Understanding The Crop Factor In Cameras Determines Your FoV (Field of View)
This is an interesting topic in photography since it has to do with the camera. When shooting, I used to think any camera would do, but then there is the crop factor to consider. When it comes to digital photography, camera sensors come in different sizes and this is where the crop factor comes into consideration for photographers when choosing what camera and lens to shoot with.
Two important elements that are important in crop factor are the camera’s sensor size and the len’s focal length. The sensor is what captures the image, while the lens is what projects the image to the sensor in digital photography. These two elements determine the crop factor in cameras and we will discuss them deeper in this article.
The Camera Sensor
Today’s cameras are built using the 35 mm format as the reference. This was the imaging format for photography prior to digital sensors. It was the size of the film used with legacy cameras that follows a 36 x 24 mm size. Camera makers have used this size for building camera sensors, which replaced film in digital photography. In the early days of digital cameras, it was a challenge making the sensor sizes match the size of 35 mm. The sensors that support the 35 mm size were called full frame sensors and they were rather expensive as a consumer product. This led to the development of smaller sensor sizes that allowed camera makers to produce a more affordable alternative for the market. The only issue is that they were not full frame but cropped sensors.
Despite smaller and more affordable sensors, this created a problem. When you capture an image with the smaller sensor size, it appears chopped off around the edges resulting in what appears to be smaller frame around the image. What is actually happening is the Field of View (FoV) of the captured image was getting cropped. Therefore, the image captured is not the same as its 35 mm equivalent.
Full Frame vs. Cropped Sensor
Full frame sensors fully support the 35 mm format, while cropped sensors did not. They have a crop factor that is smaller than the 36 x 24 mm format. Why does the image appear to be more cropped with smaller sensors? It has to do with the way the image is projected from the lens to the sensor. The lens is circular, but the sensor is rectangular. As long as the sensor is large enough to capture the circular image coming through the lens, then it covers a larger FoV. Therefore, with smaller sensor sizes it will not be able to capture the full circular image in the same way as a larger sensor.
A full frame sensor will always have a crop factor of 1, since it is the reference for all other sensors. A type of cropped sensor called APS-C (Advanced Photo Sensor type C) has a crop factor of 1.5. You can follow the chart below as a reference of the crop factor numbers of different types of sensors relative to the 35 mm full frame sensor.
Cropped sensor cameras use a crop factor number (specified by the manufacturer) multiplied with the focal length (length of the lens) to get the FoV equivalent focal length relative to a full frame sensor.
f = crop factor x focal lengthTo better understand it, let us take for example an APS-C Nikon camera using a 50 mm lens.
f = 1.5 x 50 = 75This means that when shooting with a cropped sensor with a 50 mm focal length lens, the equivalent of it to a full frame sensor would be a 75 mm lens. To explain further, if you were to take a photo with a 50 mm cropped sensor and a 75 mm full sensor camera from the same distance, it would produce similar results in FoV.
Deriving The Crop Factor Number
The crop factor can be calculated from the Pythagorean Theorem.
a² + b² = c²You get the diagonal of the crop sensor using the Pythagorean Theorem and then taking the square root of the number.
SQR(a² + b² = c²)Thus the crop factor can be defined as the ratio of the 35 mm sensor size relative to the cropped sensor size, or the cropped sensor size in relation to a full frame 35 mm sensor. In this case we take the diagonal of the 35 mm sensor with that of the cropped sensor size. Let us do another example.
Full Frame Sensor: 36 x 24 mm = SQR(36² + 24² = 1872) = 43.27
APS-C Sensor : 25.1 × 16.7 mm = SQR(25.1² + 16.7² = 908.9) = 30.14Crop Factor = 43.27 / 30.14 = 1.435
The value can be approximated to 1.5 as the crop factor number. Since not all sensor sizes are the same under the APS-C type, they are grouped under the same class and therefore use the 1.5 crop factor number. For example some Canon APS-C sensor sizes are 22.2 x 14.8 mm, while the offerings from Sony, Pentax, Fujifilm and Nikon (DX) vary from 23.5 x 15.6 mm to 23.7 x 15.6 mm (Source NewAtlas). The value of 1.5 is like an average number for these sensor’s crop factor number.
Synopsis
Knowing the crop factor gives photographers an idea about the FoV they can capture from their camera. Full frame cameras are the most like 35 mm when it comes to the image results. Cropped sensor cameras cannot match the FoV of a full frame sensor, unless you take the crop factor into consideration. A cropped sensor camera with a certain focal length can take a similar (not identical) image produced by a full sensor camera with a different focal length at the same distance.
From our example we can see that when shooting with a 50 mm cropped sensor, you have the equivalent of a 75 mm full frame sensor shot at the same distance. The images are similar but never exactly identical because larger sensor sizes will tend to produce better results (there are many factors to consider). These numbers are trivial for most photographers as many don’t need to know this when taking photos in every day life. For the photographer who works with different cameras and lenses, this is something to consider since it provides information about the FoV you are going to get when capturing an image.
