Relative atomic mass (symbol: Ar) is a dimensionless (number only) physical quantity. In its modern definition, it is the ratio of the average mass of atoms of an element in a given sample to one unified atomic mass unit. The unified atomic mass unit, symbol u, is defined being 1⁄12 of the mass of a carbon-12 atom. The mass of atoms can vary (between atoms of the same element), due to the presence of various isotopes of that element. Since both values in the ratio are expressed in the same unit (u), the resulting value is dimensionless; hence the value is relative.
Within one source (sample), it is a straight average over the individual atom weights (isotopes) present. Between sources, the atomic weight can vary when the source's origin (radioactive history) resulted in different isotopic concentrations. These differences are real and measurable, and can be used to identify a sample to its origin. For example, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.
The well-known standard atomic weight, or atomic weight, is a specific usage of relative atomic mass: it is the relative atomic mass, with the sources being terrestrial (taken from Earth). For these sources, research reports are used by the CIAAW of the International Union of Pure and Applied Chemistry (IUPAC). For this definition, "[a] normal sample is any reasonably possible source of the element or its compounds in commerce for industry and science and has not been subject to significant modification of isotopic composition within a geologically brief period".
The standard atomic weights are reprinted in a wide variety of textbooks, commercial catalogues, and periodic table wall charts. They are what chemists loosely call "atomic weights". It is the most published form of the relative atomic mass.