How does carbon dating work?

Carbon dating works by determining the amount of carbon-14 in archeological artifacts of a biological origin.

All living things take in carbon. When they die, they stop taking in new carbon.

The ratio of carbon-12 to carbon-14 at the moment of death is the same for every living thing.

But the carbon-14 decays with a half-life of 5730 years, while the amount of carbon-12 remains constant in the sample.

You can determine the ratio of carbon-12 to carbon-14 in the sample and compare it to the ratio in a living organism. Then you can determine the age of the object.

After ten half-lives (57 000 years), only about 0.1 % of the original carbon-14 will remain. So that is the limit of reliability for carbon dating.

A formula to calculate the age ##t## of a sample by carbon dating is:

##t = -ln(N_t/N_0)/ln2 × t_½##

where ##t_½## is the half-life and ##(N_t/N_0)## is the percent of carbon-14 in the sample compared to that in living tissue.

If you had a fossil with 10 percent carbon-14 compared to a living sample, then

##t = -ln0.1/ln2 × "5730 yr" = 2.303/0.6931 × "5730 yr" = "3.322 × 5730 yr" = "19 000 yr"##

The sample is 19 000 yr old.