Pan-tilt-zoom (PTZ) cameras are pervasive in modern surveillance systems. However, we demonstrate that the (pan, tilt) coordinates reported by PTZ cameras become inaccurate after many hours of operation, endangering tracking and 3D localization algorithms that rely on the accuracy of such values. To solve this problem, we propose a complete model for a pan-tilt-zoom camera that explicitly reflects how focal length and lens distortion vary as a function of zoom scale. We show how the parameters of this model can be quickly and accurately estimated using a series of simple initialization steps followed by a nonlinear optimization. Our method requires only ten images to achieve accurate calibration results. Next, we show how the calibration parameters can be maintained using a one-shot dynamic correction process; this ensures that the camera returns the same field of view every time the user requests a given (pan, tilt, zoom), even after hundreds of hours of operation. The dynamic calibration algorithm is based on matching the current image against a stored feature library created at the time the PTZ camera is mounted. We evaluate the calibration and dynamic correction algorithms on both experimental and real-world datasets, demonstrating the effectiveness of the techniques.