# Why is aperture backwards??

#### Carter Stevenson

##### TPF Noob!
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
Because it is a ratio. f stands for focal length.
so if you have a 100mm lens, f/2 would mean an aperture diameter of 50mm. f/22 would mean 4,55mm.

• Dh_T3i
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???

First of all, you need to understand that f/2 Or f/22 is not a "measurement of size" but rather a "ratio" where (f/stop = focal length of the lens ÷ the actual diameter of the effective aperture of the lens). Here's a chart you might find useful. Note under full stops if you stop down from f5.6 to f/8 you have reduced the light available by 1/2, likewise if you open up from f/8 to f/5.6 you double the amount of light avaible. Interesting to note on the chart every other f/stop is doubled ( 1, 2, 4, 8, 16, etc.) but the light passing between these is quadrupled. Below is a chart showing the calculations in the area of the opening. See the starting aperture area = 3.14", when you go up one stop the area doubles, but when double the aperture, the area quadruples. (Chart courtesy of Understanding Exposure, Part 2: Aperture | B&H Explora)

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• JBPhotog
It's a very convenient happenstance that the ratio of the aperture's size to the lens's focal length is a constant measurement of how much light gets in. An aperture iris opened to a circle of 1/4 of the lens's focal length ALWAYS lets in the same amount of light, no matter what the focal length. Expressing the aperture size as that ratio is way the &#*! easier than expressing it as a physical dimension, which differs with focal length. "I'm using a 50mm lens, so I need to set the aperture to 12.5mm. No I'm using a 300mm lens, so I need to set the aperture size to 75mm."

No, no, no!!! I'll just set the aperture to f:4 in each situation, which is 1/4 the focal length.

Since the f-number is the bottom of the fraction, a bigger number produces a smaller aperture, less exposure.

As stated just above, a "stop" change either doubles or halves the amount of light getting into the camera. With shutter speed and ISO, stops are linear: half the speed or half the ISO is half the exposure. Since aperture is a measure of area, that "squared" factors in, so a stop isn't double or twice the number, but "halfway" there, a factor of the square root of 2. That's why a stop of aperture looks fractional. A stop less exposure from f:2 is f:2.8, which is 2 time the square root of 2. Not trying to introduce a bunch of math, which you don't really need to be aware of, just explaining why the scale is what it is. 1.4 - 2 - 2.8 - 4 - 5.6 - 8 -11 - 16, etc.
Every other f-stop is double or half the ratio.

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• JT Nous and Strodav
Now if someone could also explain why wire gauge is the same. Smaller the number the bigger the wire, bigger the gauge number the smaller the wire.

I took that as a joke, but if it wasn't...

Pretty much the same reason: wire gauge is a cross-sectional area rule. Steps between gauge numbers is a constant factor of the area of the wire's cross-section, which you could think of as an electrical aperture.

So is paper.

Paper is how many sheets make a certain weight. Bigger number is thinner paper.

I've been told that my IQ is supposed to be the denominator of a fraction, not the numerator, in order to be accurate...

Yes and no on paper, years ago I worked as a press operator in college and later owned a commercial printing shop. The "Basis Weight" on bond paper is the weight of 500 sheets of the uncut paper in its basic unit, which in the case of bond paper is 17"x22". As the number of sheets remains constant, then the heavier the weight of the stack, the thicker the sheet. Even when the basic unit is cut to a smaller size the bond weight of the paper uncut is still used.

Now BTW, I know Ill get raked over the coals for this.

But "F stop" does NOT mean focal distance.

its a symbol used for mathematical functions.

Function (mathematics) - Wikipedia

simply put, its a system where multiple variables are put into an equation and a single answer comes out.
(Think ISO speed and aperture) to get shutter speed, etc.

Paper is how many sheets make a certain weight. Bigger number is thinner paper.

I've been told that my IQ is supposed to be the denominator of a fraction, not the numerator, in order to be accurate...
Yes and no on paper, years ago I worked as a press operator in college and later owned a commercial printing shop. The "Basis Weight" on bond paper is the weight of 500 sheets of the uncut paper in its basic unit, which in the case of bond paper is 17"x22". As the number of sheets remains constant, then the heavier the weight of the stack, the thicker the sheet. Even when the basic unit is cut to a smaller size the bond weight of the paper uncut is still used.

I kinda meant paper size as in A3 is bigger that A4 ets etc. It’s not all that complicated

f2 = f 1/2
f4 = f 1/4 X focal length

Don't forget us shotguners, the 12 ga. is the diameter of a lead ball that requires 12 balls to make a pound. (about .720 in.) A 20 ga. is the diameter of a lead ball that requires 20 balls to make a pound. (about .620 in.)

I blame that on the Brits.  Then there is the lowly .410 ga. It actually measures .410 in. or so.

The nice thing about the f stop is it is inversely proportional to the speed. Or in plain English, the aperture diameter gets bigger (more light), the shutter speed gets faster. (less light).

• Soocom1
For me the light really went on when I realized from the math that it is basic triganometry and that full F-stops are in multiples of 1.41 (square root of 2). Someone earlier in this thread has diagrams that show the math. That is very helpful.

It reminds me -- though not the same -- of the inverse square law and how light dissipates in 3 dimensions. It relates the fixed number of photos filling the volume of a sphere as it gets larger. Doubling the radius increases the volume exponentially, not arithmetically.