Decreasing waste materials through recycle has in the recent contributed to sustainable manufacturing in many textile industries for better resource utilization in textile mills. This has been given first priority in manufacturing, processing and finishing operations. Most of the time the yarn manufacturing and proper utilization of this material didn’t give attention in most companies. Especially yarn length variation of packages, weaving beams and copes have very critical impact on those companies which manufacture and utilize yarn products. This variation problem has great impact on their productivity and profitability. This paper describes the application of a new formula in the yarn packaging process and it is accomplished by derivation a new formula that can determine the radius of any package. The formula has integrated the basic characteristics of yarn and fiber including yarn diameter, yarn/ fiber density and mass of the yarn coiled on the cop. Finally we have concluded that package radius is the quadratic function of yarn density and package mass on the cope.