All standard lenses project an imaging circle onto a rectangular sensor. The crop factor describes how far a given sensor extends into this circle relative to another reference sensor. Higher values mean less of the imaging circle gets recorded, and vice versa.
In the stills world, the crop factor is almost always given relative to traditional 35mm frames. Since stills use a variety of aspect ratios in both portrait and landscape orientation, the crop factor is calculated as the ratio between the diagonal dimensions of each sensor.
However, with motion, footage is almost always captured in landscape orientation, and wider aspect ratios are typically created by masking out the top and bottom of the on-screen image. For this reason, the crop factors in this article and our online tools are calculated based on the ratio between sensor widths. This is also a reason why cinematic resolution is specified by horizontal pixels (such as 4K), as opposed to megapixels or vertical resolution (such as 1080P).
Perhaps the most apparent consequence of a higher crop factor is that lenses appear as though they had a longer focal length. This is particularly useful for achieving more reach with an otherwise medium telephoto lens, such as when capturing wildlife, surfers on distant waves or sports action within a large playing field.
However, another less apparent consequence is also important. At the same focal length, a higher crop factor means one has to move further away in order to achieve the same subject framing. Alternatively, one could remain in the same position and use a wider angle lens. Either way, the depth of field increases as a result.
The crop factor can also influence image quality. A larger sensor may mean correspondingly more light-gathering area, in which case many of the usual technical considerations apply (see Bayer sensor strategy). This is a primary difference between high-end digital cinema cameras and more consumer-oriented camcorders. However, the crop factor also affects image quality independent of underlying sensor technology.
The size of an imaging circle relative to the sensor is another key consideration. At one extreme, if the sensor diagonal is substantially larger than the imaging circle diameter, the edges of a frame could appear dark. At the other extreme, a much smaller sensor would mean light from only the central portion of an image is recorded, in which case image quality is also compromised since the remaining image has to be enlarged more for on-screen display. Although these scenarios are not representative of typical usage, they can help visualize the limits of crop factors.
Fortunately most camera and lens combinations lie between these two extremes. However, the image quality is still influenced more subtly, in part because imaging circles do not end abruptly at their exterior. Instead, image quality declines from the center outwards. Then, at the very edges of an imaging circle, quality typically degrades rapidly and the image eventually disappears. Although the precise circle size and rate of degradation varies depending on the particular lens model and T-stop setting, all lenses follow this same trend.
See full details and examples of sensor crop factors on the RED 101 Article: https://www.red.com/red-101/sensor-crop-factors