In order to establish critical potassium (K) concentration levels and K/calcium (Ca) plus magnesium g) (K/Ca+Mg] ratios in potato petioles associated to maximum total tuber yields, an experiment was conducted under Brazilian conditions. Six K levels (0, 60, 120, 240, 480, and 960 kg K2O/ha as potassium sulphate) were applied in a randomized complete block design experiment with four replications. Baraka potato tubers were seeded, spaced 0.8 X 0.3 m, following the agronomic cultural practices recommended for the crop. After 48-days from plant emergence, plant tissue samples was collected from each plant, the youngest fully expanded leaves (YFEL) and the oldest but not senescent leaves (ONSL). Petioles from these leaves were analysed to their K, Ca, and Mg contents. At harvest, total, high grade, and weight tuber yields were increased to 733, 719, and 660 g/plant for the 353, 335, and 384 kg K2O/ha levels, respectively. These yields are double the Brazilian potato yield average. Petiole Ca and Mg concentrations were decreased by the K fertilizer treatments, whereas the opposite occurred with the K/Ca+Mg ratio. Potassium concentrations in the petioles from the YFEL and ONSL increased up to .44 and 7.13 g K/100 g petioles dry matter at the 672 and 654 kg K2O/ha levels, respectively. The K petiole gradient concentration was not affected by K fertilization. The K/Ca+Mg ratio for YFEL associated with the maximum total tuber yield was 7.24, while the K concentrations were 8.91 and 6.16 g K/100 g dry matter in petioles for the YFEL and ONSL, respectively.