This paper will explain a generalized idea and the various applications of calculus concerning algorithms and time complexities. Prior to starting this paper, research was done to attain more knowledge concerning that of time complexities as well as how this system first came about and how it is modified depending on the algorithm. This paper will explore the modern practices and applications of time complexities and how they quantify the amount of time taken by algorithms to run as functions of length as expressed using big “O” notation. Conclusions drawn from this show that time complexities allow for the diversity and fluctuation of algorithms as well as the vast array of answers to choose from.