The standard atomic weight (Ar, standard(E)) of a chemical element is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, isotope 63Cu (Ar = 62.929) constitutes 69% of the copper on Earth, the rest being 65Cu (Ar = 64.927), so
Because relative isotopic masses are dimensionless quantities, this weighted mean is also dimensionless. It can be converted into a measure of mass (with dimension M) by multiplying it with the dalton, also known as the atomic mass constant.
Among various variants of the notion of atomic weight (Ar, also known as relative atomic mass) used by scientists, the standard atomic weight (Ar, standard) is the most common and practical. The standard atomic weight of each chemical element is determined and published by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International 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 archeological site. Standard atomic weight averages such values to the range of atomic weights that a chemist might expect to derive from many random samples from Earth. This range is the rationale for the interval notation given for some standard atomic weight values.
Of the 118 known chemical elements, 80 have stable isotopes and 84 have this Earth-environment based value. Typically, such a value is, for example helium: Ar, standard(He) = 4.002602(2). The "(2)" indicates the uncertainty in the last digit shown, to read 4.002602±0.000002. IUPAC also publishes abridged values, rounded to five significant figures. For helium, Ar, abridged(He) = 4.0026.
For thirteen 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: Ar, standard(Tl) = [204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes a conventional value. For thallium, Ar, conventional(Tl) = 204.38.
Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) and isotopic composition of a sample. Highly accurate atomic masses are available for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. For this reason, the relative atomic masses of the 22 mononuclidic 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. For example, there is an uncertainty of only one part in 38 million for the relative atomic mass of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).