C-14 dating method is based on the fact that 

 As long as a plant or animal is alive, a dynamic equilibrium exists in which an organism excretes or exhales the same amount 
of C-14 that it takes in and the ratio of C-14 to C-12 in the living organism is the same as that in the upper atmosphere. When the 
plant or animal dies, however, it no longer takes in more C-14 and ratio of C-14 to C-12 slowly decreases due to decay of C-14.

${ }_6^{14}\mathrm{C}{⟶}_7^{14}\mathrm{N}{+}_{-1}^0\mathrm{e}$

Thus, from the activity of C-14 in the dead organism and that of fresh sample (in the atmosphere), age can be decided. 

$\mathrm{\lambda }\text{ (decay constant) }=\frac{2.303}{\mathrm{t}\text{ (age) }}\log \frac{{\mathrm{N}}_0\text{ (original activity) }}{\mathrm{N}\text{ (final activity) }}$