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This question already has an answer here:

I've read the comparison between APS-C and Full Format at

When do the differences between APS-C and full frame sensors matter, and why?

The depth of field is controlled by the circle of confusion, which is the area of which light is spread when hitting the image plane. It gets "blurry" once the circle of confusion is bigger than the pixel size.

Now for a Full Format camera the pixels are significantly bigger compared to an APS-C camera (for example D7100 - 3.9um per pixel vs. D600 - around 6um per pixel), so given the same lenses (as in the linked question), I thought the DOF should be shallower for the APS-C instead, since the smaller pixel size allows only a smaller circle of confusion.

So why is it stated differently in the other question?

marked as duplicate by mattdm, coneslayer, Itai, ElendilTheTall, MikeW Jun 30 '13 at 19:17

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    The accepted answer is not talking about the same focal length, rather about the same subject and framing! The FF is zoomed in. – Unapiedra Jun 30 '13 at 16:03
  • oh, I thought it was same object, same distance, same focal length, and just cropped that subject. – SinisterMJ Jun 30 '13 at 16:11
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    The primary reason has little to do with the relative pixel sizes, but rather the amount of magnification used to print the sensor sized image at 8X10 and viewed at 10" (25cm) by a person with 20/20 vision. The circle of confusion used to calculate DoF is rarely based on pixel size, but is instead based on the ability of a human with a particular visual acuity to detect blur circles as larger than points at the specific magnification provided by the display size and viewing distance.... – Michael C Jul 1 '13 at 3:40
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    ...Most FF cameras have pixel pitches in the 6µm (0.006mm) range, yet the CoC used to compute DoF for an 8X10 print from a FF camera viewed at 10" by a person with 20/20 vision is around 0.025mm to 0.03mm. If you take two photos of the same object at the same distance using the same focal length and crop the FF image down to the size of the APS-C image, there will be no difference in the DoF of the two images providing the CoC is larger than the pixel pitch of either camera, which will almost certainly be the case for all but extremely large display sizes (like large prints or pixel peeping). – Michael C Jul 1 '13 at 3:44
  • The only time the CoC will be defined as the pixel pitch of the sensor is if you are viewing the image at a large enough size to detect the difference between individual pixels. If you are viewing a 100% crop of a 5000X3333 pixel image (16.7MP) on a monitor with a 72dpi pitch, you are looking at the equivalent display size of a 69X46 inch print! – Michael C Jul 1 '13 at 3:52