My trick for memorizing f/stops

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fjrabon

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I told somebody about this a few days ago and they found it pretty helpful.

Most beginners, heck most intermediates, have trouble calculating equivalent exposures in their head. It's a useful thing to be able to do, but they just get lost in the math. For most people shutter speed and ISO are easy enough. They're intuitive numbers. 1/100 of a second is obviously twice as fast as 1/50 and this lets in half as much light. That is, it's a stop difference. Same thing with ISO. Obviously 200 is half 400, so 400 is twice as bright and thus a stop different.

But for many photographers, things go sideways when it comes to aperture. They don't have a clear, intuitive sense of the relationship between f/8 and f/5.6.

Most experienced photographers manage this by simply having memorized f/stops through years of experience (especially when they were set tactilely on the lens and you were forced to look at the actual number each time). They know 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22 like the back of their hand. Is the only solution to just memorize these?

You only need to memorize two f/stops and then you can use a simple trick to get all the rest.

Start with f/1.4 and f/2. Have those memorized. They're 1 stop apart, meaning f/1.4 lets in twice as much light.

Then you just alternate doubling each. So the next stop after f/2 is f/2.8 which is double f/1.4. Next is f/4 (double f/2).

See the alternating pattern: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45

Now you'll note the pattern gets broken twice. But it actually doesn't. f/11 should really be f/11.2, but the .2 is such a tiny difference in light that we round it off because it's easier to write on lenses. f/22 should be f/22.4, again it's just rounded down. Then f/45 should be f/44.8.

It also works for third stops too, but you have to memorize 4 additional starting points then.

Honestly I could do without third stops for the most part. I tend to think of them more as "strong" and "weak" standard stops. Historically they were really more because a lens was either messed up or was a prime on the bleeding edge of its capabilities.

Anyway, I generally find that f/stops are the last thing keeping people from being able to find equivalent exposures in their head, which can come in incredibly handy at times when you can't simply use the camera's built in light meter.

Star photography for example. Changing from a f/2.8 wide angle to a f/2 prime? Gotta be able to do the equivalent exposure in your head because light meters are useless with star photography.

Anyway, hope somebody find that little trick helpful.
 
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It doubles every other f-stop because the 2x or 1/2x as much light a full stop change of aperture lets in is based on the square root of 2 - 1.41421356 - which multiplied by itself = 2.

Like so many things in life, doing math in your head takes practice.
"If you don't use it, you lose it."
 
Too much math. I just memorize the numbers.
Sure, that is exactly what I said most people who have done it for years do, in the post. This post obviously wasn't addressed at you. This post was addressed at people who haven't memorized the stops and need a trick to help them get the hang of it.
 
Too much math. I just memorize the numbers.

I have to agree here. For me, of course. I think it's really useful information to help beginners and intermediates even grasp the relationship between the f-stops and exposure, and help them think about what they're doing. For my own purposes, however, when it comes time to shoot, it feels a little fussy and it often ends up confusing me.

I remember figuring out my own little trick formula for going from Celsius to Fahrenheit when I was living overseas. I'd see the temperature read "16" and I'd do the calculations in my head to figure out the Fahrenheit equivalent. Then one day, I thought, "Why don't I just start associating the sensation with the new numbers? So it's 16 degrees...what does that feel like?" and I started skipping the Fahrenheit middleman.

I feel the same way when it comes to f-stops and exposure. Instead of doing calculations based on how much light is proportionally being allowed through the lens, I associate the numbers with certain looks and effects. I find that works just fine for me.

Of course everyone is different. Again, I want to repeat that I think it's a really really useful post and those who are more technically or mathematically inclined will surely benefit.
 
It doubles every other f-stop because the 2x or 1/2x as much light a full stop change of aperture lets in is based on the square root of 2 - 1.41421356 - which multiplied by itself = 2.

Like so many things in life, doing math in your head takes practice.
"If you don't use it, you lose it."
Yeah, 2x2 = 2^2 is such an interestingly useful fact.
 
If you want to get technical, the actual sequence is:

1.4142135623730950488016887242097
2
2.8284271247461900976033774484194
4
5.6568542494923801952067548968388
8
11.313708498984760390413509793678
16
22.627416997969520780827019587355
32
45.25483399593904156165403917471
 
Hu ?

I have no trouble knowing the f-stops ?

f1
f1.4
f2
f2.8
f4
f5.6
f8
f11
f16
f22
f32

Twice as much light, half the depth of field with every step upwards, half as much light, twice as much depth of field downards. And thats about all one ever needs.


Since the f-number is the ratio between focal length and pupil diameter, the lower bound for that diameter is easily computed as well:

28mm f2.8 => diameter is 28mm / 2.8 = 10mm

50mm f1.0 => diameter is 50mm / 1 = 50mm

200mm f2.0 => diameter is 200mm / 2 = 100mm

400mm f2.8 => diameter is 400mm / 2.8 ~ 140mm

Thus a 400mm f2.8 has to be a quite huge lens.


Its the same with binary, really. Every programmer can write down 2 times n easily:

1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384

And thats the first time I really have to think about the next step. All the other numbers I already know by memory.
 
