The power output of a medical ultrasonic transducer is usually determined by measuring the radiation force exerted by the ultrasonic beam on an absorbing or reflecting target. The theory of the radiation force is somewhat involved and strictly applies only to a continuous ultrasonic beam, but the method is commonly used to determine the (time-averaged) powers of both continuous and short-pulsed beams. An ultrasound calorimeter was developed so that the validity of the radiation force method might be tested by making comparative measurements of ultrasonic power in water. In the thesis, the physical origin of the radiation force exerted on absorbing and reflecting targets is explained. The force exerted by a pulsed ultrasonic beam is discussed briefly, and the significance of real deviations from the model upon which the theory is based are considered. In addition, the mean sound pressure in the ultrasonic beam is discussed. The development of the calorimeter is described. The calorimeter was of the continuous-flow type and used castor oil to absorb the ultrasonic beam. Its accuracy was thoroughly assessed and ranged from ± 7.2% at 1.5 MHz to ± 24% at 6 MHz; it could detect a minimum power of 0.1 mW. Radiation force measurements of ultrasonic power were made with an accuracy of typically ± 5% using one absorbing and two reflecting targets suspended from an analytical balance. Calorimetric and radiation force measurements of the powers of both continuous and short-pulsed ultrasonic beams were found to be in good agreement. It is concluded that the generally-accepted relationship between the radiation force and ultrasonic beam power is correct and that, as widely assumed, the (time-averaged) force exerted by a pulsed beam is equal to the force exerted by a continuous beam of the same time-averaged power.