Why do 1/3-stop aperture values look uneven, like f/8, f/9, f/10, f/11, f/13, f/14, f/16, f/18?

Asked 7/29/2018

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I’ve noticed that 1/3-stop aperture markings don’t increase by equal whole numbers. For example, the sequence goes f/8, f/9, f/10, f/11, f/13, f/14, f/16, f/18, so sometimes the jump is 1 and sometimes it’s 2. Why are these aperture numbers unevenly spaced?

Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0

Photography Stack Exchange contributor

7y ago

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For f/stops, there is a precise multiplied difference of 1.122462 X intervals (cube root of √2) between all third stops. The precise third stops are actually numbers like 8.98 or 10.08. My meaning of the Precise Numbers is of course the theoretical precise goal numbers that the camera designer certainly aims for. There can be no question about those (even if the physical camera mechanisms may not necessarily be precisely accurate to as many decimal places). But the nominal numbers that are marked and shown are arbitrarily rounded to numbers like 9 or 10, but the camera and lens design tries to actually compute with the actual precise values.

Precise Nominal Stop 8 8 Full 8.98 9 ⅓ 10.08 10 ⅔ 11.31 11 Full 12.7 13 ⅓ 14.25 14 ⅔ 16 16 Full

The same concept (of there being precise and nominal values) is true of f/stops, shutter speeds, and ISO. For shutter speed and ISO, then thirds are 1.259921 X intervals (∛2).

These are valid results, but not the fundamental definition, and complete detail is shown at my site at https://www.scantips.com/lights/fstop2.html

Originally by user38978. Source · Licensed CC BY-SA 4.0

user38978

7y ago

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AI Answer

Generated from our catalog & community — verify before relying on it.

Because f-stops are not based on adding equal numbers — they’re based on multiplying by a constant ratio.

Each full stop changes by a factor of √2 (about 1.414), and each 1/3 stop changes by the cube root of √2 (about 1.122). So the actual 1/3-stop values between f/8 and f/16 are approximately:

f/8.00, f/8.98, f/10.08, f/11.31, f/12.70, f/14.25, f/16.00

These are then rounded for display/marking to simpler nominal values:

f/8, f/9, f/10, f/11, f/13, f/14, f/16

That rounding is why the visible numbers seem to jump unevenly. The spacing is even in terms of exposure change, not in terms of arithmetic difference between the printed numbers.

So f/11 to f/13 is the same 1/3-stop exposure step as f/13 to f/14 — it just looks uneven because the true values are irrational numbers that get rounded.

UniqueBot

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7y ago

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