A touch sensing apparatus includes a first plate configured to receive a touch input, a second plate spaced apart from the first plate, a piezoelectric element disposed between the first and second plates, the piezoelectric element being configured to generate electrical signals corresponding to the touch input received on the first plate, an ultrasonic output unit configured to output ultrasonic signals based on the electrical signals generated from the piezoelectric element, a plurality of microphones configured to receive the ultrasonic signals, and a processor configured to determine a position of the touch input on the first plate based on the ultrasonic signals received by the plurality of microphones.