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 Analysis  of  the  “Pixel  Density  Advantage” 

 

36 megapixel "theoretical" full frame camera compared with a

 

24 megapixel "theoretical" APS-C camera

 

 

 

Summary of approximate mathematical relationships between image size, pixel density, and pixel size

 

 

This summary should be read in conjunction with the full explanatory article that you can see  here. Note that the analysis on this page does not include a discussion of the various complex issues that can arise in practice when estimating pixel density and the the pixel pitch or area of individual pixels. It is recommended that you study a detailed technical article if you would like to become familiar with these issues. For example, you may find this  DPR forum discussion  about pixel density and pixel size to be helpful. Therefore, the calculations set out below are presented for the purpose of calculating only a very approximate measurement of pixel density, pixel pitch, and the area of one pixel, which can be used for comparing the approximate mathematical relationships between image size and the pixel density and pixel size of different cameras.

 

This summary provides an example of how to apply the template that is published  here. In this theoretical template, the reconciliations between the percentages shown for pixel density and pixel size, work out exactly, only because the number of megapixels on the sensor is exactly the same as the image width in pixels, multiplied by the image height in pixels.  In addition, the image width divided by the image height, gives the same answer as the sensor width divided by the sensor height. In the theoretical template, the approximate area calculation for the size of one pixel is exactly equal to the pixel pitch squared. In addition, the approximate area calculation for the pixel density is exactly equal to the linear pixel density squared. These relationships are present in the theoretical example that follows.

 

The Nikon D800, introduced early in 2012, is an example of a 36mp full frame camera, and  Digital Photography Review  reports that it has image dimensions of 7360 pixels x 4912 pixels and a sensor size of 35.9mm x 24mm.

 

In October 2013, Sony announced its new mirrorless 36mp full frame camera, the Sony Alpha 7R, which also has image dimensions of 7360 pixels x 4912 pixels and a sensor size of  35.9mm x 24mm.

 

The Sony A77 and the Nikon D3200 are examples of a 24mp APS-C camera.

 

However, the cameras referred to below are "theoretical" cameras only and although their specifications are similar to those of the Nikon D800, Sony Alpha 7R, Nikon D3200, and Sony A77, they are  not  identical. Therefore, the results shown below should not be regarded as those that would be obtained when comparing the relevant specifications of the Nikon D800, Sony Alpha 7R, Nikon D3200, and the Sony A77.

 

Note: The information below is not designed to provide information about the quality of images or the quality of the cameras, because these are separate issues.

 

This summary shows that, when compared with a theoretical 36 mp FF camera, a theoretical 24 mp APS-C camera has a linear pixel density that is about 25.5% greater than that of the theoretical 36 mp FF camera. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

Note: If the (full frame) 36 mp FF had the same pixel density as the 24 mp APS-C, it would have approximately 57 megapixels, and image dimensions of about 9231 pixels x 6154 pixels.

 

The following supplementary notes have been designed to give you further information about the calculations that follow:

 

Relationships between crop factor, field of view, photographic reach, image size, pixel density, and pixel size

 

 

Relevant  Specifications of "Theoretical Cameras"

 

24 mp APS-C: Image dimensions: 6000 pixels x 4000 pixels; sensor size: 23.4mm x 15.6mm

 

36 mp FF: Image dimensions: 7353 pixels x 4902 pixels; sensor size: 36.0mm x 24.0mm

 

 

Crop  Factor

 

Approximately 1.54x  (36mm / 23.4mm)

 

 

 

Approximate  Linear  Relationships  of  "Theoretical Cameras"

 

 

Approximate pixel density  (in pixels per linear centimetre)

 

Pixel density in pixels per linear centimetre = image width in pixels  divided by  width of sensor in centimetres

 

24 mp APS-C   =    2564.1   (6000 / 2.34)

36 mp FF          =    2042.5   (7353 / 3.60)

 

Pixel Density Advantage:  24 mp APS-C  is approximately 25.5% greater than 36 mp FF

 

 

Approximate pixel pitch  (in microns)

 

Refer to the reservations  here  about calculating the "true" width and area of an individual pixel.

 

Pixel pitch in microns  = width of sensor in millimetres  divided  by  image width in pixels  multiplied by  1000

 

24 mp APS-C   =   3.900    (23.4 / 6000  x 1000)

36 mp FF          =   4.896    (36.0 / 7353 x 1000)

 

Relationship: 36 mp FF is approximately 25.5% greater than 24 mp APS-C

 

Note: Based on the specifications given above, the 24mp APS-C Nikon D3200 has a pixel pitch of about 3.9 microns (23.2 / 6016 x 1000), the 24mp APS-C Sony A77 has a pixel pitch of about 3.9 microns (23.5 / 6000 x 1000) and the 36mp full frame Nikon D800 has a pixel pitch of about 4.9 microns (35.9 / 7360 x 1000).

 

 

Crop an image from 36 mp FF to the same  field of view  as an image from 24 mp APS-C

 

Gain in image width (in pixels) as a result of the above 25.5% pixel density advantage

 

Uncropped image width of 24 mp APS-C = 6000 pixels

 

Cropped image width of 36 mp FF

to same field of view as 24 mp APS-C      = 4780 pixels  (7353 x 23.4 / 36.0)

 

Relationship: 24 mp APS-C is approximately 25.5% greater than 36 mp FF.

