# Why are full fstops the numbers they are?

Discussion in 'Beginner Questions' started by http://www.photo.net/martinw, Mar 27, 2018.

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1. ### rodeo_joe|1

Shutter speeds with electronically controlled shutters are actually more accurate than the conventional marked speed numbers.

The conventional speed sequence goes awry between 1/125th and 1/60th, and it would be difficult to adjust for the small discrepancy in a simple divider circuit. So if the electronic speed is accurate at 1/1000th of a second (=1 millisecond) then the time marked 1/60 will be 16 milliseconds or 2/125ths.

The same happens between the speeds marked 1/15 and 1/8th which aren't exact multiples or divisors of 2 either.

By the time you get to the speed marked 1 second, the precise electronic timer is giving 1024 milliseconds, and whole stop speeds after that get doubled up exactly. So no surprise that a marked 30 seconds gets rounded up to the 32 seconds it should have been in the first place.

FWIW, can anyone work out the stupid 1/10th stop markings on modern digital lightmeters? For example; what the h*ll is f/5.6 subscript 7??? I know it means f/5.6 minus 7 tenths of a stop, but what's that in an f number I can set on the camera? Why don't the lazy b*st*rd programmers convert it to a real number? The maths is simple, even for an ancient 8 bit CPU.

2. ### BeBu Lamar

The shutter speed of 30 seconds is actually calibrated for 32 second. While a 1/1000 shutter speed rarely accurate within a few percent but it's calibrated for 1/1024 second. Similarly the 1/60 is calibrated for 1/64.

3. ### Vincent PeriMetairie, LA

Hmm... too much math for
me... I'm going to eat a
banana...

4. ### chuck909

Ya got one for me? The OP has to be totally confused by now.

5. ### Andrew Garrard

FWIW, the Camera Museum in London (on the location where Aperture used to be before they moved) has a 1000mm f/6.3 refractor (wide open aperture) sitting under a table. I believe it was a medium format lens, although I could be conflating my stories. (They also used to have a 300mm f/2, although I think they've sold it.) Quite a few zooms are f/6.3 by the long end. Although pretty much all parameters in camera design come with an "...ish".

6. ### alan_marcus|2

Actually the number set for whole f-numbers to three decimal places is: 1.000 -- 1.414 - 2.000 - 2.828 - 4.000 - 5.657 - 8.000 - 11.314 - 16.000 - 22.627 - 32.000
Each number going right is its neighbor on the left multiplied by 1.4142 then the answer rounded for elegance.

For 1/2 f-stop increments the multiplier is the 4th root of 2 = 1.189

For 1/3 f-number set the multiplier is the 6thr root of 2 = 1.122.

7. ### anniebowenn

this is due to the geometric parameters of the lens and so on. And f/ is just a system of notation, for how many (blades) the aperture opens. Read on Wikipedia about this

8. ### James G. DainisModerator

To answer the OP's question, "Why are full fstops the numbers they are?" I don't know. Most people who use cameras aren't lens makers and don't know how to calculate that f/ number anyway. Why not make it simple? Change the numbers on the lens and on exposure meters etc. so

f/1.0 = 1
f/1.4 = 2
f/2.0 = 4
f/2.8 = 8
f/4.0 = 16
etc.

If a meter calls for 1/500 sec at No.8, the user would just turn the aperture ring to No.8. Why bother to think that is 2.8 on the old aperture ring?

9. ### Vincent PeriMetairie, LA

The numbers would get unwieldy using that system:

f.5.6 = 32
f/8.0 = 64
f/11 = 128
f/16 = 256
f/22 = 512
f/32 = 1024

Where would a lens manufacturer put "1024" on an already crowded aperture ring?

Last edited: Mar 29, 2018
chulster likes this.
10. ### John Seaman

Numerical systems of referring to relative aperture were used in the early days - see the table in the Wikipedia article in JDM's post.

I always thought the current sequence of (more or less) doubling and halving shutter speeds was introduced with the light value shutters of the 1950's - until I acquired a little Primo Jr TLR, which had a light value shutter, but using the old shutter speeds, 1/50, 1/100 etc.

