The Crop Factor Explained

Teaching in the Career Training, Workshops and Photo Weekends programs for RMSP I get a lot of questions. (Bring ‘em on, I love questions!)  One equipment-related topic seems to be more of a stumbling block for new photographers than any other.  At some point we’re all told that our lenses are going to perform differently from camera to camera.  Friends, camera store employees and magazines throw around words like crop factor and explanations are given, but many people still are left scratching their heads.

I’m going to try to break it down for you in hopes that it will clear things up.  Hold on tight because it’s gonna seem like math class for a while.  If nothing else, enjoy the pictures of the cute kid.

Here it goes…

Before the days of digital SLRs, lenses were pretty straightforward.  A 100mm lens was a 100mm lens.  Nowadays the same lens will behave very differently based on the camera on which the lens is mounted.

This phenomenon is commonly called Crop Factor or Field of View (FOV) crop.  To understand what’s going on we first need to review a few basics:

 

Field of View describes the amount of your scene a given lens takes in.

  • A wide angle lens takes in large amount of the scene.
  • A telephoto lens takes in a very narrow part of the scene

 

How your Lens Works…well kind of.

Your lens is a cylinder that focuses light inside your camera, which is probably not a surprise to you.  Being a cylinder, your lens projects a circle of light onto the digital sensor in the back of your camera (upside down and backwards of course, but that’s for another article).  This is called the image circle. (fig. 1)

Figure1

Figure 1

 

Film and Digital Sensors

Your digital sensor sits inside the image circle just as your film did back in the day.  The lens and your DSLR camera body were designed based on Film SLR dimensions and the need to cover a piece of 35 mm film with the image circle.  The image circle was projected onto the film so that most of the circle was recorded by the rectangular piece of film. A full frame digital sensor is the same size as a piece of film (approx. 1”x1.5”) and, as a result, takes in the same amount of the image circle. (fig. 2)

Fig2

Figure 2

Digital Sensors and Their Sizes

A full frame digital sensor doesn’t alter the field of view of the lens because it fills the image circle in the same way that a piece of film did. Not all digital sensors are the same size, however, and this affects the Field of View that your lens takes in.

The two most common sensor sizes are “Full Frame” and APS-C or “crop sensor”.  An APS-C sensor measures roughly .8”x.5 inches, or half the length and width of a full frame sensor.  The image circle projected by a given lens remains the same on all cameras but the APS-C sensor takes up a smaller area within the circle. When placed inside the same image circle, the APS-C sensor will take in significantly less of the image circle than the Full Frame sensor.  (Fig. 3)

Fig3

Figure 3

So by using the same lens on a camera with an APS-C sensor you will get an image with a Field of View that is narrower than with a Full Frame Sensor. (Fig. 4)  This is due to the fact that the smaller sensor records less of the image circle.

 

Fig4

Figure 4

Crop Factor

Here’s another way of thinking about it…as your sensor gets smaller it will result in an image that appears like it has been taken by a lens with a longer focal length because the field of view is getting more narrow.  This change in the Field of View of your lens can also be called your effective focal length.  To determine your effective focal length you must first know the crop factor of your sensor.

Knowing the crop factor of your camera is pretty straightforward; specific cameras have specific crop factors.  Below are some common cameras and their associated crop factors.

 

Camera Crop Factor
Nikon D5200, D7100 (APS-C) 1.5
Nikon D3s, D4, D800, D600 (Full Frame) 1
Canon 60D, 70D, 7D, Rebel (APS-C) 1.6
Canon 1Dx, 5D mkIII, 6D (Full Frame) 1

 

Determining your effective focal length is a matter of following the formula below.

 

Actual Focal Length   X   Crop Factor   =    Effective Focal Length

 

So if you put the same 100mm lens on a Nikon D800 and a D7100 you will get the following effective focal lengths

 

Camera                        Lens                        Crop Factor                        Effective Focal Length

Nikon D810                   100mm     x                     1                                                100mm

Nikon D7200                 100mm     x                    1.5                                              150mm

 

Okay, so how does all this affect you? When buying a new lens (you know you want one and it’s just a matter of time) you’ll need to consider the crop factor of your camera and the resulting effects on focal length.  A 24mm lens will end up with an effective focal length of 36mm on most crop sensor cameras.

To find out which courses Tony is teaching in 2016, click here!

 

 

8 thoughts on “The Crop Factor Explained

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John Davis

Hi Tony, thanks for the article. I am in my 60s and I go back to the film days and the rules of the film days. One rule I think I remember is that an 85mm lens was a good choice for portrait work using 35mm cameras. Using the information in your article and rearranging the math, I calculate that a 53mm lens on a Canon 7D would be about right for portrait work. Am I correct?
Thanks,
John in Spokane.

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Sarah Chaput de Saintonge

Hi John!

Yes, you are correct in thinking that a roughly 50mm lens will create images that appear to have been taken with an 85mm lens. Great math! An 85mm lens is the perfect lens for beautiful, smooth portraits, and you will be very happy with that 50mm equivalent. The 7D is a wonderful camera, too. I used it for years! Also, if you’re looking to buy a 50mm lens soon, I would recommend the Sigma 50mm F1.4 DG HSM Art. It is currently ranking as sharper than the Canon 50mm lenses, and is a decent price as well. I own that lens, and it is by far my favorite lens that I’ve ever owned.

Good luck shooting, and Happy New Year!

Keith MacMurdie

It might be helpful for people to see one more figure, that is a figure 5.
Figure 4 shows the “final” images as two different sizes.
However, after processing images are the same size with the crop photo being more “close up”.
An added figure would help demonstrate the telephoto effect of the crop sensor.
Just a thought.

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Sarah Chaput de Saintonge

Thanks for the tip, Keith! That’s a great idea that we will pass along to Tony. Happy New Year!

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PsyDocTms

Tony, I really appreciate the article. It raised a question which I hope you or your colleagues can answer. The question goes to why? I totally understand that in the movement from a film based 35 mm camera to a digital SLR that what you call a full frame sensor would have been developed. From 35 mm to 35 mm — duh. So why did Nikon and Canon develop a smaller sensor? My assumption over the years is that this was a purely economic, marketing decision … to have a pro line and a non-pro line … but it’s hard to imagine that cranking up production lines to manufacture a smaller sensor would have made sense on its own. Do you know the history here?

Forest Chaput de Saintonge

As far as Canon is concerned, I’m unsure of the reasoning behind both sensor sizes. It could be marketing, or it could be that in the past it was much harder to make a high-quality large sensor. It took Nikon much longer to make a full-frame digital camera and it was rumored for quite some time that their lens barrel bayonet mount was too small to accommodate a full-frame sensor. Full-frame sensors require more than just 35mm of space because of the necessary electronics that must be positioned on the edges of the CCD or CMOS array. It was only as the technology became smaller that they were able to fit it in the smaller mount. This of course hasn’t been confirmed by Nikon but it was definitely a common idea a few years ago.

bruce hyman

wait a minute. the angle of view of a lens depends on its focal length, period. and that is independent of the sensor. so a 2mm lens with a tiny sensor is a *very* wide angle lens, with resulting foreshortening, etc. just *look* at the nose on a portrait taken with a 50mm lens on a DX camera vs a 75-90mm lens on an FX.

Forest Chaput de Saintonge

That’s exactly right Bruce. In your example, the 2mm lens would “look” like a normal lens but have the depth of field of a 2mm lens. It would also have the same distortions associated with a 2mm lens. However those distortions are greatly reduced because we are only using the very center of the lenses light circle.

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