 

 

Crop an image from 36 mp FF to the same  field of view  as an image from 24 mp APS-C

 

Gain in comparable widths of  print sizes  as a result of the above 25.5% pixel density advantage

 

If the uncropped image of 24 mp APS-C (of 6000 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is 30 inches (6000 / 200).

 

If the cropped image of 36 mp FF (of 4780 pixels width) is printed at 200 ppi, the width of the print is 23.9 inches (4780 / 200).

 

Relationship: The net effect of the 25.5% “pixel density advantage” of 24 mp APS-C, is to produce a print at 200 ppi, that is about 6.1 inches wider (or about 25.5% wider) than that produced with the same  field of view  from the cropped image of 36 mp FF.

 

 

Crop an image from 36 mp FF to the same   field of view  as an image from 24 mp APS-C, and compare the changed field of view of 36 mp FF with that of 24 mp APS-C: Assume that a 300mm lens is on both cameras and that the field of view of an uncropped 36 mp FF image is 300mm

 

Field of view of 24 mp APS-C = focal length of lens  x  crop factor of 24 mp APS-C = approx. 462mm  (300mm x 36mm / 23.4mm)

 

Changed field of view of a 36 mp FF image when it is cropped to the same field of view as a 24 mp APS-C image

 

= uncropped image width of 36 mp FF  /  cropped image width of 36 mp FF  x  focal length of lens  =  approx. 462mm  (7353 / 4780  x  300mm)

 

Relationship: The fields of view of 24 mp APS-C and 36 mp FF are the same, that is, approx. 462mm.

 

Note: The image width of a 36 mp FF image, when it is cropped to the same field of view as a 24 mp APS-C image, is approx. 4780 pixels (7353 x 23.4 / 36.0). Click  here  to go to an article titled "Advantages and disadvantages of cropping images instead of using lenses with longer focal lengths". This article gives further details in support of the formulas used above.

 

 

Crop an image from 36 mp FF to the same  image width  as an image from 24 mp APS-C, and compare the changed field of view of 36 mp FF with that of 24 mp APS-C: Assume that a 300mm lens is on both cameras

 

Field of view of 24 mp APS-C is 300mm x crop factor = approx. 462mm  (300mm x 36.0 / 23.4)

 

Changed field of view of a 36 mp FF image when it is cropped to the same image width as a 24 mp APS-C image

 

= uncropped image width of 36 mp FF  /  cropped image width of 36 mp FF  x  focal length of lens  =  approx.  368mm  (7353 / 6000 x 300mm)

 

Relationship: 24 mp APS-C is approximately 25.5% greater than 36 mp FF.

 

Note:  Click  here  to go to an article titled "Advantages and disadvantages of cropping images instead of using lenses with longer focal lengths". This article gives further details in support of the formulas used above.  Click  here  to see a forum discussion titled: "How do you calculate the reach advantage? Sony A900 vs Nikon D3S" Digital Photography Review, Sony SLR Talk Forum, April 2010.

 

 

 

Approximate  Area  Relationships

 

 

Approximate pixel density  (in megapixels per square centimetre)

 

Pixel density in megapixels per square centimetre = number of megapixels on the sensor  divided by  sensor area in square centimetres

 

24 mp APS-C   =   6.5746    (24.0 / 3.6504)         or pixel density in pixels per linear centimetre squared / 1,000,000 = (2564.1 x 2564.1 / 1,000,000)    

 

36 mp FF          =   4.1718    (36.044406 / 8.64)   or pixel density in pixels per linear centimetre squared / 1,000,000 = (2042.5 x 2042.5 / 1,000,000)

 

Relationship: 24 mp APS-C is approximately 57.6% greater than 36 mp FF

 

 

Approximate pixel area  (approximate area of one pixel in square microns)

 

Refer to the reservations  here  about calculating the "true" width and area of an individual pixel.

 

Area of one pixel in square microns = area of sensor in square microns  divided by  the number of pixels on the sensor

 

24 mp APS-C   =   15.2100    (365,040,000 / 24,000,000)  or pixel pitch squared   (3.9 microns x 3.9 microns)

 

36 mp FF          =   23.9704    (864,000,000 / 36,044,406)  or pixel pitch squared   (4.895961 microns x 4.895961 microns)

 

Relationship: 36 mp FF is approximately 57.6% greater than 24 mp APS-C

 

 

Crop an image from 36 mp FF to the same field of view as an image from 24 mp APS-C

 

Gain in image area  (in megapixels)

 

Uncropped image area of 24 mp APS-C = 24 megapixels  (6000 pixels x 4000 pixels)

 

Cropped image area of 36 mp FF

to same field of view as 24 mp APS-C   = approx. 15.23 megapixels  (4780 pixels x 3186 pixels)

 

Relationship: 24 mp APS-C is approximately 57.6 % greater than 36 mp FF

 

 

 

 

Click  here  to go to an index of further camera comparisons showing the mathematical relationships between image size, pixel size, pixel density, and reach etc.

 

Click  here  to go to the index of all the technical articles and blogs on this site.

 

 

 

 

 

 

 

 

 

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