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The article highlights the main concepts of calculus, decade long development, and numerous applications. Calculus, which was derived from the revolution work by Newton and Leibniz in the late 17th century, has greatly affected mathematical problem solving and the analytical thinking. Calculus concepts of Euler, Lagrange, and Cauchy were developed during the 19th century which moved closer to a more rigorous comprehension. A major idea of calculus--limits, derivatives, and integrals--is explained, stressing the role of these ideas for dealing with motion, rates of change, and value accumulation. In unlike circumstances with motion and velocity in the physical world, derivatives rates of change symbols are applicable, while indefinite and definite integrals find their use for calculating cumulative values and finding net change over intervals. The article explores the many uses of calculus in computer science, biology, engineering, economics, and physics. Calculus is used in physics to understand dynamic systems and forecast object motion, in engineering for optimization, in economics to model economic variables, in biology to explain biological systems, and in computer science for machine learning and artificial intelligence algorithms, such as gradient descent optimization. All things considered, the essay offers a thorough review of the background information, essential ideas, and real-world uses of calculus in a range of scientific and technical domains.