How to Calculate the Carbon-14 in a Fossil

Calculate the number of atoms of carbon in the sample. Twelve grams of carbon equals one mole, which is 6.022 x 10^23 atoms. One pound of carbon would therefore contain approximately 2.73 x 10^26 atoms. Living things do contain other elements, but radiocarbon dating is concerned with only the carbon, which is extracted by a variety of chemical means. Carbon accounts for about 18% of a human body mass; the amount may vary in other species.

Divide the total number of carbon atoms by 1 trillion (10^12) to estimate how many carbon-14 atoms would have been present in the living specimen.

Divide the age of the fossil by 5,730 years to find its age in carbon-14 half-lives. A half-life is the period of time it takes for half of the atoms in a sample to decay.

Raise 2 to the power of the number of half-lives. For example, if your sample is 17,190 years old, or three half-lives, you would raise 2 to the power of 3 to get 8. Or if your sample is only 2,865 years old, or half a half-life, you would raise 2 to the power of 0.5 to get 1.414.

Divide the original number of carbon-14 atoms calculated in Step 2 by the number determined in Step 4. The quotient is the number of the original C-14 atoms that have survived.