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Is there a formula to calculate DOF?

Is there an easy way to establish, on paper, which of these two lenses, shot wide open and with the same subject size in frame, would result in a shallower DOF?

I've tried using some of the online calculators but got a bit stuck because the 85 would need a larger camera-subject distance to get the same subject size, but has a longer focal length, but a smaller aperture.

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Assuming you use the Canon 550D and using the online depth of field calculator following calculations can be made:

50 mm f1.4

Focal length: 50mm
F-stop: f/1.4
Subject distance: 3m

Depth of field
Near limit: 2.91m
Far limit: 3.1m
Total: 0.19m

85 mm f1.8

Focal length: 85mm
F-stop: f/1.8
Subject distance: 3 * (85/50) = 5.1m

Depth of field
Near limit: 4.89m
Far limit: 5.12m
Total: 0.23m

More on subject distance with different focal lengths can be found in this answer.

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  • \$\begingroup\$ Thanks. Is it therefore true that subject size in the frame varies proportionally with subject-camera distance? \$\endgroup\$
    – Rich
    Jan 24, 2013 at 13:26
  • \$\begingroup\$ I suspect you've got a copy-and-paste typo in your second table: should the focal length be 85mm and the f-stop f/1.8? (I would just edit your answer, but making those changes didn't hit the 6 character limit...) \$\endgroup\$
    – Philip Kendall ♦
    Jan 24, 2013 at 13:42
  • \$\begingroup\$ @PhilipKendall Thanks, was a copy-paste typo indeed. \$\endgroup\$
    – Saaru Lindestøkke
    Jan 24, 2013 at 13:43
  • \$\begingroup\$ @Rich I'm not sure I understand the question. How could it vary non-proportionally? \$\endgroup\$
    – Saaru Lindestøkke
    Jan 24, 2013 at 13:44
  • \$\begingroup\$ Well, "proportional" means that if you double one variable, you double the other. In this case, it's certainly not proportional: if you double the subject-camera distance, you don't double the subject size in the frame - to a first order approximation, you half it. \$\endgroup\$
    – Philip Kendall ♦
    Jan 24, 2013 at 13:52

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