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If you were teaching someone new to photography the full stop scales, is there a better way then flat out memorizing these values? Does anyone have an easy way that they remember the scale? Would it make more sense as a type of mathematical equation without getting overly complex?

Aperture Full Stops:

1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64

Shutter Full Stops:

1/1000s, 1/500s, 1/250s, 1/125s, 1/60s, 1/30s, 1/15s, 1/8s, 1/4s, 1/2s, 1s

Obviously the shutter stop scale is very easy to remember, but how can I use the square root to determine the aperture easily in my head?

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Remember 1 and 1.4. From then on it's interleaved doubling with never more than 2 significant digits. 1 2 4 8 is easy. | Hardly harder is 1.4 2.8 5.6 11.2 -> 11 due to 2 signifcant digits so then 22 44 . Interleave them and "Bob's your uncle". Knowing that sqrt(2) = 1.414 = 1.4 to 2 digits helps but is not essential. –  Russell McMahon Dec 19 '13 at 22:06
    
This has been said in answers already, but for me it has been as simple as memorizing "3". I take a base aperture and know that three cliks up or down is a full aperture stop. In My case I use 5.6 since that is the max that my current zooms have at max focal length. Constantly using only full stop apertures has led me to remembering them whithout specifir effort on memory. Ultimatelly I use f5.6, f.8 and f.11 the most, so they are in my head all the time, if I need to go somewhere else, I go three clicks every time... –  Jahaziel Aug 18 at 22:45
    
Once you've read this thread you know the numbers –  Alex Aug 26 at 16:41

9 Answers 9

up vote 21 down vote accepted

F-stops deal with doubling/halving the amount of light hitting the sensor. Everything revolves around twos.

With the shutter speed, it's easy to understand, as you say. Every shutter f-stop is (roughly) half/double the amount of time as the previous one. Personally, I don't even bother paying attention to the numerator ("1/") part of the shutter speed; I've drilled it into my head that bigger denominator = faster = less light = darker exposure.

Note that shutter speeds aren't exactly doubles/halves. I think that this is just because manufacturers think people like to see "round" numbers. At the fast end, that means 1000, 500, 250. At the slow end, you need more accuracy, so you have true halving of speed (1, 2, 4, 8). Then, they have to make the numbers meet in the middle, so they start to fudge the numbers a bit (15 is almost 8 * 2, 125 is almost 60 * 2). (I'm a programmer, so personally, I'm fine with seeing a shutter speed of 1/1024s :-) )

Aperture is a bit trickier. Double the light means doubling the area of the aperture, which is where the squares/roots come into play (Area of a circle = pi * r^2). That's a pain to mentally calculate, but there is an easier trick to consider: every two stops represents a doubling (or halving) of the aperture's f-number:

1, 2, 4, 8, 16, 32, 64.

If you know those, then you can guesstimate the in-between stops by calculating slightly less than half of the average of the surrounding f-stops:

1.5 -> 1.4, 3 -> 2.8, 6 -> 5.6, 12 -> 11, 24 -> 22, 48 -> 45.

As with shutter speed, bigger number = smaller aperture = less light = darker exposure.

Something similar happens with ISO. Each doubling of the ISO value represents a stop, which you can trade off (with consequences) with stops of shutter and aperture. Note that this transition is reversed though: bigger number = more sensitive = more light = brighter exposure. The common ISOs are:

50, 100, 200, 400, 800, 1600, 3200, 6400, 12800

And just to be complete, there's another similar scale with flash power:

1 (Full power), 1/2 power, 1/4 power, 1/8, 1/16, 1/32, 1/64, 1/128

This is very much like shutter: bigger denominators (forget the numerators) = less power = less light = darker exposure. (Note that true powers of two is fine here).

Honestly though, I don't bother with any of these mnemonics myself. I usually do "three clicks of my control wheels on my camera" when I want to go up/down one stop. (My camera, and many others, set one click of the control wheel to be 1/3 of a stop.) The absolute numbers aren't usually as important as the amount of change relative to "where you are now".

