A term that appears in connection with digital cameras is the "crop factor". Often this is seen as an extension for focal length - but that is wrong! In digital photography, the crop factor is the ratio of the film format’s diagonal, with respect to the sensor diagonal of another recording format.
Let’s look back to the time of analogue photography. The 24 x 36 mm (known as 35 mm format) became the standard for recording light information. With the advent of digital technology, a digital sensor has taken the place of film. The sizes of the digital recording components vary depending on manufacturer and camera model. Sensors, whose dimensions are similar to those of the analogue 35 mm format, i.e. 24 x 36 mm are referred to as full-frame sensors. In this case the sensor diagonal is about 43 mm. In many cameras, especially compact cameras, even smaller sensors are installed.
Due to the different formats, the corresponding sensor diagonals are usually smaller than that of the 35 mm format. Let’s consider an APS-C sensor, which has a size of 22 x 15 mm. The sensor diagonal can be determined based on the sensor dimensions. By using the Pythagoras Theorem for rectangular triangles (a2 + b2 = c2), the sensor’s diagonal can be calculated. In the case of the APS-C sensor this is about 26.6 mm.
Digital sensor formats are still generally set in relation to the analogue 35 mm format. In this context, the term crop factor can be found.
The crop factor describes the aspect ratio of the diagonal of two recording formats.
Here, the 35 mm format is usually the comparison format. To determine the ratio of the recording formats, the diagonal of the film format is set in relation to the diagonal of the sensor. This gives the aspect ratio, the so-called format factor. This term is less common. The more common term is "crop factor".
Typical crop factors are 1.5x,1.6x and 2x (MFT)
Why does the focal length seem larger?
Sometimes the crop factor is understood as a focal length extension factor. This would mean that, for example, a 35 mm lens would have a 56 mm focal length when used on an APS-C camera (crop factor 1.6). This assumption is wrong. A lens is an optical system whose actual focal length cannot change due to a calculated size factor.
Where does the idea of the supposedly longer focal lengths come from and how is this connected to the crop factor? To illustrate this, we consider a lens that is calculated for 35 mm format. The lens produces an image circle with a diagonal of just 43 mm and can thus fully illuminate the sensor surface of a full-frame camera. The image circle also covers the receiving surface of a smaller APS-C sensor.
Consequently, 35 mm lenses can be used on both full-frame as well as APS-C size cameras. The bayonet connector (lens mount) determines the body-lens-compatibility. For our example, we take a fixed focal length, which can be used both on an APS-C as well as a full-frame camera from the same manufacturer. With both cameras, we will create a recording with the same shooting distance from the subject and compare them with each other.
While the actual focal length remains unchanged, the viewing angle will change, i.e. the angle that results between the optical center of the lens and the imaging sensor of the camera. This does not only depend on the focal length of the lens, but also on the sensor format of the recording system.
This gives the impression that the recording was done with a larger focal length. Therefore, logically, one could speak of an "apparent focal length multiplier" because the focal length of the lens remains fixed.
35 mm format equivalent focal length
Consider the following diagram to illustrate the relationship between the focal length and the angle of view.
If an APS-C sensor is used, the angle of view becomes narrower due to the smaller recording surface. By putting this smaller angle of view in relation to the 35 mm format, it would correspond to a larger focal length and is referred to as the 35 mm equivalent focal length. This is where the crop factor comes into play. It acts as a multiplier, with which the 35 mm equivalent focal length can be calculated. That is the focal length, which would result in accordance with the angle of view for inclusion in the 35 mm format. In other words, to achieve the same image impression with a full-frame camera as with an APS-C camera, a larger focal length must be used.
35 mm focal length equivalent = Crop Factor * actual focal length
So be careful! Manufacturers of interchangeable lenses always label their lenses with the focal length corresponding to the 35 mm format. Therefore, if a lens is used on a camera that has a smaller image circle than the 35 mm format, the according crop factor has to be taken into consideration. On cameras with integrated lenses (mainly compact cameras), some manufacturers calculate and label the lenses already with the 35 mm equivalent focal length.