Barchan dunes are among the most common accumulative phenomena made by wind erosion, which are usually formed in regions where the prevailing wind direction is almost constant throughout the year and there is not enough sand to completely cover the land surface. Barchans are among the most common windy landscapes in Pashoueyeh Erg in the west of Lut Desert, Iran. This study aims to elaborate on morphological properties of barchans in this region using mathematical and statistical models. The results of these methods are very important in investigating barchan shapes and identifying their behavior. Barchan shapes were mathematically modeled by simulating them in the coordinate system through nonlinear parabolic equations, so that two separate equations were calculated for barchan windward and slip-face parabolas. The type and intensity of relationships between barchan morphology and mathematical parameters were determined by the statistical modeling. The results indicated that the existing relationships followed the power correlation with the maximum coefficient of determination and minimum error of estimate. Combining the above two methods is a powerful basis for stimulating barchans in virtual and laboratory environments. The most important result of this study is to convert the mathematical and statistical models of barchan morphology to each other. Focal length is one of the most important parameters of barchan parabolas, suggesting different states of barchans in comparison with each other. As the barchan\'s focal length decreases, its opening becomes narrower, and the divergence of the barchan\'s horns reduces. Barchans with longer focal length have greater width, dimensions, and volume. In general, identifying and estimating the morphometric and planar parameters of barchans is effective in how they move, how much they move, and how they behave in the environment. These cases play an important role in the management of desert areas.