An inflatable sport ball, such as a basketball, a football, a soccer ball, a volleyball or a playground ball, is provided with a self-contained inflation mechanism, or multiple self-contained inflation mechanisms, for inflating or more likely adding pressure to the ball. The mechanism is a pump which is inside of the ball and which is operable from outside of the ball to pump ambient air into the ball. The pump contains an integral pressure-indicating device to readily determine the relative pressure of the ball.