Although most of them are relatively small, stable isotope deltas of naturally occurring substances are robust and enable workers in anthropology, atmospheric sciences, biology, chemistry, environmental sciences, food and drug authentication, forensic science, geochemistry, geology, oceanography, and paleoclimatology to study a variety of topics. Two fundamental processes explain the stable isotope deltas measured in most terrestrial systems: isotopic fractionation and isotope mixing. Isotopic fractionation is the result of equilibrium or kinetic physicochemical processes that fractionate isotopes because of small differences in physical or chemical properties of molecular species having different isotopes. It is shown that the mixing of radioactive and stable isotope end members can be modelled to provide information on many natural processes, including 14C abundances in the modern atmosphere and the stable hydrogen and oxygen isotopic compositions of the oceans during glacial and interglacial times. The calculation of mixing fractions using isotope balance equations with isotope deltas can be substantially in error when substances with high concentrations of heavy isotopes (e.g. 13C, 2H, and 18O ) are mixed. In such cases, calculations using mole fractions are preferred as they produce accurate mixing fractions. Isotope deltas are dimensionless quantities. In the International System of Units (SI), these quantities have the unit 1 and the usual list of prefixes is not applicable. To overcome traditional limitations with expressing orders of magnitude differences in isotope deltas, we propose the term urey (symbol Ur), after Harold C. Urey, for the unit 1. In such a manner, an isotope delta value expressed traditionally as−25 per mil can be written as−25 mUr (or−2.5 cUr or−0.25 dUr; the use of any SI prefix is possible). Likewise, very small isotopic differences often expressed in per meg ‘units’ are easily included (e.g. either+0.015 ‰ or+15 per meg can be written as+15 μUr.