Rectilinear Lenses on Film Bodies
The calculator below converts between the focal length f and the field of view (FOV) of a rectilinear lens. The formula that it implements is FOV = 2 arctan (x / (2 f)), where x is the diagonal of the film. The FOV is measured across the frame's diagonal, and is therefore smaller across the horizonal dimension, and even smaller across the vertical dimension.
Rectilinear Lenses on DSLR with 1.5 Crop-Factor
Until now all Pentax DSLRs use a sensor smaller than the standard 24 x 36 mm film frame. The lens still produces a 24 x 36 mm image, but the sensor only captures the central portion of that image — your wide-angle is not so wide and your tele is even longer. The calculator below takes the 1.5 x crop-factor into account.
The Pentax fish-eye zoom lens has a diagonal FOV varying between 180° at the wide end and 90° at the long end. The Birds-Eye lens forms a circular fish-eye image with FOV of 180° across the image circle. All other Fish-Eye lenses form full-frame images with a diagonal FOV equal to 180°.