Camera Lens F-Stop Values Explained.
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Lens aperture settings are commonly knows as f-stops. The letter "f" is an abbreviation of the term "focal-ratio", which describes the ratio of the lens's focal length to the diameter of the light entrance pupil (more commonly called the aperture).
The standard sequence of f-stops is:
f/1.4 f/2 f/2.8 f/4 f/5.6 f/8 f/11 f/16 f/22
On this scale, an f/1.4 setting is the largest aperture, while f/22 is the smallest, and each f-stop in the sequence is half the size of its neighbour to the left, and twice the size of its neighbour to the right. In other words, f/5.6 permits the passage of twice as much light as f/8, but only half the light of f/4.
Low f-stop numbers represent larger apertures, and higher f-stop numbers indicate smaller apertures because the f-stop is a ratio is between the size of the aperture and the focal length of the lens; i.e. a bigger number represents a larger difference.
Here's the maths for a 50mm lens.
f-stop / Diameter (mm) / Focal length: aperture ratio
f/1.4 / 35.7 / 1:1.4
f/2.0 / 25.0 / 1:2
f/2.8 / 17.9 / 1:2.8
f/4 / 12.5 / 1:4
f/5.6 / 8.9 / 1:5.6
f/8 / 6.3 / 1:8
f/11 / 4.5 / 1:11
f/16 / 3.1 / 1:16
f/22 / 2.3 / 1.22
This ratio is commonly detailed around the front element on most lenses (e.g. "50mm 1:1.8", or sometimes "50mm f:1.8").
Here's a bit more maths, but don't stop reading, because it's really quite simple, and all the calculations have been done, so you just need to follow the logic. Let's start with f/2 on a 50mm lens. This f-stop has a diameter size that is half the focal length of the lens: that is 25mm.
The area of a circle is calculated using the formula - πr2.
Expressed in words, this is "Pi" (the common name of the π symbol, which represents 22 / 7) times the radius (r) squared, which is another of way of saying radius x radius. You will no doubt remember that the radius of a circle is half the size of its diameter.
The calculation of the area of f/2 for a 50mm lens is therefore: (22 / 7) x (12.5 x 12.5).
Repeating this calculation for each f-stop produces the following results:
f-stop Diameter(mm) / Area (mm2)
f/1.4 / 35.7 / 1,002
f/2.0 / 25.0 / 491
f/2.8 / 17.9 / 250
f/4 / 12.5 / 123
f/5.6 / 8.9 / 63
f/8 / 6.3 / 31
f/11 / 4.5 / 16
f/16 / 3.1 / 8
f/22 / 2.3 / 4
What you should see in this table is proof that the area of each f-stop is double/half the size of each neighbour (results shown to the nearest whole number).
The point of all this dull maths is three-fold: it proves the claimed relationship made at the beginning of this article, it explains why lenses use such and odd sequence of numbers to name f-stops, and it equips us to understand the in-between apertures, such as f/1.8, and other idiosyncrasies of the naming system.
If 35mm film photography is your thing, you will have inevitably encountered some f-stops that don't fit the opening sequence: f/1.7, f/1.8, f/1.9, f/3.5 and f/4.5 are some of the most common ones.
f/1.7 is one-half-stop larger than f/2.
f/1.8 is one-third-stop larger than f/2.
f/1.9 is one-quarter-stop larger than f/2.
f/3.5 is one-third-stop larger than f/4.
f/4.5 is one-third-stop smaller than f/4.