Inscience andtechnology, anarbitrary unit (abbreviatedarb. unit,[1]see below)orprocedure defined unit[2] (p.d.u.)is a relativeunit of measurement to show the ratio ofamount of substance,intensity, or otherquantities, to a predeterminedreference measurement. The reference measurement is typically defined by the local laboratories or dependent on individual measurement apparatus. It is therefore impossible to compare "1 arb. unit" by one measurer and "1000 arb. unit" by another measurer without detailed prior knowledge on how the respective "arbitrary units" were defined; thus, the unit is sometimes called anunknown unit.[2] The unit only serves to compare multiple measurements performed in similar environment, since the ratio between the measurement and the reference is a consistent anddimensionless quantity independent of what actual units are used.Units of such kind are commonly used in fields such as physiology to indicatesubstance concentration, andspectroscopy to express spectral intensity.
When the reference measurement is precisely defined and internationally agreed upon, arbitrary units can also be a unit capable of public comparison. One example of a publicly defined arbitrary unit is theWHO International Unit.[2]
Abbreviations for "arbitrary unit" include:arb. unit,[1]arb. u.,AU,[3] anda.u.[4]Among these, "AU" and "a.u." are common abbreviations forastronomical units andatomic units.[5] For this reason,Physical Review journals, theJapanese Journal of Applied Physics, and an increasing number of otheracademic journals, recommend against using "a.u." (Jpn. J. Appl. Phys recommends "arb. unit" instead).[6]
InUCUM, arbitrary unit is represented as "[arb'U]".[7]
While arbitrary unit is not a formally recognized unit,[1]IUPAC andIFCC recognize the need to deal with "unknown units", and decided in 2008 to use the term "procedure defined unit" in their database.[2] The decision forbids using factors or denominators in conjunction with p.d.u. (such as "p.d.u./L").