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Analysis  of  the  “Pixel  Density  Advantage” 

 

APS-C  Sony  A6300  (ILCE-6300)  compared  with 

 the  full  frame  Sony  A7R II  (ILCE-7R M2)

 

 

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 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.

 

However, in the practical example that follows, the arithmetical reconciliations demonstrated in the template do not work out exactly because of roundings in the specifications used, and also because of the way the effective number of pixels of the cameras is calculated (that is, the image width multiplied by the image height, does not exactly equal the effective number of pixels published for the cameras). For example, the specifications for the Sony A7R II state that it has approximately 42.4 million effective pixels, and that the image size is 7952 pixels x 5304 pixels. But, when you multiply 7952 pixels x 5304 pixels, you obtain 42.177 million pixels, not 42.4 million pixels.

 

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 the Sony A7R II, the Sony A6300 has an approximate linear pixel density that is about 15.3% greater than that of the A7R II. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

Note: If the (full frame) Sony A7R II had the same pixel density as the (APS-C) Sony A6300, it would have approximately 56 megapixels. In addition, if the Sony A6300 had the same pixel density as the Sony A7R II, it would have about 18 megapixels.

 

 

Relevant  Specifications

 

Sony A6300: Image dimensions: 6000 pixels x 4000 pixels  (approx. 24.3 million effective pixels); sensor size: approx. 23.5mm x 15.6mm

 

Sony A7R II: Image dimensions: 7952 pixels x 5304  pixels (approx. 42.4 million effective pixels); sensor size: approx. 35.9mm x 24.0mm

 

The specifications for the E-Mount Sony A7R II  and the E-Mount Sony A6300 were obtained from  this Sony web site.

 

 

Crop  Factor

 

Approximately 1.5x  (35.9mm / 23.5mm).

 

 

 

Approximate  Linear  Relationships

 

 

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

 

A6300   =    2553   (6000 / 2.35)

A7R II =      2215   (7952 / 3.59)

 

Pixel Density Advantage:  A6300  is approximately 15.3% greater than A7R II

 

 

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

 

A6300   =   3.9167    (23.5 / 6000  x 1000)

A7R II   =   4.5146    (35.9 / 7952 x 1000)

 

Relationship: A7R II is approximately 15.3% greater than A6300

 

 

Crop an image from A7R II to the same  field of view  as an image from A6300

 

Gain in image width (in pixels) as a result of the above 15.3% pixel density advantage

 

Uncropped image width of A6300  = 6000 pixels

 

Cropped image width of A7R II

to same field of view as A6300      = approx. 5205 pixels *  (7952 x 23.5 / 35.9)

 

Relationship: A6300 is approximately 15.3% greater than A7R II.

 

* The "actual" cropped width of a Sony A7R II image is 5168 pixels as roundings etc can cause the above "theoretical" calculation to differ slightly from the actual cropped image width as calculated by the camera.

 

 

Crop an image from A7R II to the same  field of view  as an image from A6300

 

Gain in comparable widths of print sizes as a result of the above 15.3% pixel density advantage

 

If the uncropped image of A6300 (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 A7R II (of 5205 pixels width) is printed at 200 ppi, the width of the print is about  26.03 inches  (5205 / 200).

 

Relationship: The net effect of the 15.3% “pixel density advantage” of A6300, is to produce a print at 200 ppi, that is about 4 inches wider (or about 15.3% wider) than that produced with the same  field of view  from the cropped image of A7R II.

 

 

Crop an image from A7R II to the same   field of view  as an image from A6300, and compare the changed field of view of A7R II with that of A6300:

 

Assume that a 300mm lens is on both cameras and that the field of view of an uncropped A7R II image is 300mm

 

Field of view of A6300 = focal length of lens  x  crop factor of A6300 = approx. 458mm  (300mm x 35.9mm / 23.5mm)

 

Changed field of view of an A7R II image when it is cropped to the same field of view as an A6300 image

 

= uncropped image width of A7R II  /  cropped image width of A7R II  x  focal length of lens  =  approx. 458mm  (7952 / 5205  x  300mm)

 

Relationship: The fields of view of A6300 and A7R II are the same, that is, approx. 458mm.

 

 

Crop an image from A7R II to the same  image width  as an image from A6300, and compare the changed field of view of A7R II with that of A6300: Assume that a 300mm lens is on both cameras

 

Field of view of A6300 is 300mm x crop factor = approx. 458.3mm  (300mm x 35.9mm / 23.5mm)

 

Field of view of an A7R II image when it is cropped to the same image width as an A6300 image

 

= uncropped image width of A7R II  /  cropped image width of A7R II  x  focal length of lens  =  397.6mm  (7952 / 6000 x 300mm)

 

Relationship: A6300 is approximately 15.3% greater than A7R II.

 

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

 

A6300   =   6.628    (24.3 / 3.666)

A7R II   =   4.921    (42.4 / 8.616)

 

Relationship: A6300 is approximately 34.7% greater than A7R II

 

 

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

 

A6300   =   15.086    (366,600,000 / 24,300,000)

A7R II   =   20.321    (861,600,000 / 42,400,000)

 

Relationship: A7R II is approximately 34.7% greater than A6300

 

 

Crop an image from A7R II to the same field of view as an image from A6300:  Gain in image area  (in megapixels)

 

Uncropped image area of A6300 = approx.  24.3 megapixels  (6000 pixels x 4000 pixels)

 

Cropped image area of A7R II

to same field of view as A6300   = approx.   18.06 megapixels  (5205 pixels x 3470 pixels) *

 

Relationship: A6300 is approximately 34.5% greater than A7R II

 

* The "actual" cropped image area of a Sony A7R II image is 5168 pixels x 3448 pixels (17.8 megapixels) as roundings etc can cause the above "theoretical" calculation of 18.06 megapixels to differ slightly from the actual cropped image size as calcuated by the camera.

 

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.