A field experiment was conducted during the main 2018 cropping season at Yilmana Densa farmer’s plot to determine the critical value of available soil potassium and optimum K/Mg ratio for wheat production. The field experiments comprised seven treatments, (0, 50, 100, 150, 200, 250 and 300 kg ha_1 K2O) laid down in a randomized complete block design with four replications. All experimental units were supplied with a uniform rate of 92 kg ha-1of nitrogen in the form of urea and 46 kg ha-1 of P2O5 in the form of DAP at planting time. KCl was used as K2O source and applied two weeks before planting by broadcast method. Soil samples were collected two weeks after planting and after harvesting in each plot for analyzing selected soil properties. Available soil K was determined using the ammonium acetate extraction methods method. The results of the study indicated that potassium content in the study area is at optimum level. Therefore, there was no significant response of wheat yield and yield component parameters to adding of potassium fertilizer. Determining the critical value was difficult in the study area because of the soil laboratory result which shows that the potassium content including the control treatment in the study area was at the optimum level. The optimum K/Mg ratio of the same soil sample was 0.67. From the results of the study, it is possible to conclude that there is no need for adding potassium fertilizer in the study area. The result falsifies the potassium fertilizer recommended by EthioSIS for Yilmana Densa district. Keywords: tay variety, potassium fertilizer, yields components, EthioSIS,