According to the sensor spec, it has 1920 * 1080 square pixels of 2.9µm size, giving

• a physical sensor size of 5.568mm * 3.132mm,
• a 16:9 aspect ratio
• a diagonal size of 6.388mm

Plausibility check: according to Wikipedia on image sensors, your 1/2.8" sensor should have a diagonal between the listed 1/2.9" and 1/2.7" formats, i.e. between 6.23mm and 6.72mm. So, the calculation above, based on the pixel size, seems correct.

Relating the dimensions to the focal length of 50mm, and converting to angular degrees, gives:

• horizontal FOV: 6.37°
• vertical FOV: 3.59°
• diagonal FOV: 7.31°

How to calculate:

For sensors much smaller than the focal length (as in your case), you can ignore any trigonometric functions and simply get the approximate FOV in degrees using

FOV = 57.3 * dimension / focalLength

You see, for FOV calculation, you just need the lens focal length and the sensor dimensions. Any FOV values given in lens specs are just meant as a convenience for the reader, but can easily cause confusion if the user's sensor isn't identical to the one assumed in the lens spec.

Regarding resolution:

The sensor is a Full-HD one, natively giving 1920 * 1080 resolution. If used in 720P mode (1280 * 720), it will most probably still use the full sensor size, and only digitally reduce the resolution, effectively simulating larger pixels of 4.35µm. So, this does not change the FOV calculation, as still the full sensor dimensions are in use.