Abstract: A compressor driving torque estimating apparatus estimates driving torque of a compressor. The apparatus includes a discharge-side detecting device, an inlet-side detecting device, first and second calculating devices, and an estimated driving torque determining device. The discharge-side detecting device detects discharge-side quantity about fluid discharged from the compressor. The inlet-side detecting device detects inlet-side quantity about fluid drawn into the compressor. The first calculating device calculates first estimated driving torque based on the discharge- and inlet-side quantity. The second calculating device calculates second estimated driving torque based on the discharge-side quantity. The estimated driving torque determining device chooses a smaller value between the first and second estimated driving torque as the driving torque. A compressor driving source control apparatus includes the apparatus.