If the sensor is 3.39 mm tall (referenced to landscape mode), then half that is 1.695 mm. Focal length for the iPhone 4 is listed as 3.85 mm. atan(1.695/3.85) is 23.75 degrees from center to top, or 47.5 degrees top to bottom.
For the longer dimension 4.52/2 = 2.26 mm, atan(2.26/3.85) = 30.41 center to side, or 60.8 degrees left to right (again referencing with respect to landscape orientation).
So 60.8 degrees horizontal by 47.5 degrees vertical.
ADDED much later:
The focal length for the newer iPhone 4S back camera is listed as 4.28 mm, but with the same sensor dimensions as the older iPhone 4. So:
2*atan(2.26/4.28) = 55.7 degrees, by 2*atan(1.695/4.28) = 43.2 degrees
or roughly a 4 to 5 degree smaller field-of-view compared with the iPhone 4.
ADDED much much later:
The sensor size for the iPhone 5S back camera is reported to be 4.89 x 3.67 mm, with a focal length of 4.12 mm. Thus:
2*atan((4.89/2)/4.12) = 61.4 degrees wide
2*atan((3.67/2)/4.12) = 48.0 degrees top to bottom
...or an FOV just a smidge larger than the back camera the iPhone 4.
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