Old photographers loved fractions

One of the things that seems to confuse new photographers is the fact that everything seems to be the opposite. For example, a small f-number lets in less light than a large f-number. The reason for this is that many of these controls are represented as reciprocals, or fractions.

The fractions representing shutter speed are intuitive. People understand when “250” is displayed, it means 1/250 of a second for example, and “500” (1/500) is a shorter time. However when it comes to aperture, people don’t equate the f-numbers with fractions1. f16 is a smaller hole than f8, just as 1/16 is a smaller number than 1/8. Maybe the issue is some of the larger apertures are called f2.8. We are not used to seeing a fraction mixing decimals.. 1/2.8 looks wrong, however it is just a way to show 5/14. Just like shutter speeds, the “1/” is assumed and not printed to save space.

Once you realize the number is just a fraction, it makes sense that a smaller f-number, like f4 (1/4), lets in more light than something like f16 (1/16). just like a smaller printed shutter speed number like 60 (1/60 second) lets in more light than a printed 500 (1/500 second).

f-numbers, or f-stops, are listed so that each number in the series (1.4, 1.8, 2.8, 4, 5.6, 8, 11, 16, 22…)2 lets in twice the amount of light (or one stop more) than the previous number3. This makes it easy to match an f-number and a shutter speed to give a consistent exposure. If you halve the shutter speed, say from 1/30 to 1/60, you can open the aperture from f8 to f5.6. This will allow the exact same amount of light to reach your sensor.

In the next post I will talk about depth of field and how to control it with aperture.



Footnotes    (↵ returns to text)
  1. An f-number is the focal length of the lens divided by the diameter of the opening. In theory an f-number such as f8 should let in the same amount of light, ie exposure, regardless of lens, however due to physical differences in the glass and construction of lenses the actual amount of light may differ slightly. For this reason high end cinematic lenses will be marked in T-stops, which is a measured transmission of light for each lens.

  2. some cameras will show 1/2 or 1/3 stop f-numbers between this standard series.

  3. If you accept that some numbers are rounded to make things easier, you may also notice that each number is double the number two places away, and if you are really mathematically nerdy, each number is root two times the previous number, and a circle with root 2 times the diameter has twice the area.