Editing F-number (section)

=== Fractional stops ===
{{multiple image
 | width = 120
 | image1 = Povray focal blur animation.gif
 | alt1 = Changing a camera's aperture in half-stops
 | image2 = Povray focal blur animation mode tan.gif
 | alt2 = Changing a camera's aperture from zero to infinity
 | footer = Computer simulation showing the effects of changing a camera's aperture in half-stops (at left) and from zero to infinity (at right)
}}

Most twentieth-century cameras had a continuously variable aperture, using an [[iris diaphragm]], with each full stop marked. Click-stopped aperture came into common use in the 1960s; the aperture scale usually had a click stop at every whole and half stop.

On modern cameras, especially when aperture is set on the camera body, f-number is often divided more finely than steps of one stop. Steps of one-third stop ({{1/3}} EV) are the most common, since this matches the ISO system of [[film speed]]s. Half-stop steps are used on some cameras. Usually the full stops are marked, and the intermediate positions click but are not marked. As an example, the aperture that is one-third stop smaller than {{f/|2.8}} is {{f/|3.2}}, two-thirds smaller is {{f/|3.5}}, and one whole stop smaller is {{f/|4}}. The next few f-stops in this sequence are:

<math display=block>f/4.5,\ f/5,\ f/5.6,\ f/6.3,\ f/7.1,\ f/8,\ \ldots</math>

To calculate the steps in a full stop (1 EV) one could use

<math display=block>(\sqrt{2})^{0},\ (\sqrt{2})^{1},\ (\sqrt{2})^{2},\ (\sqrt{2})^{3},\ (\sqrt{2})^{4},\ \ldots</math>

The steps in a half stop ({{1/2}} EV) series would be

<math display=block>(\sqrt{2})^{\frac{0}{2}},\ (\sqrt{2})^{\frac{1}{2}},\ (\sqrt{2})^{\frac{2}{2}},\ (\sqrt{2})^{\frac{3}{2}},\ (\sqrt{2})^{\frac{4}{2}},\ \ldots</math>

The steps in a third stop ({{1/3}} EV) series would be

<math display=block>(\sqrt{2})^{\frac{0}{3}},\ (\sqrt{2})^{\frac{1}{3}},\ (\sqrt{2})^{\frac{2}{3}},\ (\sqrt{2})^{\frac{3}{3}},\ (\sqrt{2})^{\frac{4}{3}},\ \ldots</math>

As in the earlier DIN and ASA film-speed standards, the ISO speed is defined only in one-third stop increments, and shutter speeds of digital cameras are commonly on the same scale in reciprocal seconds. A portion of the ISO range is the sequence

<math display=block>\ldots 16/13^\circ,\ 20/14^\circ,\ 25/15^\circ,\ 32/16^\circ,\ 40/17^\circ,\ 50/18^\circ,\ 64/19^\circ,\ 80/20^\circ,\ 100/21^\circ,\ 125/22^\circ,\ \ldots</math>

while shutter speeds in reciprocal seconds have a few conventional differences in their numbers ({{frac|15}}, {{frac|30}}, and {{frac|60}} second instead of {{frac|16}}, {{frac|32}}, and {{frac|64}}).

In practice the maximum aperture of a lens is often not an [[integer|integral]] power of {{sqrt|2}} (i.e., {{sqrt|2}} to the power of a whole number), in which case it is usually a half or third stop above or below an integral power of {{sqrt|2}}.

Modern electronically controlled interchangeable lenses, such as those used for SLR cameras, have f-stops specified internally in {{frac|8}}-stop increments, so the cameras' {{1/3}}-stop settings are approximated by the nearest {{frac|8}}-stop setting in the lens.{{citation needed|date=December 2021}}

==== Standard full-stop f-number scale ====
Including [[APEX system|aperture value]] AV:
<math display=block>N = \sqrt{2^{\text{AV}}}</math>

