# Crop Factor (CF) or Cropping Percentage (CP)

This post has an explanation of the ‘Crop Factor’ (CF) which I’ve started displaying with the photographs. I wanted to include with the photographs metadata how much it was cropped. I’ve gotten questions about it, and I often don’t remember how much I cropped a photograph.

Contents

# Definitions

The amount of cropping, and all the photograph metadata for that matter, doesn’t really matter much to the viewer of the photograph. They can evaluate whether they like the photograph based on its merits without knowing anything about the cropping, shutter speed, aperture, focal length, etc. However, to the photographer its interesting information to know how the picture was created.

The amount of cropping is, I think, important information about the photograph. With no cropping, the focal distance tells you something about how far away the subject was. With cropping, it seems to me that the focal distance only tells part of the story. Cropping is equivalent to multiplying the focal length by a factor. Cropping also reduces the resolution of the picture, which impacts how much detail you can make out, and how large the picture can be blown up without appearing blurry, grainy, or pixelated.  Cropping is sometimes referred to as ‘digital zoom’ because you magnify the picture digitally rather than with the lens, at the expense of losing resolution.

I did a little bit of web research on how to measure cropping. I found out that there isn’t a standard definition of it. Lets say that the original picture is Wo X H0 pixels, and after cropping its Wc X Hc pixels. Some people use the formula:

Definition 1:

CroppingPercentage1 = (Wc * Hc) / (Wo * Ho) * 100

Definition 1 is the percentage reduction in total pixels. While it is logical, it isn’t intuitive to me, and it doesn’t represent what I want to know. If I divide the height of a subject by 2, then it seems to me that the cropping should be 50%, which is Hc/Ho. So I have:

Definition 2:

CroppingPercentage2 = Hc/H0 * 100

Since I maintain the aspect ratio, both height and width would be reduced by 50%. It’s easy to interpret when viewing the picture. If I use Definition 1, I would display a cropping percentage of 25%, which I think can be misleading.

When I crop I almost always maintain the aspect ratio. If I don’t, then the ratios Wc/Wo and Hc/Ho will be different. I think the best way to handle this is to display the minimum of the two ratios.

Definition 3:

CroppingPercentage3 = minimum(Hc/H0, Wc/Wo) * 100

Rather than using a percentage, I could use a factor to multiple the focal length by to get the ‘equivalent’ focal length. I’ll call it the ‘Crop Factor’ (CF). The crop factor is just the inverse of the cropping percentage from Definition 3.

Definition 4:

CropFactor = maximum(Ho/Hc, Wo/Wc)

For example, if I crop by 50% using Definition 3, then the CF is 2 (i.e. 1/50 * 100). If CF=2, and the focal distance is 300 mm, then the equivalent focal distance is 300 * 2 = 600 mm.

I’ve decided to display both the CF and the CP with the following format: CF = <CF> (<CP>%). For example if Definition 4 gives 4.3, then I’ll display: CF = 4.3 (23%).

Here are features of this that I like:

1. It’s easy to apply to a picture being viewed. For example, for a Cropping Percentage of 50%, you can easily understand that the original picture was twice as high and twice as long.
2. It’s easy to know how large you can blow up the picture. This is usually given by the pixels per inch. A common guideline is about 115 pixels per inch. For example, I know that the Canon 7D sensor is approximately 5000 X 3500 pixels (it’s 5184 X 3456 to be exact).  I know that to blow a picture up to 20 x 30 inches (I’d have to like it a lot :)), then I need a resolution of about 3400 x 2300, so I can only crop by 3400/5000 * 100 = 68%. If I wanted an 8 X 12 inch, then I could crop by 28%.
3. It’s easy to compute the equivalent focal distance. For example, say the lens focal distance is 200 mm, and the cropping factor is 2. Then the focal distance I would have needed to take the picture with no cropping would be 200 * 2 = 400 mm. This is the ‘equivalent’ focal distance to account for cropping.

# Implementation

I wanted to be able to compute the CF automatically in the software based on metadata. Unfortunately I couldn’t find any meta data that gave me the information. For now I decided to use the metadata field called ‘User Comment’, which is available in Lightroom. I don’t know what that field is for, and I don’t use it for anything now, so I’ll use it. I may decide later that I need User Comment for something else, and not to use it for the cropping information. I use the format: ‘keyword:value ;’, where the keyword is ‘crop’, and the value is W x H, and the delimiter between keyword value pairs is ‘;’ or ‘,’. Right now I only have one keyword, but I made it flexible if I need it for something else in the future. For example, in Lightroom I would put the following in the User Comment field: crop:2603×1736. The software would then compute the string “CF = 2 (50%)”. Note that this uses the camera’s sensor resolution of WoXHo = 5146X3456.

I added software in my WordPress theme to extract the crop value and then compute and display CF and CP based on the resolution of the camera sensor.

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