# Thread: Calculating f-stop progression . . .how are the numbers derived?

1. ## Calculating f-stop progression . . .how are the numbers derived?

I have noodled around online, but can't quite find out what I would like to know:

How are the f-stop numbers derived? i\I understand that it is a ratio of focal length to aperture . . .but can't quite get the math right. I have inklings of the natural log of 2 being involved somehow.

I do not have any pressing reason to do this, but its still early and the coffee has kicked in.  Reply With Quote

2. ## Re: Calculating f-stop progression . . .how are the numbers derived?

Drew,

I believe it is a progression of the square root of 2.

But would be interested in hearing what the right answer might be as well.

Len  Reply With Quote

3. ## Re: Calculating f-stop progression . . .how are the numbers derived? Originally Posted by Len Middleton Drew,

I believe it is a progression of the square root of 2.

But would be interested in hearing what the right answer might be as well.

Len
That's right. Each full stop step halves (going up from 1.0 to 1.4, 1.4 to 2.0, ...) the amount of light the film receives given subject illumination and shutter speed.  Reply With Quote

4. ## Re: Calculating f-stop progression . . .how are the numbers derived?

Aperture controles light intensity. So it controls the SURFACE of the opening of the diaphragm. But it is expressed as a ratio of linear dimensions. Doubling the surface is done by making the diameter square root of 2 larger. So you get a progression by square root of 2: 1-1.4-2-2.8-4...  Reply With Quote

5. ## Re: Calculating f-stop progression . . .how are the numbers derived?

A pretty much complete explanation:
https://www.slrlounge.com/a-thorough...ehind-f-stops/
For me the key was remembering that doubling the area of a lens opening, and thereby the amount of light, is accomplished by changing the diameter by the square root of 2 (1.4 rounded)  Reply With Quote

6. ## Re: Calculating f-stop progression . . .how are the numbers derived?

As Havoc notes, f/# values change by the area size. As such, the numbers change by the square root if 2.  Reply With Quote

7. ## Re: Calculating f-stop progression . . .how are the numbers derived?

On a side note, the longer the lens focal length, the larger the glass surface area must be to give the same f/stop. The diameter of the aperture on a 360mm lens is considerably larger than on a 50 mm lens.  Reply With Quote

8. ## Re: Calculating f-stop progression . . .how are the numbers derived?

Hello from France!
The present f-number system was not standardized when manufacturers started to sell photographic optics.

See this comparative chart of old f-stop systems

And after the f-number was adopted, it took again some time before all lenses would be engraved (except for max aperture) according the modern standard series 1.4 - 2 - 2.8 - 4 - 5.6 - 8 - 11 - 16 - 22 - 32 - 45 - 64  Reply With Quote

9. ## Re: Calculating f-stop progression . . .how are the numbers derived?

Another way of looking at it is the progression of the area of a sphere with change in radius, where radius is the f number in any units (inches, meters, furlongs). The area doubles with each f number. The area of a sphere is given by 4 pi r^2, so taking the ratio of 2 radii r1 and r2 yields r1^2/r2^2.  Reply With Quote

10. ## Re: Calculating f-stop progression . . .how are the numbers derived? Originally Posted by Jim Michael Another way of looking at it is the progression of the area of a sphere with change in radius, where radius is the f number in any units (inches, meters, furlongs). The area doubles with each f number. The area of a sphere is given by 4 pi r^2, so taking the ratio of 2 radii r1 and r2 yields r1^2/r2^2.
surely the area of a circle is all that's needed  Reply With Quote

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•