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.
[To address my original concern – was it worth paying double for a lens that was a half-stop faster? I concluded it was not.]
An understanding of these in-between f-stops has a further day-to-day application: setting a lens aperture in-between f-stops. Most lenses have an aperture ring that is “click stopped”. That is to say, rather than visually aligning an aperture setting, the ring clicks into place when alignment is correct. Some lenses also have clicked half-stops. If your lens does not, when half-stops are set visually, they fall about 1/3rd of the distance from the wider aperture alignment (take my word for it, but you can do the maths is you wish). If you have a lens that has half-click-stops, you might even be able to see this one-third spacing.
With different focal length lenses, the standard apertures will be physically different sizes (e.g. f/2 on a 100m lens will have a diameter of 50mm), but fortunately the expression of f-stops as ratios means that, say f/2, will always permits the same level of light to pass whether it’s f/2 on a 50mm lens, or a 100mm lens, or any other focal length (i.e. 50mm focal length: 25mm aperture diameter is a ratio of 1:2. 100mm focal length: 50mm aperture diameter is also a ratio of 1:2).
Zoom lenses often have two maximum aperture values (e.g. f/3.5-f/4.5), and this reflects changes to the maximum aperture relative to the increase in the focal length setting of the zoom.
In conclusion, if you didn’t already know this, you should now understand why apertures are called f-stops, why lens f-stops follow a seemingly illogical sequence of numbers, why longer focal length lenses tend to have a smaller maximum aperture (due to the high cost of making really wide lens glass, and why slightly faster lenses can be so very much more expensive), why some zooms have a variable maximum aperture, how much faster those in-between apertures really are, and how to set half-stops (if your doing everything the old fashion manual way without TTL metering).
It’s time for me to go bid on that f/2 lens, and stop watching the f/1.7.