Conventional and calculated f-numbers, full-stop series:
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −2 || −1 || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16
|-bgcolor="#CCFFCD"
! scope="row" | ''N''
| 0.5 || 0.7 || 1.0 || 1.4 || 2 || 2.8 || 4 || 5.6 || 8 || 11 || 16 || 22 || 32 || 45 || 64 || 90 || 128 || 180 || 256
|-
! scope="row" | calculated
| 0.5 || 0.707... || 1.0 || 1.414... || 2.0 || 2.828... || 4.0 || 5.657... || 8.0 || 11.31... || 16.0 || 22.62... || 32.0 || 45.25... || 64.0 || 90.51... || 128.0 || 181.02... || 256.0
|}

==== Typical one-half-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −1 || −{{frac|2}} || 0 || {{frac|2}} || 1 || {{frac|1|1|2}} || 2 || {{frac|2|1|2}} || 3 || {{frac|3|1|2}} || 4 || {{frac|4|1|2}} || 5 || {{frac|5|1|2}} || 6 || {{frac|6|1|2}} || 7 || {{frac|7|1|2}} || 8 || {{frac|8|1|2}} || 9 || {{frac|9|1|2}} || 10 || {{frac|10|1|2}} || 11 || {{frac|11|1|2}} || 12 || {{frac|12|1|2}} || 13 || {{frac|13|1|2}} || 14
|-bgcolor="#FFFFCC"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 0.7 || 0.8 ||style="background:#CCFFCC;"| 1.0 || 1.2 ||style="background:#CCFFCC;"| 1.4 || 1.7 ||style="background:#CCFFCC;"| 2 || 2.4 ||style="background:#CCFFCC;"| 2.8 || 3.3 ||style="background:#CCFFCC;"| 4 || 4.8 ||style="background:#CCFFCC;"| 5.6 || 6.7 ||style="background:#CCFFCC;"| 8 || 9.5 ||style="background:#CCFFCC;"| 11 || 13 ||style="background:#CCFFCC;"| 16 || 19 ||style="background:#CCFFCC;"| 22 || 27 ||style="background:#CCFFCC;"| 32 || 38 ||style="background:#CCFFCC;"| 45 || 54 ||style="background:#CCFFCC;"| 64 || 76 ||style="background:#CCFFCC;"| 90 || 107 ||style="background:#CCFFCC;"| 128
|}

==== Typical one-third-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| −1 || −{{frac|2|3}} || −{{frac|3}} || 0 || {{frac|3}} || {{frac|2|3}} || 1 || {{frac|1|1|3}} || {{frac|1|2|3}} || 2 || {{frac|2|1|3}} || {{frac|2|2|3}} || 3 || {{frac|3|1|3}} || {{frac|3|2|3}} || 4 || {{frac|4|1|3}} || {{frac|4|2|3}} || 5 || {{frac|5|1|3}} || {{frac|5|2|3}} || 6 || {{frac|6|1|3}} || {{frac|6|2|3}} || 7 || {{frac|7|1|3}} || {{frac|7|2|3}} || 8 || {{frac|8|1|3}} || {{frac|8|2|3}} || 9 || {{frac|9|1|3}} || {{frac|9|2|3}} || 10 || {{frac|10|1|3}} || {{frac|10|2|3}} || 11 || {{frac|11|1|3}} || {{frac|11|2|3}} || 12 || {{frac|12|1|3}} || {{frac|12|2|3}} || 13
|-bgcolor="#e5d1cb"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 0.7 || 0.8 || 0.9 ||style="background:#CCFFCC;"| 1.0 || 1.1 || 1.2 ||style="background:#CCFFCC;"| 1.4 || 1.6 || 1.8 ||style="background:#CCFFCC;"| 2 || 2.2 || 2.5 ||style="background:#CCFFCC;"| 2.8 || 3.2 || 3.5 ||style="background:#CCFFCC;"| 4 || 4.5 || 5.0 ||style="background:#CCFFCC;"| 5.6 || 6.3 || 7.1 ||style="background:#CCFFCC;"| 8 || 9 || 10 || style="background:#CCFFCC;"|11 || 13 || 14 ||style="background:#CCFFCC;"| 16 || 18 || 20 ||style="background:#CCFFCC;"| 22 || 25 || 29 ||style="background:#CCFFCC;"| 32 || 36 || 40 ||style="background:#CCFFCC;"| 45 || 51 || 57 ||style="background:#CCFFCC;"| 64 || 72 || 80 ||style="background:#CCFFCC;"| 90
|}

