Nowadays, natural gas pricing, particularly for the residential sector, has always been a challenging issue in the natural gas market due to the rapidly changing factors affecting natural gas supply and demand mechanisms. Weather temperature and demand are the most important and influential factors that have repeatedly attracted scholars to mathematically model natural gas prices, especially for forecasting purposes. Traditionally, the prices of other major substitute energy sources, such as oil, gas oil, and coal, have also been formally used in natural gas pricing mechanisms across different natural gas markets worldwide. However, there are almost no studies that specifically discuss natural gas pricing based solely on weather temperature, demand, and residential end users' average income simultaneously. In this study, we are fundamentally determined to model natural gas prices in terms of weather temperature and demand for different income levels using a curvature-based formula under two scenarios. The main strategies underlying this research are that higher prices should be paid when the weather temperature decreases and the demand increases, respectively. In addition, we deliberately reformulate the proposed basic model (Scenario One) using the income elasticity of demand to define natural gas prices for different demand levels. There are two notable features of this study: (1) the proposed mathematical pricing models are sufficiently flexible to simultaneously incorporate weather temperature, demand, and average income to categorize residential end users; and (2) the curvature formula provides the flexibility to reconfigure the proposed models into alternative natural gas pricing equations, which can strategically benefit .