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Saturday, July 31, 2004

The F Number - Demystified

In any camera that allows you to have control over aperture, the aperture setting is done using what is referred to as F stops. For example, in my Canon G5, the F stops are as follows.

2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, 4.5, 5.0, 5.6, 6.3, 7.1, 8.0

What this means is, I can set the Aperture on my Canon G5 to any of these values. So what does it mean to set the aperture to F2.0 or F4.5 etc ? Every newbie, faces some confusions with these F numbers.

  • They don't seem to follow a linear series like 1, 2, 3, 4
  • Notation keeps varying like f/2.0 or F2.0.
  • The number is supposed to indicate a value of Aperture but there is no "A" in the notation!
  • Any time there is a discussion about increasing or decreasing aperture, people don't use these numbers. They talk about "stops", like move up 1 stop or move down half a stop etc.

So what's up with this numbers ? The concept behind these number is not that complicated, but the notations and varying terminology to describe the same thing leaves some room to explain.

Aperture is the size of the opening that lets light in to be exposed on your CCD or film. To control the amount of light that is exposed, you vary the size of the Aperture, i.e. the area of the opening. To reduce the amount of light entering by half, the aperture area can be reduced to half. When the aperture is reduced to half the size, than that is called one full stop reduction of aperture area. Similarly when the aperture i.e. the area of the opening is doubled, that is called one full stop increment of aperture area. Let's say the maximum opening of aperture is the zero stop and we keep reducing the aperture from there, each time reducing the area by half i.e. by one full stop. In the figure below, the circles on the left show what the area would look like from zero stop to 5 stops. On the right is a graph, showing how diameter changes as we reduce area by half with each stop.

If you are technical or if you remember your geometry class, you can figure out that, to reduce the area to half (divide by 2), the diameter of the circle must be divided by square-root of 2 = 1.41421356.

Now in any cameras, if we had to deal with measurements of the diameter to control the aperture, it would be impractical to operate. So instead of actual dimension, the diameter is noted as a fraction of focal length f of the lens of the camera. So let's say maximum diameter of aperture is equal to half of the focal length, then this diameter is noted as f/2.0.

Next, let's say we want to move to next stop, then
the diameter of aperture at next stop = f/2.0 *1/1.41421356 = f/2.82842.
Similarly as we continue to next stops, we see the diameter as indicated by following series.

stop 0 = f/2.00000
stop 1 = f/2.82842
stop 2 = f/4.00000
stop 3 = f/5.65685
stop 4 = f/8.00000
stop 5 = f/11.31370
stop 6 = f/16.00000
stop 7 = f/22.62741
stop 8 = f/32.00000

The F number that you see on your dial or on your LCD when you play around with Aperture is this divider. However, in any camera, having aperture values at full stop intervals only is not enough. One would definitely want to have finer level of control over aperture than just double the light coming in or reduce it by half. That's why most of the cameras provide aperture values at half stops or 1/3 stops. You can imagine intermediate values of diameter at 1/2 or 1/3 positions between various full stop positions on the STOPS graph above.

In case of half stops, between each consecutive full stop aperture values, there will be one more value which is derived by dividing the bigger diameter by fourth root of 2 = 1.1892071 . Another thing worth note over here is that each move to next F number reduces the amount of light to about 71% (70.71% to be precise) of previous setting. So moving twise reduces the light to 0.7071*0.7071 =0.5 = 50% = full stop as desired.

We are more interested in one third stops because that is what G5 has.

In case of one third stop intermediate aperture values, each time next diameter is derived by dividing previous diameter by sixth root of 2 = 1.1224620

With that formula, the series you'll get is...

f/2.00000 = stop 0
f/2.24492 = stop 0 + 1/3
f/2.51984 = stop 0 + 2/3
f/2.82842 = stop 1
f/3.17480 = stop 1 + 1/3
f/3.56359 = stop 1 + 2/3
f/4.00000 = stop 2
f/4.48984 = stop 2 + 1/3
f/5.03968 = stop 2 + 2/3
f/5.65685 = stop 3
f/6.34960 = stop 3 + 1/3
f/7.12718 = stop 3 + 2/3
f/8.00000 = stop 4

As you can see below, this is what canon G5 offers.

