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Radial structure of accretion discs around compact objects is often described using analytic approximations which are derived from averaging or integrating vertical structure equations. For non-solar chemical composition, partial ionization, or for supermassive black holes, this approach is not accurate. Additionally, radial extension of 'analytically-described' disc zones is not evident in many cases. We calculate vertical structure of accretion discs around compact objects, with and without external irradiation, with radiative and convective energy transport taken into account. For this, we introduce a new open Python code, allowing different equations of state and opacity laws, including tabular values. As a result, radial structure and stability 'S-curves' are calculated for specific disc parameters and chemical composition. In particular, based on more accurate power-law approximations for opacity in the disc, we supply new analytic formulas for the farthest regions of the hot disc around stellar-mass object. On calculating vertical structure of a self-irradiated disc, we calculate a self-consistent value of the irradiation parameter C irr for stationary α-disc. We find that, for a fixed shape of the X-ray spectrum, C irr depends weakly on the accretion rate but changes with radius, and the dependence is driven by the conditions in the photosphere and disc opening angle. The hot zone extent depends on the ratio between irradiating and intrinsic flux: corresponding relation for |$T_{\rm irr,\, crit}$| is obtained. [ABSTRACT FROM AUTHOR]