Too much math. I just memorize the numbers.

I have to agree here. For me, of course. I think it's really useful information to help beginners and intermediates even grasp the relationship between the f-stops and exposure, and help them think about what they're doing. For my own purposes, however, when it comes time to shoot, it feels a little fussy and it often ends up confusing me.

I remember figuring out my own little trick formula for going from Celsius to Fahrenheit when I was living overseas. I'd see the temperature read "16" and I'd do the calculations in my head to figure out the Fahrenheit equivalent. Then one day, I thought, "Why don't I just start associating the sensation with the new numbers? So it's 16 degrees...what does that feel like?" and I started skipping the Fahrenheit middleman.

I feel the same way when it comes to f-stops and exposure. Instead of doing calculations based on how much light is proportionally being allowed through the lens, I associate the numbers with certain looks and effects. I find that works just fine for me.

Of course everyone is different. Again, I want to repeat that I think it's a really really useful post and those who are more technically or mathematically inclined will surely benefit.
Sure, the ideal method is to just know them. In the same way that the ideal way to know your multiplication tables is to just memorize them. But the title is "trick to memorizing" this is aimed at getting people to the point of memorizing them.

Most people if you give them a set of 10 random numbers can't memorize them effectively without MASSIVE repitition unless they can see a pattern. The kids who learn their multiplication tables the fastest are the ones who understand the underlying pattern first. Then at some point they no longer use the pattern, they just know the result by heart.

I don't calculate out that f/16 is 3 stops difference from f/8. I just know it. But at one point I did have to use the trick to get there instead of it being purely memorized.
 
Hu ?

I have no trouble knowing the f-stops ?

f1
f1.4
f2
f2.8
f4
f5.6
f8
f11
f16
f22
f32

Twice as much light, half the depth of field with every step upwards, half as much light, twice as much depth of field downards. And thats about all one ever needs.


Since the f-number is the ratio between focal length and pupil diameter, the lower bound for that diameter is easily computed as well:

28mm f2.8 => diameter is 28mm / 2.8 = 10mm

50mm f1.0 => diameter is 50mm / 1 = 50mm

200mm f2.0 => diameter is 200mm / 2 = 100mm

400mm f2.8 => diameter is 400mm / 2.8 ~ 140mm

Thus a 400mm f2.8 has to be a quite huge lens.


Its the same with binary, really. Every programmer can write down 2 times n easily:

1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384

And thats the first time I really have to think about the next step. All the other numbers I already know by memory.

Do you consider yourself a beginner?

Wish I didn't have to keep repeating "this isn't for people who have already memorized f/stops" the title is clearly "trick for memorizing f-stops"

If there was a thread titled "trick for kindergarteners to memorize how to tie their shoes" would you chime in "I have no trouble remembering how to tie my shoes?"
 
i just pull out my phone and go here: F-number - Wikipedia the free encyclopedia

I also cheat and have my function button setup as "1 step spd/aperture" so I can quickly dial in/out a step of light without thinking.
 
If you want to get technical, the actual sequence is:

1.4142135623730950488016887242097
2
2.8284271247461900976033774484194
4
5.6568542494923801952067548968388
8
11.313708498984760390413509793678
16
22.627416997969520780827019587355
32
45.25483399593904156165403917471
Why would I want to get that technical in a post aimed at helping people who are having trouble memorizing f/stops.

For someone who has trouble memorizing them "just memorize them" isn't a solution, it's circular. I gave one thing that helped me, and seems to have helped some beginners I know. It may not be useful to everyone, as I clearly stated. For some, even multiplying by two may be too much math. For some it has been helpful and maybe some other beginner will find it helpful. This is the beginner's forum right?

Not sure what your issue here is.
 
Honestly, those numbers automatically stuck in my head after using the camera for awhile.
 
Sure, the ideal method is to just know them. In the same way that the ideal way to know your multiplication tables is to just memorize them. But the title is "trick to memorizing" this is aimed at getting people to the point of memorizing them.

Most people if you give them a set of 10 random numbers can't memorize them effectively without MASSIVE repitition unless they can see a pattern. The kids who learn their multiplication tables the fastest are the ones who understand the underlying pattern first. Then at some point they no longer use the pattern, they just know the result by heart.

I don't calculate out that f/16 is 3 stops difference from f/8. I just know it. But at one point I did have to use the trick to get there instead of it being purely memorized.

Oh I totally get it. I actually see patterns pretty easily - more often with words and shapes than with numbers, but that's the kind of thing my brain seems to do all on its own. Like I said, I think your post was really helpful for people still sorting out f-stops and their relationship to the image. I just thought I'd offer a variant to that for those beginners who might get freaked out by math :) Rather than looking at mathematical relationships between the f-stops and seeing that pattern, they could also link those f-stop numbers to images and establish a different kind of pattern.

Edit: I suppose it's not really a 'variant' but a corollary perhaps? "Once you have an understanding of the relationship between these numbers, start looking at how changing those numbers affects your images and understand that relationship."
 
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