Differences in the abundance of stable isotopes among natural materials are usually very small (natural differences in the ratio of rare to common isotope are almost always below 0.1%, and sometimes much smaller). Nevertheless, these very small differences can record meaningful biological and geological processes. To facilitate comparison of these small but meaningful differences, isotope abundances in natural materials are often reported relative to isotope abundances in designated standards. The convention for reporting the measured difference between a sample and a standard is called "delta notation." For example, imagine an element X for which we wish to compare the rare, heavy stable isotope with atomic mass A (X) to the light, common isotope with atomic mass B (X). The abundance of X and X in any given material is reported with the notation δX. δX for the sample material is calculated as follows:
:R = (total amount of X)/(total amount of X)
:δX = (R − R)/R
δ values are most commonly reported in parts per thousand, commonly referred to in isotope chemistry as per mille and represented by the symbol ‰. To report δ values in per mille, the δ value as calculated above should be multiplied by 1000:
:δX (‰) = ((R − R)/R) * 1000