Heating, Ventilating and Air Conditioning Systems (HVAC) are applied for primarily cooling purpose as well as to maintain quality of air. Since, most of the HVAC company has lack of data for the designing purpose – leads to uncomforting. Less standardization in designing criteria of HVAC Systems (Except ASHRAE which provides data for refrigeration systems) leads to write this paper. There is no any sources available that can exactly says how to design an energy efficient HVAC Systems. This paper provides the mathematical aspects for designing the HVAC Systems. This paper includes the process of designing HVAC with components by using mathematical framework – confirmed by software. This paper provides proper selection of capacity of systems and life cycle cost analysis too. For the simplicity of understanding, we have provided a demonstration with the example of 1000 seats auditorium situated at Vadodara, Gujarat. As the result of this designing, we got an emission free HVAC Systems with low GWP (Global Warming Potential) and ODP (Ozone Depletion Potential) – providing best comfort condition with reduction trunk duct arrangement and low life cycle cost. However production side of the Ducting Systems will become more expensive and complex due to numbers of joints and duct sizes but after applying it properly – better performance and less frictional losses lead the system to high Energy Efficiency Ratio (EER).