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Ultra violet (UV) solar energy can cause several negative effects to the skin and eyes in case of overexposure. To protect people from erythemal damage, personal erythemal exposure must be carefully assessed when outdoor activities are carried out. The direct measure with scientific instruments is impracticable to common people, and indirect methods assess the exposure only on the horizontal plane: this work developed a mathematical model to assess erythemal exposure to all the body districts. UVA irradiance and erythemal irradiance were measured on several inclined planes, oriented to the four cardinal directions, in seven environments with multiple sky conditions. The UV erythemal (UVE) ratio between erythemal irradiance on an inclined plane (Iery°) and UVA irradiance on a horizontal plane (IUVAh) was calculated. The results indicate that the UVE = Iery°/IUVAh is variable across the day and depends on the plane orientation, its degree of inclination, and sky conditions. Mathematical models to calculate erythemal exposure in clear, intermediate and overcast sky conditions on planes with different inclinations and orientations were derived from the daily trends of the UVE = Iery°/IUVAh. The application procedure of the mathematical model to the vertical plane oriented to the south is provided as an example. [ABSTRACT FROM AUTHOR]