (as opposed to a 'sample': the single heap of material being investigated). It appears that some elements have a differentisotopic mix per source. For example, thallium in igneous rock has more lighter isotopes, while in sedimentary rock it has more heavy isotopes. There is no Earthly mean number. These elements show the interval notation:A_r°(Tl) = [204.38, 204.39]. For practical reasons, a simplified 'conventional' number is published too (for Tl: 204.38).

These three uncertainties are accumulative. The published value is a result of all these.

Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) andisotopic composition of a sample. Highly accurate atomic masses are available^[7][8] for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples.^[9][10] For this reason, the relative atomic masses of the 22mononuclidic elements (which are the same as the isotopic masses for each of the single naturally occurring nuclides of these elements) are known to especially high accuracy.

The calculation is exemplified forsilicon, whose relative atomic mass is especially important inmetrology. Silicon exists in nature as a mixture of three isotopes:²⁸Si,²⁹Si and³⁰Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for²⁸Si and about one part in one billion for the others. However the range ofnatural abundance for the isotopes is such that the standard abundance can only be given to about ±0.001% (see table).The calculation is

A_r(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854

The estimation of theuncertainty is complicated,^[11] especially as thesample distribution is not necessarily symmetrical: theIUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties,^[12] and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1×10^–5 or 10 ppm. To further reflect this natural variability, in 2010, IUPAC made the decision to list the relative atomic masses of 10 elements as an interval rather than a fixed number.^[13]

The use of the name "atomic weight" has attracted a great deal of controversy among scientists.^[14] Objectors to the name usually prefer the term "relative atomic mass" (not to be confused withatomic mass). The basic objection is that atomic weight is not aweight, that is theforce exerted on an object in agravitational field, measured in units of force such as thenewton orpoundal.^[15]

In reply, supporters of the term "atomic weight" point out (among other arguments)^[14] that:

• the name has been in continuous use for the same quantity since it was first conceptualized in 1808;^[16]
• for most of that time, atomic weights really were measured by weighing (that is bygravimetric analysis) and the name of a physical quantity should not change simply because the method of its determination has changed;
• the term "relative atomic mass" should be reserved for the mass of a specificnuclide (orisotope), while "atomicweight" be used for theweighted mean of the atomic masses over all the atoms in the sample;
• it is not uncommon to have misleading names of physical quantities which are retained for historical reasons, such as
  • electromotive force, which is not a force
  • resolving power, which is not apower quantity
  • molar concentration, which is not a molar quantity (a quantity expressed per unit amount of substance).

It could be added that atomic weight is often not truly "atomic" either, as it does not correspond to the property of any individual atom. The same argument could be made against "relative atomic mass" used in this sense.

IUPAC, through itsCommission on Isotopic Abundances and Atomic Weights (CIAAW), publishes a formal value, called the standard atomic weight for each element that has at least one stable isotope or a well-characterised terrestrial isotopic composition.^{[17]: Table 1} Updates are made only when justified by new high-precision measurements; they are no longer issued on a fixed biennial schedule.^[18] The most recent revisions (January 2025) affected three elements: gadolinium, lutetium, and zirconium.^[18][19]

The published value may be given with an uncertainty, e.g. neon:20.1797(6), or as an interval, e.g. boron: [10.806, 10.821].

Currently 83 elements have an assigned standard atomic weight.^[17] In addition to the full-precision values, CIAAW publishesabridged standard atomic weights (to five significant digits) and, for the twelve elements whose atomic weights are expressed as intervals, single-numberconventional atomic-weight values for use when isotopic variation is unimportant.^[20]

The symbolA_r(E) denotes the relative atomic mass of a particular sample of element E, whereas the standard atomic weight is denotedA_r°(E) (the circle ° indicating the defined standard-state composition).^[21]

Theabridged atomic weight, also published by CIAAW, is derived from the standard atomic weight, reducing the numbers to five digits (five significant figures). The name does not say 'rounded'.

Interval borders are roundeddownwards for the first (low most) border, andupwards for theupward (upmost) border. This way, the more precise original interval is fully covered.^{[1]: Table 2}

Examples:

• Calcium:A_r°(Ca) = 40.078(4) →A_{r, abridged}°(Ca) = 40.078
• Helium:A_r°(He) = 4.002602(2) →A_{r, abridged}°(He) = 4.0026
• Hydrogen:A_r°(H) = [1.00784, 1.00811] →A_{r, abridged}°(H) = [1.0078, 1.0082]

Fourteen chemical elements – hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, argon, bromine, thallium, and lead – have a standard atomic weight that is defined not as a single number, but as an interval. For example, hydrogen hasA_r°(H) = [1.00 784, 1.00811]. This notation states that the various sources on Earth have substantially different isotopic constitutions, and that the uncertainties in all of them are just covered by the two numbers. For these elements, there is not an 'Earth average' constitution, and the 'right' value is not its middle (which would be 1.007975 for hydrogen, with an uncertainty of (±0.000135) that would make it just cover the interval). However, for situations where a less precise value is acceptable, for example in trade, CIAAW has published a single-numberconventional atomic weight. For hydrogen,A_{r, conventional}°(H) = 1.008.^{[1]: Table 3}

By using the abridged value, and the conventional value for the fourteen interval values, a short IUPAC-defined value (5 digits plus uncertainty) can be given for all stable elements. In many situations, and in periodic tables, this may be sufficiently detailed.^{[1]: Tables 2 and 3}

