A processing element, a neural processing device including the same, and a method for calculating thereof are provided. The processing element includes a weight register configured to receive and store weights, an input activation register configured to store input activations, a flexible multiplier configured to receive the weight and the input activation, to perform a multiplication calculation in a first precision or a second precision different from the first precision according to a mode signal, occurrence of an overflow, and occurrence of an underflow, and to generates result data; and a saturating adder configured to receive the result data and generate subtotals.