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Another key point in the round numbers is that the actual physical reality of optics and aperture blades and mechanical shutters isn't that precise anyway, so in a sense it's more honest to round off. (And we really should do the same thing with high ISO values. Say 250k rather than 256,000.) –  mattdm Jun 14 '11 at 17:40
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+1 for "three clicks". Extremely useful to learn. –  Jukka Suomela Jun 14 '11 at 18:43
    
+1 for the last paragraph –  Vian Esterhuizen Jun 14 '11 at 19:58
    
The "three click" part is the easy way the OP is really asking for, the rest is too complicated for people who don't like math. –  Jahaziel Aug 18 at 22:30

Well, one way of remembering the f-stop scale is to remember that every other value is a multiplication by two, or in more photographic terms...every four-fold jump in light availability is twice the f-stop number. As an example:

Double-stops starting at the beginning: 1, 2, 4, 8, 16, 32, 64
Double-stops starting skipping the first stop: 1.4, 2.8, 5.6, 11.2 (11), 22.4 (22), 44.8 (45)

As you can see, remembering the full f-stop scale is pretty much the same as remembering the full shutter speed scale, only interleaved. So long as you can remember a couple of whole and fractional stop values, you should be able to remember the full scale.

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I remember that it starts at 1 and 1.4, double to get next number, and that anything over 10 is rounded. –  rfusca Jun 14 '11 at 16:46
    
I never even realised this. –  Nick Bedford Jun 14 '11 at 21:45
    
This was the only way I could remember them when I first started. I thank my mathematical friends...always analyzing patterns. You'd be amazed how many simple patterns exist in just about everything. ;) –  jrista Jun 14 '11 at 21:46

I think the (practically-used part of the) sequence is short enough that it's probably easiest to just memorize it. It's useful not just for aperture but for other things in photography as well, like fractional flash power guide numbers.

But one simple fact can help: since squaring the square root of two is back to plain old two again, every two stops the number doubles: f/1 skip f/2 skip f/4 skip f/8, and so on; and also, f/1.4 skip f/2.8 skip f/5.6 skip ... mumble mumble we start rounding things off.

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The "mumble, mumble" part reminds me of your comment at photo.stackexchange.com/questions/4157/… :-). –  whuber Jun 14 '11 at 18:28
    
We started rounding things off right at the beginning, there -- root 2 is irrational. At some point, the guy engraving the stop numbers on "proper" lenses is just going to give up trying, y'know? And who really wants a 14-digit aperture display in the viewfinder anyway? –  user2719 Jun 15 '11 at 22:10
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@Stan: yes, good point. But at f/11 we start rounding to whole numbers. And by f/22, we're rounding the wrong way, as f/23 would really be closer. But by that time, the difference is really quite small either way. –  mattdm Jun 15 '11 at 23:29
    
@whuber — heh, I'd forgotten about that. –  mattdm Jun 15 '11 at 23:30
    
@StanRogers (2.5 years on) -> See it as using 2 significant digits and it all follows "proper like" –  Russell McMahon Dec 19 '13 at 23:14

If you were teaching someone new to photography the full stop scales, is there a better way then flat out memorizing these values? (1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64 ...)

Note that all results have 2 significant digits only.
Remember 1 and 1.4 as the first two entries. From then on it's interleaved doubling (with never more than 2 significant digits.

1 2 4 8 is easy.
Hardly harder is 1.4 2.8 5.6 11.2 -> 11 due to 2 significant digits
so then 22 44 .

Interleave them and "Bob's your uncle".

Knowing that sqrt(2) = 1.414 = 1.4 to 2 digits helps but is not essential.

