δ¹³C

In geochemistry, paleoclimatology, and paleoceanography δ¹³C (pronounced "delta c thirteen") is an isotopic signature, a measure of the ratio of the two stable isotopes of carbon—¹³C and ¹²C—reported in parts per thousand (per mil, ‰). The measure is also widely used in archaeology for the reconstruction of past diets, particularly to see if marine foods or certain types of plants were consumed.

The definition is, in per mille:

${\displaystyle \delta {\ce {^{13}C}}=\left({\frac {({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {sample} }}{({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {standard} }}}-1\right)\times 1000}$

where the standard is an established reference material.

δ¹³C varies in time as a function of productivity, the signature of the inorganic source, organic carbon burial, and vegetation type. Biological processes preferentially take up the lower mass isotope through kinetic fractionation. However some abiotic processes do the same. For example, methane from hydrothermal vents can be depleted by up to 50%.