What is an easy way to remember the full stop scale?

Question

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?

Answer 1

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 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".

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

The f-number set is rooted in the geometry of circles.

This is true because the iris diaphragm of a lens normally opens and closes as a circular opening. The f-number set establishes a set of numbers that when applied to lenses, doubles or half’s the lens ability to transmit light. In other words, open up one full f-stop and the working surface area doubles. Close down the one full f-stop and the working surface area is cut in half.

Truism : Multiply the diameter of any circle by the square root of 2 = 1.414 – you have calculated a revised circle diameter that yield twice the surface area.

The f-number set going right is its neighbor on the left multiplied by 1.4

1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22 – 32 -45 -64 Conversely, going left it is its neighbor on the right divided by 1.4 (or multiplied by 0.7).

Incidentally, the analogous multiplier that creates a number set In 1/2 f-numbers is the fourth root of 2 = 1.189. A number set using the sixth root of 2 = 1.12 generates the f-number set in 1/3 f-number increments

Answer 7

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

Answer 8

Didn’t anyone mentioned that you only really need two know just two stops: (A) 1 and (B) 1.4 and from there multiply by 2 to obtain the next stop in each sequence.

e.g 
Set (A): 1   => 1x2   = 2   -> 2x2   = 4   -> 4x2   =  8 -> 8*2  = 16 -> 16*2 = 32  
Set (B): 1.4 => 1.4x2 = 2.8 -> 2.8x2 = 5.6 -> 5.6x2 = 11 -> 11x2 = 22
Full F-Stop Scale: 1 -> 1.4 -> 2 -> 2.8 -> 4 -> 5.6 -> 8 -> 11 -> 16 -> 22 -> 32

Observe that in the full scale: Each f-stop from set (A) is an EVEN number, with the exception of its first f-stop 1 which’s odd and each one of them is followed by an ODD f-stop from set (B), with the exception its last f-stop 22 which’s even.

But when using the camera and you have setup aperture to change ⅓, ½ or 1 f-stops, you would only need think in rotating the dial (to either side depending if you what to increase or decrease the aperture) by 3 clicks for the first option, 2 for the second and just one for the last one to change the aperture one f-stop.

Tip: Remember that the lower the f-stop, the larger the aperture (more light will enter thru the lenses)

Answer 9

Associate certain picture taking or equipment aspects/gotchas with certain stops, for example...

f1.2? It will be expensive...

f1.4? It will be soft...

f2.8? Maximum practical aperture for 3 or 4 element lenses, and for inexpensive non-normal primes

f3.5? The economy version of f2.8

f5.6? Optimum for most any lens (unless it is only f5.6 fast!).

f11 ? Have you cleaned your sensor lately? Also, "diffraction".

f16 ? Sensor spots will ruin the SOOC experience...again.

Answer 10

The most simple rule, use common sense, use what film photographers have been doing since the down of photography, write the f-stop scale on paper or whatever and stick it on the back of your camera and in no time you will be able to say it forward and backwards without any effort.

Forget about any mnemonic rules or anything that anyone that have learned photography using digital cameras tell you.

Go and stick them on the back of your camera and without thinking about them you’ll learn them by heart in no time. (If you want to do it for ⅓ of a stop, don’t be afraid it is as easy and fast as for full stops).