Attempts to measure sustainability of farms are usually based on indicators of a set of sustainability dimensions. According to the literature, analyses should (but quite often do not) cover not only the level, but also the relations between the sustainability dimensions, because we could expect complementarity, synergies or competition between the sustainability goals. The aim of this paper was to measure and assess the interdependencies between dimensions of farms’ sustainability. The research was carried out on 601 farms that participate in the Polish Farm Accountancy Data Network (FADN), with the use of standard FADN data supported by additional information from interviews. Based on many variables, economic, environmental, social, and composite sustainability indices were collected. From the correlation and correspondence analyses it was concluded that the farms reached the balance of all three dimensions simultaneously when the level of sustainability indices was medium, while a high level of sustainability in one dimension made it very difficult to reach a high level in the others. It was also emphasized that assessing farms’ sustainability with the use of a simple aggregation of variables may be not correct since sustainability goals may compete with each other.