11. ### rodeo_joe|1

"And f/ is just a system of notation, for how many (blades) the aperture opens."

- LOL. That one should have been saved for posting on April 1st.

12. ### Andrew Garrard

Yes. I haven't checked, but I really hope someone hasn't edited Wikipedia to say that.

That's actually quite frustrating, because the number is a useful one. A 100mm f/2 lens has an entrance aperture 50mm (100mm/2) across. A 50mm f/2 lens has an entrance aperture 25mm (50mm/2) across. Look in the front of the lens and you'll see it. The "f" stands for the focal length of the lens. Does it matter for calculating exposure? No. Is it useful when you then start thinking about how the aperture affects the depth of field in your scene? Yes. Which is why I go nuts when people say "f2" instead of "f/2" and start talking about bigger numbers for smaller apertures.

Well, you could define "f/1" as 0, and then use the log base (sqrt 0.5) for the fraction. (For those with maths as rusty as mine, that means ln(f-stop as a fraction, so f/2 = 0.5)/ln(sqrt(0.5)).) Which, with a few common non-whole-stop values in parentheses:

(f/0.95 = -0.15)
f/1.0 = 0 (f/1.2 = 0.5)
f/1.4 = 1 (f/1.8 = 1 2/3)
f/2.0 = 2 (f/2.5 = 2 2/3)
f/2.8 = 3 (f/3.3 = 3.5)
f/4.0 = 4
f/5.6 = 5 (f/6.3 = 5 1/3)
f/8.0 = 6
f/11 = 7
f/16 = 8
f/22 = 9
f/32 = 10

...which is how people have to calculate the exposure difference between stops anyway. But then you'd really need a calculator to work out depth of field, whereas multiplying by 1.4 isn't so tricky, especially if you're allowed to round it off.

Now, we could also have my pet argument about how ISO is an irritating measurement if you're comparing sensor sizes and relative apertures and focal lengths, and redefine the whole scheme. But we probably shouldn't.

steven_endo likes this.
13. ### steven_endo

Huh! It's been over 40years since I took my first photography class in high scool and during that time I have never stopped to think why the f-stop designation is engraved f/ on the lens even though I would occasionally wonder why... Learn something new everyday... Thanks

Last edited: May 12, 2018
14. ### Andrew Garrard

Glad to be of service, Steven. Of course, it's all theoretical and actual lens design complicates things considerably, and then everything becomes approximate when you manufacture it... but I find it a useful first approximation to what's going on!

15. ### BeBu Lamar

Andrew do you know what numbers Nikon use for aperture from f/1 to f/2 in 1/3 stop increments? I ask because the may round them off in some what different fashion than mathematically correct. I don't know because I don't have fast lenses like you do.

16. ### Wouter Willemse

Since Nikon has nothing faster than f/1.2, any guess about the 1/3 stop increments between f/1 and f/1.4 would be entirely academic. As for the f/1.2 lens, it only has stops at f/1.2 and f/1.4 and next f/2.
The 1/3rd stops between f/1.4 and f/2 on a Nikon, as far as I know, are f/1.6 and f/1.8.

17. ### Andrew Garrard

Thanks, Wouter - I don't have a 1.2 and couldn't check whether it had a stop at 1.4. The 50 f/1.8 (both E and AF-D) does have a stop at f/2.

As Wouter says, the my D850 reports 1.6 and 1.8 when doing 1/3 stops with the Sigma 85 f/1.4. Set to half stop steps, it reports f/1.7, 2, 2.4, 2.8, 3.3...

Power aperture in movie live view seems to report 1/3 stops, although it's quite hard to be precise.

I don't believe anything faster than f/1.4 has electronics, and Nikon aperture rings (that I've seen) only have clicks at whole stops, except where wide open isn't a whole stop.

I can't vouch for the 1-series f/1.2 or the faster rangefinder lenses, though!

18. ### rodeo_joe|1

Andrew, as Alan already explained, the 1/3rd stop multiplier is the 6th root of 2 = 1.1225.

