# Calculating FOV for mismatched lens/sensor size

I have this 50mm lens that gives the FOV for a 2/3" sensor in its spec sheet:

• Diagonal: 12.6°
• Horizontal: 10.1°
• Vertical: 7.6°

I have this camera, which, according to its spec sheet, has a 1/2.8" sensor.

I am running the camera at 720P, a 16:9 aspect ratio. I am not sure if the sensor is 4:3 or 16:9, physically... Googling seems to suggest all sensors are 4:3 but this camera doesn't support any 4:3 resolutions so I don't know.

If I use this lens with this camera, given that the sensor size differs from the specs of the lens and that I'm running at 16:9, how can I calculate the effective horizontal and vertical FOV of the image?

I don't really understand the meaning of a lot of these numbers but I'm assuming that 1/2.8" is the diagonal, which means the sensor dimensions are something like 7.9mm x 4.45mm.

Also 10.1°/7.6° is about 4:3 so it looks like the lens spec sheet assumes the 2/3" sensor is 4:3.

I'm not really sure where to go from there.

• "I'm assuming that 1/2.8" is the diagonal" It's not, see e.g. photo.stackexchange.com/questions/24952/… Apr 9 at 12:53
• @PhilipKendall Interesting, thanks. It's very confusing... Apr 9 at 12:56

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.