Aims. In this work, we have investigated the relation between the radially resolved thermodynamic quantities of the intracluster medium in the X-COP cluster sample, aiming to assess the stratification properties of the ICM. Methods. We modeled the relations between radius, gas temperature, density, and pressure using a combination of power-laws, also evaluating the intrinsic scatter in these relations. Results. We show that the gas pressure is remarkably well correlated to the density, with very small scatter. Also the temperature correlates with gas density with similar scatter. The slopes of these relations have values that show a clear transition from the inner cluster regions to the outskirts. This transition occurs at the radius r_t = 0.19(±0.04) R₅₀₀ and electron density n_t = (1.91 ± 0.21) × 10⁻³ cm⁻³ E²(z). We find that above 0.2 R₅₀₀ the radial thermodynamic profiles are accurately reproduced by a well defined and physically motivated framework, where the dark matter follows the NFW potential and the gas is represented by a polytropic equation of state. By modeling the gas temperature dependence upon both the gas density and radius, we propose a new method to reconstruct the hydrostatic mass profile based only on the relatively inexpensive measurement of the gas density profile.