In this study, 14 equations have been investigated to calculate pan-evaporation in arid and semi-arid regions (based on the De Martonne aridity index). Two indicators, normalized root mean square error (nRMSE) and mean bias error (MBE), were used to analyze the results. The Kohler-Nordonson-Fox (K-N-F) (1955) equation, on the one hand, is more precise than other original equations and, on the other hand, is one of the equations that have less impact from the improving process and, in other words, has a higher consistency compared to other equations in arid and semi-arid regions. Three improved equations, including improved K-N-F (1955), improved Linacer (1994), and improved Kohler (1954), have better precision in calculating the pan-evaporation compared to the other equations. According to the mathematical form of these three equations, this finding shows the importance of temperature, relative humidity, and wind velocity in arid and semi-arid regions. The improved Linacer (1954) equation had low precision in high-humidity regions, emphasizing relative humidity in calculating pan-evaporation in arid and semi-arid regions. Also, among the studied 14 equations, several equations with more precision have been from the category of improved equations, so it becomes clear that the empirical mathematical equations must be improved specifically for arid and semi-arid regions.HIGHLIGHTSFourteen equations have been investigated to calculate pan-evaporation in arid and semi-arid regions. K-N-F (1955) equation has a higher consistency compared to other equations in arid and semi-arid regions. The improved K-N-F (1955), improved Linacre (1994), and improved Kohler (1954) have better precision in calculating the pan-evaporation compared to the other equations.