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So, I read the question and thought how complicated all the answers were. So decided to just write down the numbers and look at them. Here is what I found ... If you look at them you can simply break them apart into sub sets. So first work with the first set of two numbers which by chance start with the digit "1". They are:

1 and 1.4 (easy to remember)

Then go to the next sub set which happen to start with the digit "2"

2 and 2.8 (easy enough)

Then go to the next set .. wait they do NOT start with same digit but they are close to each other being "4" and "5" and the are:

4 and 5.6

Now it starts to get a little easier being there are no decimals. And if you look the third number is twice the first and the fourth is twice the second. but lets simply break them up into two sets. the first set it:

8 and 11

The second set is:

16 and 22

The last number is 32 if you are lucky enough to own a lens that steps down that far.

Break it down like this and you will memorize it in less than a day.

Good luck!

Or perhaps a poem:

ONE, ONE FOUR,
TWO, TWO EIGHT,
FOUR, FIVE SIX,
ELEVEN AFTER EIGHT, ...
SIXTEEN, TWENTY-TWO,
Nothin' else left to do.

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Hahah, nice poem :-P –  dpollitt Sep 22 '13 at 15:10

Just write it down and read it out loud 20 times. Parrot style :)

Not being a douche - that's honestly how I learned it.

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I understand. Straight memorization works great for some people, but not for me(and I imagine others as well). The point of this question was to illicit responses that could outline techniques for learning this information beyond memorization. If you read the first sentence of my question, I clearly stated I was looking for something BEYOND memorization. I voted you down because your answer does not meet that requirement and is not helpful. –  dpollitt May 2 '13 at 18:11
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Yes you did say that. Sorry. In that case: Remember the first two numbers 2.8 and 4. Every second number is the previous number x2. f2.8 x 2 = f5.6 and f4 x 2 = f8 etc. (f5.6 x 2 = 11.2, but just except it's f11) –  Theo May 3 '13 at 12:46

Well... what I figured is that you turn the aparture so three times, you go up one full stop scale... at least that's how it seemed to me. Not sure if that works all the way, but it certainly did work on mine... maybe you need to remember how many many times the aparture clicks while turning it a full stop?

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This will vary from camera to camera; many use third-stop increments but others use half-stop. –  mattdm May 1 '13 at 15:38
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And some let you SET the increment! –  Paul Cezanne May 1 '13 at 16:12
    
but still... how much you turn it, it will still be the same amount for every time you're supposed to turn it. Like, if you need to turn it twice first to get up one full stop scale, then you would need to just note how much you need to turn it to go up one full stop scale. But yea, setting it manually could be a challenge. I can see the pattern, but how you're supposed to remember it easily is a mystery. seems like every second full stop, the number is multiplied by 2, at least. At least it looks like that to me. –  user19692 May 1 '13 at 17:59
    
Right, every second full stop is double the previous. –  mattdm May 2 '13 at 13:37

Get a lens with a proper aperture ring with the stops engraved... After seeing and using it often, you will quickly become familiar with it.

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Hmmm. I have several of those. I think this only works if you also actually use that scale rather than leaving the lens/camera on auto aperture. –  mattdm Jul 21 '13 at 13:49
    
How is this different then seeing the stops on an LCD screen as far as learning? –  dpollitt Jul 21 '13 at 14:58
    
@mattdm that's why added "using it often", if you leave it sitting there, it won't help at all xD –  fortran Jul 21 '13 at 15:09
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@dpollitt first, you see all the apertures at once, second, the LCD will probably show 1/3 or 1/2 steps depending on the model –  fortran Jul 21 '13 at 15:10
    
@fortran - Good points. I might even be able to flip over to full stops in a custom function. Thanks! –  dpollitt Jul 21 '13 at 16:26

Maybe thinking of it as the square root of powers of 2:

sqrt(1) = 1
sqrt(2) ~= 1.4
sqrt(4) = 2
sqrt(8) ~= 2.8
sqrt(16) = 4
sqrt(32) ~= 5.6
sqrt(64) = 8
sqrt(128) ~= 11
sqrt(256) = 16

Personally, though, outright memorization seems the easier route. :D

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