The radiocarbon dating method of (_6^14)C is one of the newest methods in archeology. Knowing and applying this method is possible by using the methods of natural sciences in general and mathematical sciences in particular. The use of radiocarbon dating method has been expanded in recent years in Iran in archaeological excavations and often, citing this method, findings and works related to them are dated absolutely (Mofidi Nasrabadi, 2018: 23-41). Therefore, this study has been done by describing and determining the radioactive equations used in calculating the age of (_6^14)C. (_6^14)C is one of the isotopes of carbon, a radioactive substance and the result of interactions with (_6^14)N. Living organisms absorb some (_6^14)C in their food cycle, and when they die, the absorption of radioisotopes stops, and the absorbed (_6^14)C gradually decreases according to the half-life of radioactive carbon with the physical characteristic, i.e., the rate of transformation (the numerical interpretation of the derivative). This physical law is expressed in the form of a mathematical equations, and two basic and dynamic mathematical tools are used, i.e. differential and integral, and With the help of (_6^14)C properties, the activity equation (exponential function) is obtained, which is used in the calculation of (_6^14)C dating.