Crop factor math, aperture, focal length and sensor size

Crop factor math, aperture, focal length and sensor size

Let’s see how crop factor math works. If you are using APS-C or Micro Four Thirds camera or even some camera with smaller sensor, you can easily calculate your real focal length and depth of field. Bear in mind that most versatility you will have with full frame sensor and large aperture lens. This is the first post on my blog. It is also a boring subject for me because everybody is talking about and not many people want the learn this. Despite it is very, very simple, people still find this controversial and spooky.

The problem is made not by users, not by honest engineers silently working and making us better tools and toys, but, of course, by marketing department people. With the simple idea of telling us one part of the truth good for them and hiding another part of the “truth” that is bad for them.

The problem

Digital sensors are made in any size and shape, but that can be easily fixed with little honest math. We have to go back in the days when film ruled. Although other sizes of film existed, even in everyday use, 35mm standard was a universal language. 35mm means 36x24mm film size. So you will always get same framing and depth of field when you use same settings.

Crop factor became much more important in a digital age. We have a long way until we get to the full frame 36x24mm sensors and even today that sensor size is reserved for, at least, enthusiasts. Majority of cameras still use a smaller sensor and that is why crop factor applies. Some companies actually make strategy on their smaller sensors telling us that we are getting reach with a smaller lens. Not telling us that we are loosing in terms of depth of field management. And high ISO performance because of the smaller sensor.

Measuring crop factor

To make things simpler, I will say that crop factor represents how much width of the sensor is smaller than 36mm. Here we have a small problem with shapes of the sensors. For example, Micro Four Thirds sensors have 2x crop, but 4:3 aspect ratio. If we want to make standard 3:2 picture with that sensor, crop goes up to 2.08x. I will stick to the 3:2 aspect ratio, because that makes math easier and the situation more realistic. Without any desire to make Panasonic or Olympus worse. Real crop factor is measured with diagonal of the sensor. But, let’s say, realistic crop factor should be measured using the width of the sensor.

The confusion is applying crop factor only to the focal length of the lens. But not many people apply the crop factor to the aperture of the lens. With compact cameras, the problem is even prominent, because it is not easy to find crop factor at all. Applying crop factor to the aperture is a way of getting an idea how much depth of field you are going to get. In terms of exposure setting, you should not apply crop factor. Only when you need to get a realistic picture of the depth of field control.

Crop factor math

For example, 50mm f1.8 lens on full frame is going to be around 80mm f2.9 lens on 1.61x crop APS-C (Canon) camera and around 104mm f3.7 lens on 2.08x crop Micro Four Thirds camera. Another way around you will need 31mm f1.1 lens on APS-C or 24mm f0.9 lens on Micro Four Third to get same aesthetics of the 50mm f1.8 full frame picture. You always need to multiply crop factor on both focal length and aperture.

Notice that how spoken and written word is often different. For Canon G7 X camera everybody saying that has 24-100mm f1.8-2.8 lens. Actually, this camera has 8.8-36.8mm f1.8-2.8 lens or, when you calculate, 24-100mm f4.9-7.6. Because the width of G7 X sensor is 2.72x narrow then Full Frame 36x24mm sensor. For the 300mm f4 Micro Four Third lens, many people are going to say that is 600mm lens, without adding is then f8 lens. You can say “it is 300m f4 lens” or “it is a 600mm f8 lens in 35mm format,” but you cannot say “it is a 600mm f4 lens.”

Examples made from the same distance

 

Canon 1D X Mark II (full frame 36x24mm 1x crop) 50mm f7.1 ISO 6400

 

Canon 800D/T7i (APS-C 22.3×14.9mm 1.61x crop) 30mm f4.5 ISO 3200 – equivalent 48mm f7.3

 

Canon G7 X (13.2×8.8mm 2.73x crop) 18.1mm f2.5 ISO 800 – equivalent 49mm f6.8

As you can see, we use 50mm, 30mm, and 18mm focal length and from the same point, we have the same image, thanks to different sensor size. But more interesting is aperture. The smallest sensor has aperture open up to f2.5 but still makes the same depth of field as the closed f7.1 aperture on Full Frame. APS-C is obviously in the middle with f4.5 aperture and identical depth of field. This is proof that you just must multiply both focal length and aperture by crop factor on any camera with a smaller sensor than 36x24mm Full Frame.

One more thing, somebody is going to say that achieving more depth of field on large sensor camera means that you have to close aperture more, therefore increase ISO and noise, but actually larger sensor produces less noise than the smaller sensor, even in increased ISO to achieve same depth of field and often even more. Here is an example.


1. 1x crop 20MP 100% crop sensor ISO 6400
2. 1.61x crop  24MP>20MP 100% crop ISO 3200
3. 2.73x crop 20MP 100% crop ISO 800


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2 thoughts on “Crop factor math, aperture, focal length and sensor size

  1. […] subject in the world. With 100mm f2.8 it is better than any RX100 camera in this category. You have this and this blog posts on my website showing why G7 X is great for separating background. Even better […]