Sometimes the same number is included on several scales; for example, an aperture of {{f/|1.2}} may be used in either a half-stop<ref>
{{cite book
 | url = https://books.google.com/books?id=YjAzP4i1oFcC&pg=PA136
 | title = Set lighting technician's handbook: film lighting equipment, practice, and electrical distribution
 | author = Harry C. Box
 | edition = 3rd
 | publisher = Focal Press
 | year = 2003
 | isbn = 978-0-240-80495-8
 }}</ref>
or a one-third-stop system;<ref>
{{cite book
 | url = https://books.google.com/books?id=DvYMl-s1_9YC&pg=PA19
 | title = Underwater photography
 | author = Paul Kay
 | publisher = Guild of Master Craftsman
 | year = 2003
 | isbn = 978-1-86108-322-7
 }}</ref>
sometimes {{f/|1.3}} and {{f/|3.2}} and other differences are used for the one-third stop scale.<ref>
{{cite book
 | url = https://books.google.com/books?id=IWkpoJKM_ucC&pg=PA145
 | title = Manual for cinematographers
 | author = David W. Samuelson
 | edition = 2nd
 | publisher = Focal Press
 | year = 1998
 | isbn = 978-0-240-51480-2
 }}</ref>

==== Typical one-quarter-stop f-number scale ====
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| 0 || {{frac|4}} || {{frac|2}} || {{frac|3|4}} || 1 || {{frac|1|1|4}} || {{frac|1|1|2}} || {{frac|1|3|4}} || 2 || {{frac|2|1|4}} || {{frac|2|1|2}} || {{frac|2|3|4}} || 3 || {{frac|3|1|4}} || {{frac|3|1|2}} || {{frac|3|3|4}} || 4 || {{frac|4|1|4}} || {{frac|4|1|2}} || {{frac|4|3|4}} || 5 
|-bgcolor="#5D8AA8"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 1.0 || 1.1 ||style="background:#FFFFCC;"| 1.2 || 1.3 ||style="background:#CCFFCC;"| 1.4 || 1.5 ||style="background:#FFFFCC;"| 1.7 || 1.8 ||style="background:#CCFFCC;"| 2 || 2.2 ||style="background:#FFFFCC;"| 2.4 || 2.6 ||style="background:#CCFFCC;"| 2.8 || 3.1 ||style="background:#FFFFCC;"| 3.3 || 3.7 ||style="background:#CCFFCC;"| 4 || 4.4 ||style="background:#FFFFCC;"| 4.8 || 5.2 ||style="background:#CCFFCC;"| 5.6
|}
{|class="wikitable" style="text-align:center"
! scope="row" | AV
| 5 || {{frac|5|1|4}} || {{frac|5|1|2}} || {{frac|5|3|4}} || 6 || {{frac|6|1|4}} || {{frac|6|1|2}} || {{frac|6|3|4}} || 7 || {{frac|7|1|4}} || {{frac|7|1|2}} || {{frac|7|3|4}} || 8 || {{frac|8|1|4}} || {{frac|8|1|2}} || {{frac|8|3|4}} || 9 || {{frac|9|1|4}} || {{frac|9|1|2}} || {{frac|9|3|4}} || 10
|-bgcolor="#5D8AA8"
! scope="row" | ''N''
|style="background:#CCFFCC;"| 5.6 || 6.2 ||style="background:#FFFFCC;"| 6.7 || 7.3 ||style="background:#CCFFCC;"| 8 || 8.7 ||style="background:#FFFFCC;"| 9.5 || 10 ||style="background:#CCFFCC;"| 11 || 12 ||style="background:#FFFFCC;"| 14 || 15 ||style="background:#CCFFCC;"| 16 || 17 ||style="background:#FFFFCC;"| 19 || 21 ||style="background:#CCFFCC;"| 22 || 25 ||style="background:#FFFFCC;"| 27 || 29 ||style="background:#CCFFCC;"| 32
|}