This article provides an in-depth exploration of mathematical formulas critical to the textile industry, focusing on environmental impact, mechanical properties, production efficiency, and material characteristics. By presenting precise equations for carbon footprint, tensile strength, fiber yield, moisture regain, and other key metrics, this work aims to equip researchers, engineers, and industry professionals with tools to optimize textile processes and enhance sustainability. Each formula is accompanied by detailed explanations, practical applications, and considerations for real-world implementation.