Why is aperture backwards??

[ac12]

So, I get that larger f numbers like f/22 actually mean that it's a smaller opening and that smaller f number like f/2 is a big opening. I learned that thanks to a really helpful beginner video I just watched - this video. But my question is this...WHY is the size of the aperture backwards from the numbers. Shouldn't f/22 be a big aperture since it's a big number and f/2 should be a small aperture since it's a small number???

Yes, it is confusing to a newbie.
small number = larger opening, bigger number = smaller opening
I explain it with the same equation that @smoke665 gave:

f/stop = focal length of the lens ÷ the actual diameter of the effective aperture of the lens​

In the old days, of prime lenses, it was easy to demo.

50mm lens, front element was about 25mm diameter, 50mm / 25mm = f/2. And it was a f/2 lens.​

The demo does not work with most zooms.

Even with that, it is one of those things that you get used to, and don't think about.

Same with ASA/ISO speed numbers.
Why is a larger number a more light sensitive value, why not a smaller number?
I don't know, but it is what it is, and I just accept it.
As it turned out, it was for the better, otherwise we would be using huge fractional numbers a the films got faster and sensors became more sensitive.
ASA/ISO > 1, 2, 4, 8, 16, 32, 64, 125, 250, 500, 1000, 2000, 4000, 8000 . . .
reverse ASA/ISO > 1, 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625

 

[Jeff15]

Some aspects of photography are very confusing at first.....

 

[smoke665]

Same with ASA/ISO speed numbers.
Why is a larger number a more light sensitive value, why not a smaller number?
I don't know, but it is what it is, and I just accept it.

In the case of ISO and shutter speed they are linear progressions, such that the difference between the consecutive terms is constant, both doubling/halving the setting result in a doubling of light +/-.

Aperture diameter change being a mathematical function of the focal length, based on the constant provided by the Inverse Square Law doesn't appear linear, but there are certain lineal progressions that come into play. For example since each aperture is rounded to the nearest 1/3 stop, each doubling of focal length results in a linear progression of 2/3 stops (2:3), equivalent f/stop. Then consider that each full stop requires changing the working diameter of the lens to deliver a 2X (double of half) change in light energy. As @photoflyer pointed out earlier, if you multiply the diameter of any circle by the square root of 2 (1.414), you get a revised circle with twice the surface area, for photography purposes it's rounded to 1.4. Now look at the f/number set, 1, 1.4, 2, 2.8 , 4, 5.6, 8, 11, 16, 22, 32, each number going right is its neighbor on the left multiplied by 1.4. Each number going left is its neighbor on the right divided by 1.4. This also fits the definition of a linear progression.

 

[JBPhotog]

And if you pace off the inverse square law in feet you will loose one full stop between 1.4 and 2 feet or 16 and 22 feet, convenient that.

 

[Scott Murphy]

f/ stop is an actual ratio of focal length/opening diameter of the aperture blades. For example, for a 50mm f/2 lens the maximum aperture would be 50mm/2 = 25mm. But for f/8 of that same lens, it would be 50mm/8 or about 6mm. For each f/ there is either a doubling or halving of the light that actually reaches the film or sensor.

 

[snowbear]

It is like pie ... 1/4 pie is bigger than 1/8 pie so f/4 is bigger than f/8.

 

[petrochemist]

Exactly the same question was posted on DPR at much the same time the OP hasn't been back there either!

 

[Grandpa Ron]

While it is convenient to live in a linear world, most thing in nature are not. Light follow the Square root of 2, heat dissipates at a log rhythmic rate etc. I once asked a teacher why sound is not linear? He commented suppose you were in the woods listening to the quite sound of leaves falling, and a jet plane flew over. Nature knows best.

The f stop scale is an attempt to make the non-linear action easier to manage. It has worked for almost 200 years.

 

[phlash46]

So, I get that larger f numbers like f/22 actually mean that it's a smaller opening and that smaller f number like f/2 is a big opening. I learned that thanks to a really helpful beginner video I just watched - this video. But my question is this...WHY is the size of the aperture backwards from the numbers. Shouldn't f/22 be a big aperture since it's a big number and f/2 should be a small aperture since it's a small number???

Because the f numbers are the bottom oaf fractions! f22 is 1/22 which is smaller than f4 which is 1/4. Got it?

 

[DaveAllen]

Plenty of good answers here that explain the technical reason. For people that have a hard time wrapping their head around it, it can be easier for them to remember that smaller number = smaller DoF and bigger number = bigger DoF

 

[smoke665]

Because the f numbers are the bottom oaf fraction

A common misconception, but F/stops are "ratios" not fractions. A "fraction" is a number that names part of a whole or part of a group. The denominator represents the total number of equal parts the whole is divided into. A "ratio" is a "comparison" of two quantities.

@DaveAllen now you've opened another can of worms, why is it so?

 

[rambler]

Okay Allen, if I want the shallow end of the pool, I head for the 4 foot marker, if I want deep, I go to the 16 foot marker. Shallow DOF f/4......etc.

Which weighs more, a pound of feathers or a pound of lead? Think that's funny? Which carries more weight in your photo, a 4" square of white or a 4" square of black? Hmm...want a hint? Think about mass.

 

[johngpt]

We've got three pages of replies.
I'm wondering if we'll see something from the person who asked the question.

 

[Lonnie1212]

So, I get that larger f numbers like f/22 actually mean that it's a smaller opening and that smaller f number like f/2 is a big opening. I learned that thanks to a really helpful beginner video I just watched - this video. But my question is this...WHY is the size of the aperture backwards from the numbers. Shouldn't f/22 be a big aperture since it's a big number and f/2 should be a small aperture since it's a small number???

 

[Lonnie1212]

I agree with you Carter. You have a very good question.