Therefore the 1/3rd stop increments between f/1 and f/2 are:
f/1.1
f/1.3
f/1.4
f/1.6
f/1.8
Rounded to 1 decimal place, or the nearest integer, as is the convention with stop numbers. Regardless of anything Nikon might think.

The half-stops are 1.2 and 1.7.

It should be remembered that these are just labels and the real stop diameter might be closer to its mathematically correct value.... or not!

Though how you figure that out with a pentagonal, heptagonal or nonagonal aperture I can't be bothered to work out. And it doubtless gets worse with semi-rounded iris leaves.

BTW, the reason (or so I've read) that Nikon only provides whole stop detents is to give enough distance between 'clicks' to guesstimate fractional stops and set the aperture accordingly. Not necessary with modern cameras of course.

Last edited: May 12, 2018
19. ### kenduntonEdinburgh

ZZZZzzzz

Martin was last seen March 29th....

20. ### Andrew Garrard

Joe: agreed about the theory (as in my "proposal" of a log2 system above) - BeBu just asked how Nikon indicate them, so I reported what the camera shows - which happens to be "correct", at least in the 1.4-2 range.

That said, the D850 reports the following "1/3" stops with the Sigma 85mm:

1.4, 1.6, 1.8, 2, 2.2, 2.5, 2.8, 3.2, 3.5, 4, 4.5, 5, 5.6, 6.3, 7.1, 8, 9, 10, 11, 13, 14, 16. Strictly speaking the two values in bold should be 3.6 and 5.7, though I imagine the convention of saying "5.6" avoids novice questions about its relation to 2.8.

The half-stop sequence is:

1.4, 1.7, 2, 2.4, 2.8, 3.3, 4, 4.8, 5.6, 6.7, 8, 9.5, 11, 13, 16. The bold values should be 3.4 and 5.7.

Nikon have several lenses with fastest apertures aligned to half a stop, as I showed in my list, including the f/1.2 lenses. With the f/1.2 lenses, you can only set the aperture with the ring on the lens (on an SLR - an FA could do it), so the granularity of partial stops is irrelevant, though I certainly concur that the f/2 stop on my f/1.8 lenses is a very small movement of the aperture ring. If the Nikkors had partial stops throughout, no doubt someone would complain (and the oldest cameras were a bit iffy with metering). Control from the camera means there's a choice in step size that the user can configure, making partial stops practical. I believe some Fuji cameras with aperture on the lens resort to a "shift" control on the body to support partial aperture sizes - but their aperture rings won't be implemented with a mechanical stop like Nikkors.

You can (and must) set the aperture from the camera with the 28-80 f/3.3-5.6G, however. At 28mm (and therefore an f/3.3 maximum), the "1/3" stop smaller than f/3.3 is f/3.5, as if the lens were actually f/3.2. With half stops, the camera jumps straight to f/4.

I no longer commonly use variable-aperture lenses, but the D850 reports the following maximum aperture sequence with the 28-80 as it zooms:

3.3, 3.5, 3.8, 4, 4.2, 4.5, 4.8, 5, 5.3, 5.6. If those are supposed to be 1/6 of a stop (which is how I'd implement a system that had to handle 1/3 and 1/2), the bold values should actually be 3.4, 3.6 and 5.7. I suspect that some odd rounding is traditional, however. I've not checked with a macro to see whether distance changes follow the same sequence.

Forgive me if I don't try to get one of my Canon bodies working to see whether it uses the same numbering scheme.

On a related note, Nikon's non-CPU lens data menu seems to include only maximum apertures that Nikon has actually used (or you could make with a teleconverter): 1.2, 1.4, 1.8, 2, 2.5, 2.8, 3.3, 3.5, 4, 4.5, 5, 5.6, 6.3, 7.1, 8, 9.5, 11, 13, 15, 16, 19, 22. I'm not sure it's exhaustive even then.

Ken: Yes. I think we answered the original question a while ago (if we'd gone on a tangent without doing so I'd worry). While the tangent may make more sense on the Nikon forum, I think it's harmless here. And I certainly didn't know this without checking, so I'm learning!