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Air traffic control systems condensed ATC, are faculty liable for the protected, methodical, and quick progression of air traffic in the worldwide aviation authority framework. Typically positioned in airport regulation focuses and control towers on the ground, they screen the position, speed, and elevation of an airplane in their doled-out airspace outwardly and by radar, and give headings to the pilots by radio. The place of air traffic regulator requires profoundly specific information, abilities, and capacities. Therefore, it's very important to draw and analyze the model for that system. In this paper an Air Traffic Control (ATC) radar mathematical model is built using Mathcad software. The model has the capability of taking into account various radar parameters and converting them into Mathcad codes. Calculations throughout the model are based on basic theoretical equations as well as empirical engineering formulas which give acceptable error tolerances. Results are displayed graphically, particularly the maximum radar range for various essential radar parameters such as the probability of detection, probability of false alarm, and several integrated pulses.