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The critical value of soil exchangeable potassium (K) (mg K kg −1 ) is a valuable tool for an efficient K fertilization management in potato production systems. The aim of the present study was to determine the critical value of soil exchangeable K for potato crops grown in different environments and differing availabilities of initial exchangeable K. The data used in this study were taken from 34 experiments on K fertilization conducted in southern Chile from 1977 to 2017 by the National Potato Center at the Instituto de Investigaciones Agropecuarias (INIA). Yield responses to K fertilization rates were assessed with linear-plateau and Mitscherlich models in order to determine the critical soil exchangeable K across environments. Across experiments, the average fresh tuber yield ranged between 18 and 91 Mg ha −1 . Fresh tuber yields decreased by up to 70% when no K fertilization was applied. Yield reduction was concentrated around 25% in response to K deficiency. Relative yields were described as significant by both linear-plateau and Mitscherlich models. However, relative yields were better described by the linear-plateau model ( p <  0.01, R 2  = 0.62; SEE  = 0.11). The critical soil exchangeable K value identified with the linear-plateau model was 224 mg K kg −1 . This critical K value will be useful for potato farmers that produce their crops in volcanic soils, such as Andisols. Moreover, this critical K value will help to increase K use efficiency through better K fertilization management strategies aimed at building and/or maintaining K levels in soils.