The favorable location of the critical point close to common ambient temperatures makes carbon dioxide (CO₂) highly attractive to be used as working fluid for supercritical power cycles. The combination of the thereby wide usable range of temperatures with the special fluid properties close to the critical point, e.g. high densities and low viscosities, holds a distinctive potential for significant efficiency increases as well as smaller component sizes compared to the actual state of the art. However, due to the highly non-ideal behavior of the fluid properties in the regions of interest, especially at near-critical conditions, reliable equations of state (EoS) are needed to correctly predict the fluid behavior. This concerns all steps in design and development of supercritical power cycles, from the preliminary modeling of the cycle up to tasks of detailed engineering of individual components. If, in addition, mixtures or impurities are considered instead of a pure substance, the deviation of the EoS of each component is also included in the mixture calculation, which underlines the importance of accurate EoS. Therefore, a certain sensitivity is required to what extent the selection of the EoS may influence the expected results. In this work, the influence of different equations of state on the thermodynamic design of CO₂ power cycles is investigated. Within this context, five different equations of state were compared to each other by calculating a selection of power cycle configurations, which are typically considered for sCO₂ applications. Aside characteristic process parameters such as relevant fluid properties at each state point of the cycle and the thermal efficiency, differences in the sizes for the internal heat exchangers are considered. The results show, with some exceptions, a largely good agreement in the cycle efficiencies for most of the considered EoS. However, it can also be seen, that the thermophysical properties can differ significantly between the EoS, which is also reflected in notable variations in the heat exchanger performance parameters and furthermore may lead to non-negligible deviations in subsequent evaluations.