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The study examined the decoupling relationship between industry carbon emissions and economic growth using the most current updated data. We collected data from the industry sector of Pakistan from 1991 to 2018. This study used two techniques, Tapio’s elasticity and fluctuation index, to test the decoupling relationship and the relationship’s stability between industry carbon emissions and economic growth. First, we analyzed the decoupling relationship between industry carbon emissions and economic growth in Pakistan using Tapio’s decoupling model, decoupling the elasticity of technology, scale and structure. Second, the decoupling volatility index was used to determine the stability of the technology, scale and structure elasticity. The Tapio decoupling elasticity technique results confirmed the significant relationship between industry CO2 emissions, economic growth and added value comes out to be a simple feature of each stage and undergoes expansive negative and strong decoupling processes. The outcomes of elastically decoupled volatility indexes suggest that three out of four indices are high, indicating unstable decoupling conditions. This study concludes that growth and volatility were the crucial characteristics of industrial carbon emissions during 1991–2018. Hence, the industry’s carbon emissions were increased from 16.67 million tons in 1991 to 55.70 million tons in 2018, an average yearly growth of 4.56%.