Changes in dilution curves of critical nitrogen concentration in sweetpotato under different potassium conditions

China is the largest producer of sweetpotato in the world. The unreasonable application of fertilizer in actual production has led to the imbalance of sweetpotato source and sink. Reasonable use of fertilizer requires proper proportion of nitrogen (N) and potassium (K) to balance nutrients of shoots and roots to achieve optimal growth. The changes of critical N dilution curves of shoot, root and whole plant of sweetpotato were analyzed according to different K levels to quantify the effect of K levels on critical N concentration. In this study, two sweetpotato varieties (Yan25 and Shang19), two K application levels (K0 and K1) and five N application levels (N0-N4) were used to construct a dilution model for the critical N concentration of sweetpotato shoot, root and whole plant. Xinxiang was used for model validation. The critical N concentration dilution model of sweetpotato shoot is as follows: K0: Nc = 4.391DM−0.504; K1: Nc = 4.572DM−0.418. The critical N concentration dilution model of sweetpotato root is as follows: K0: Nc = 0.93DM−0.24; K1: Nc = 1.06DM−0.205. The critical N concentration dilution model of sweetpotato whole plant is as follows: K0: Nc = 3.44DM−0.415; K1: Nc = 3.742DM−0.348. Application of K fertilizer increased the dilution curve of critical N concentration in all parts of sweetpotato. At the K0 level, the optimal N application rate of Yan25 and Shang19 was 120 kg N ha−1 (N2), and at the K1 level, the optimal N application rate was 180 kg N ha−1 (N3). We found that (i) K has greater ability to improve the N absorption of sweetpotato than its ability to increase the dry matter. Differences in critical N curves between different K levels could quantify the effect of K on critical N concentration of sweetpotato. (ii) Under low N conditions, applying K fertilizer will make N more deficient; Under high N conditions, applying K fertilizer will make N suitable and inhibit overgrowth of shoots. (iii) The critical N concentration dilution model based on the whole plant is more suitable for root crops such as sweetpotato and shows high practicability. This study identified changes in the critical N concentration of sweetpotato under different K application levels.