Radiocarbon dating ($t={\lambda }^{-1}\ln (R_0/R)$)

Radiocarbon dating uses the loss of carbon-14 relative to stable carbon after carbon exchange stops. It can measure either an isotope ratio by accelerator mass spectrometry or radioactive activity per fixed carbon content. Interpreting an age requires radiocarbon calibration and control of contamination and reservoir differences.

A radiocarbon age estimates elapsed time from a measured carbon-14 ratio $R$, an assumed initial ratio $R_0$ and a specified nuclear decay constant $\lambda$. The displayed exponential decay inversion gives the age on that model's timescale. A conventional radiocarbon age uses a prescribed reference and decay convention; it is not generally a calendar age. Radiocarbon calibration accounts for changes in the atmospheric isotope ratio and maps the measurement to a calendar-age estimate.

Radiocarbon calibration converts conventional radiocarbon ages into calendar-age information using independently dated material and models of changes in reservoir isotope ratios. Conventional ages use the historical $5568$-year half-life, whereas the physical carbon-14 half-life is about $5730$ years.^[ref]