The question of how to calculate the numerical value of the fine structure constant from theory was one of the most outstandingly difficult problems in mathematical physics for the greater part of the 20-th century. There were many unsuccessful attempts by researchers including famous ones such as Dirac to find a formula for the fine structure constant. This study is an attempt to demonstrate how to find a mathematical description and to find an idea of the enormous effects this dimensionsless constant has to physics. The formula was found due to the incorporating of the maximal speed a particle can reach. Since this speed is slightly below speed of light but not even relativistic treatment of atoms and other structure must involve corrections that are in its simplest form given by the mysterious factor α called the fine-structure constant. It is shown that the fine-structure constant is a direct consequence of the limited speed of an electrical charged particle in vacuum.

special relativity, classical field theory, quantum mechanics