A Primer On The Math Behind F-Stops

Have you ever wondered why the aperture number skip in such a weird way? What does 1.4 has to do with 2? The video below by Dylan Bennett has a great primer on the relations between focal length, aperture and the amount of light hitting the sensor.

A Primer On The Math Behind F-Stops

My favorite part is the trick to remember aperture stops -> Start with 1.4 and 2. and then double the numbers for the next stop => 1.4, 2, 1.4×2=2.8, 2×2=4, 2.8×2=5.6, 4×2=8 and so on.

A Simple Explanation of F-Stop | Dylan Bennett

Thanks for the tip, Brian.

  • gaksland

    Thanks for the great teaching skill. Now I have a concept in place about doubling and halving the amount of light through the adjustment of the F stop number.

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  • http://www.joelmeaders.com/ Joel Meaders

    This may be a lot to ask, but along with YouTube videos you should offer a written explanation.

    Before I get flak, the reason is that I cannot stand listening to people drone on and on about portions I don’t care about. I can read and take in information much more efficiently by reading rather than waiting. I can also go over the same sections multiple times without having to skip all over a video and wait through ads.

    • http://www.diyphotography.net/ udi tirosh

      Hi Joel
      I can see your point, and we do offer original content too. but if I “extracted” the video onto text form you would have no reason to watch it :) and I’ll be “borrowing” content.

      • http://www.joelmeaders.com/ Joel Meaders

        Good points. Thanks!

  • Ray Brown

    So, having watched this video – I couldn’t wait to apply this to my gear. So I plopped out my Canon 6D and the 24-105mm F/4 L lens and I got the following: 4.0, 4.5, 5.0, 5.6, 6.3, 7.1, 8.0, 9.0, 10.0 11.0 13, 14 16 18 20 22 As you can see – it didn’t follow the rule of using the first 2 numbers (F-Stop) of a lens and complete the pattern. Will I still be doubling or halving the amount of light with each changed f-stop? Its no big deal – but Im trying to figure out the theory behind why they put these values on my lens.

    I then pulled out my f1.8 nifty fifty and its scale was:
    1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0 (after 4.0 it follows the same pattern as the above f/4 lens).

    From the video and its explanation I was expecting the following:
    1.8, 2.0, 3.6, 4.0, 7.2 or rounded to 7.1, 8.0 etc

    • Andy

      You’re clicking through 1/3 stops there: The full stops are every third number (in Bold in the following sequence)
      1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, 4.5, 5.0, 5.6, 6.3, 7.1, 8.0, 9.0, 10.0 11.0 13, 14 16 18 20 22

      • Andy

        OK, the bold numbers didn’t post, buts it’s every third number, starting from 2.0 on your list.
        The f1.8 lens’ max aperture is actually 1/3 of a stop brighter than a whole f/stop (f2 in this case) which can be confusing.

        • Ray Brown

          Hey Thanks Andy! I was suspecting something like this.

  • Guest

    Area is mm SQUARED!

  • John

    Thanks, Dylan. Thanks.
    From now on I won’t have to remember the f-stop scale, I can simply computer it using elementary arithmetic. (Or the square rt (2) if I forget 1.4).
    I will now have this forever (my perspective) thanks to you.
    Are you now going to do the maths on field of view?

  • soli

    Great rxplanation. thanks