What is crop factor?
According to Wikipedia:
In digital photography, the crop factor, format factor, or focal length multiplier of an image sensor format is the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference.
How is it calculated?
The crop factor of a camera is determined by dividing its diagonal dimension by the diagonal dimension of a 'full-frame' sensor, 43.3mm. For example, the Raspberry Pi HQ camera has a sensor size of 6.287mm x 4.712mm. Using the Pythagorean theorem, we can determine that the diagonal size of this sensor is 7.85mm. Now, taking 43.3mm and dividing it by the number we just found, 7.85mm, we get a crop factor of 5.5x.
So, what does all this mean? Well, because the focal length for just about any lens uses a 43.3mm diagonal sensor as a reference point, a much smaller sensor with the same lens only capturing the center of the image would make the image appear much more zoomed in. The image below compares full-frame sensors with APS-C sensors. As you can see, the smaller APS-C sensor will have a narrower field of view and will appear more zoomed in.
So, what does all this mean? Well, because the focal length (the field of view, sometimes just referred to as the zoom) uses a 43.3mm diagonal sensor as a reference point, a much smaller sensor with the same lens would only capture the center of the image. The image below compares full-frame sensors with APS-C sensors. As you can see, the smaller APS-C sensor will have a narrower field of view and will appear more zoomed in.
Crop factor and video
Since the CSI connector in the Raspberry Pi transfer the Bayer data from every single one of the 12.7 million pixels on the Pi sensor 30 times a second,
raspividyuv both take the center 1920x1080. This effectively crops the image, and for the Pi HQ camera, this is an especially large issue. When shooting a video, the Pi HQ Camera uses around 3mmx1.7mm of the sensor, giving it a crop factor of 12.5x. This isn't really an issue with the other Raspberry Pi cameras, as they have very wide-angle lenses to counteract this, but with the HQ camera, this can be very problematic.
Here are 3 images. The first was taken with a full-frame camera at 50mm.
The second has a 5.5x crop applied in editing, giving it a focal length of 275mm. This is the same crop factor the Raspberry Pi HQ camera has at full resolution when taking a photo.
The third image has a 12.5x crop applied, which is the crop factor you'd experience when taking a video. The focal length is effectively 625mm.