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Periodic table

Group	1	2		3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
	Hydrogen & alkali metals	Alkaline earth metals												Triels	Tetrels	Pnicto­gens	Chal­co­gens	Halo­gens	Noble gases
Period 1	Hydro­gen1H​1.0080																		He­lium2He​4.0026
2	Lith­ium3Li​6.94	Beryl­lium4Be​9.0122												Boron5B​10.81	Carbon6C​12.011	Nitro­gen7N​14.007	Oxy­gen8O​15.999	Fluor­ine9F​18.998	Neon10Ne​20.180
3	So­dium11Na​22.990	Magne­sium12Mg​24.305												Alumin­ium13Al​26.982	Sili­con14Si​28.085	Phos­phorus15P​30.974	Sulfur16S​32.06	Chlor­ine17Cl​35.45	Argon18Ar​39.95
4	Potas­sium19K​39.098	Cal­cium20Ca​40.078		Scan­dium21Sc​44.956	Tita­nium22Ti​47.867	Vana­dium23V​50.942	Chrom­ium24Cr​51.996	Manga­nese25Mn​54.938	Iron26Fe​55.845	Cobalt27Co​58.933	Nickel28Ni​58.693	Copper29Cu​63.546	Zinc30Zn​65.38	Gallium31Ga​69.723	Germa­nium32Ge​72.630	Arsenic33As​74.922	Sele­nium34Se​78.971	Bromine35Br​79.904	Kryp­ton36Kr​83.798
5	Rubid­ium37Rb​85.468	Stront­ium38Sr​87.62		Yttrium39Y​88.906	Zirco­nium40Zr​91.224	Nio­bium41Nb​92.906	Molyb­denum42Mo​95.95	Tech­netium43Tc​[97]	Ruthe­nium44Ru​101.07	Rho­dium45Rh​102.91	Pallad­ium46Pd​106.42	Silver47Ag​107.87	Cad­mium48Cd​112.41	Indium49In​114.82	Tin50Sn​118.71	Anti­mony51Sb​121.76	Tellur­ium52Te​127.60	Iodine53I​126.90	Xenon54Xe​131.29
6	Cae­sium55Cs​132.91	Ba­rium56Ba​137.33		Lute­tium71Lu​174.97	Haf­nium72Hf​178.49	Tanta­lum73Ta​180.95	Tung­sten74W​183.84	Rhe­nium75Re​186.21	Os­mium76Os​190.23	Iridium77Ir​192.22	Plat­inum78Pt​195.08	Gold79Au​196.97	Mer­cury80Hg​200.59	Thallium81Tl​204.38	Lead82Pb​207.2	Bis­muth83Bi​208.98	Polo­nium84Po​[209]	Asta­tine85At​[210]	Radon86Rn​[222]
7	Fran­cium87Fr​[223]	Ra­dium88Ra​[226]		Lawren­cium103Lr​[266]	Ruther­fordium104Rf​[267]	Dub­nium105Db​[268]	Sea­borgium106Sg​[269]	Bohr­ium107Bh​[270]	Has­sium108Hs​[271]	Meit­nerium109Mt​[278]	Darm­stadtium110Ds​[281]	Roent­genium111Rg​[282]	Coper­nicium112Cn​[285]	Nihon­ium113Nh​[286]	Flerov­ium114Fl​[289]	Moscov­ium115Mc​[290]	Liver­morium116Lv​[293]	Tenness­ine117Ts​[294]	Oga­nesson118Og​[294]
				Lan­thanum57La​138.91	Cerium58Ce​140.12	Praseo­dymium59Pr​140.91	Neo­dymium60Nd​144.24	Prome­thium61Pm​[145]	Sama­rium62Sm​150.36	Europ­ium63Eu​151.96	Gadolin­ium64Gd​157.25	Ter­bium65Tb​158.93	Dyspro­sium66Dy​162.50	Hol­mium67Ho​164.93	Erbium68Er​167.26	Thulium69Tm​168.93	Ytter­bium70Yb​173.05
				Actin­ium89Ac​[227]	Thor­ium90Th​232.04	Protac­tinium91Pa​231.04	Ura­nium92U​238.03	Neptu­nium93Np​[237]	Pluto­nium94Pu​[244]	Ameri­cium95Am​[243]	Curium96Cm​[247]	Berkel­ium97Bk​[247]	Califor­nium98Cf​[251]	Einstei­nium99Es​[252]	Fer­mium100Fm​[257]	Mende­levium101Md​[258]	Nobel­ium102No​[259]

‹ Thetemplate below (Periodic table legend/State of matter) is being considered for deletion. Seetemplates for discussion to help reach a consensus. ›

Primordial From decay Synthetic Border shows natural occurrence of the element

Standard atomic weightA_{r, std}(E)^[1]

• Ca: 40.078 — Abridged value (uncertainty omitted here)^[22]
• Po: [209] —mass number of the most stable isotope

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• International Union of Pure and Applied Chemistry (IUPAC)
• Commission on Isotopic Abundances and Atomic Weights (CIAAW)

• IUPAC Commission on Isotopic Abundances and Atomic Weights
• Atomic Weights of the Elements 2011

• Amount of substance
• Chemical properties
• Stoichiometry
• Periodic table
• Chemical quantities

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