2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, 4.5, 5.0, 5.6, 6.3, 7.1, 8.0

In this case, each time you move to next F number in aperture setting, the amount of light reduces to approximately 80% (79.37% to be precise) of the previous setting. This way after three moves, the amount of light reduces to 0.7937 * 0.7937 * 0.7937 = 0.5 = 50% or full stop as desired.

Things to remember about Aperture setting and F number

  • F number is an indicator of aperture of camera, it denotes the diameter of the aperture as a fraction of the focal length of the lens.
  • F2.0 or f/2.0 means the same thing, they are just different notations.
  • Smaller F number means larger aperture = more light.
  • Larger F number = smaller aperture = less light.
  • Moving one full stop to a higher F number reduces the light to half and moving one full F stop to lower number means doubling the amount of light.
  • If your camera provides 1/3 stops, then to move a full stop will require moving to the third number in the series. Similarly, if your camera provides 1/2 stops you will have to move two numbers in the series, to move a full stop.
    For example, in G5 a move from F2.0 to F2.8 is a full stop and reduce the light by half. But a move from F2.2 to F3.2 or F2.5 to F3.5 is also a full stop and reduces the light by half.
  • 1/2 stop movement reduces the light to 71%
  • 1/3 stop movement reduces the light to 80%

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Blogger nick said...

thanks so much for the detailed explanation! i've just picked up photography and i was about to go crazy about photography terms. gonna put his blog in my favourites! pls don't mind.

2/27/2005 07:49:00 PM  
Anonymous Anonymous said...

An f/ number of 1 would mean the diameter of the lens opening is the same as its focal length (focal length of 50 mm and opening of 50 mm) is optically impossible.

7/26/2005 03:57:00 PM  
Anonymous Anonymous said...

Most simply stated, the f/ number is the reciprocol of the focal length / opening diameter ratio. focal length 50 mm, opening 25 mm (1/2) = f/2, focal length 50 mm, opening 3.125 mm (1/16) = f/16. Once you get past the range of f/45 you start to get "pin hole" effect. A good pin hole camera may have a f stop that exceeds 1000, marvelous depth of field but unbelieveably long exposure time.

7/26/2005 07:23:00 PM  
Anonymous Anonymous said...

jni said...

An f/ number of 1 would mean the diameter of the lens opening is the same as its focal length (focal length of 50 mm and opening of 50 mm) is optically impossible.

Canon had an EF 50mm f/1.0 lens for sale at least 7 years back. I got a chance to play with one myself when I worked in a camera store. Very nice but also quite heavy and expensive. A quick perusal of Canon's site makes me wonder if the market for such a thing has dried up, as they no longer advertise it.

7/27/2005 09:09:00 AM  
Anonymous Anonymous said...

The best explanation I've seen of f-stop!

Here's a link to an artcle about the 1.0 Canon Lens: http://www.shutterbug.net/test_reports/0402sb_canons/

and here's a Nikkor: http://homepage2.nifty.com/akiyanroom/redbook-e/repro/repro1pon.html

Consumer Zooms end up in the f/3.x+ range and usually can't maintain that through out their range ( f/3.5-5.6 ) - Pro zooms f/2.x+

Prime (single focal length lenses) are often in the f/1.x area

Also for people like nick, you may heat things about the "Speed" of a lens - this usually refers to f-stop, with smaller numbers being "fast".

8/02/2005 12:43:00 PM  
Blogger Basket said...

Bon jour. Le temps amer que je vois.

Chercher le temps et quelques comment terrien ici.

Blog agréable.

Je devrai revenir plus tard.

10/25/2005 01:39:00 PM  
Blogger Admin said...

This is a great article. Thanks for explaining it so well. I am going to recommend this on my forum!

3/02/2006 08:33:00 AM  
Anonymous Anonymous said...

Good explanation. One side point, though: the f-number is not the ratio of the focal length of the lens to the actual diameter of the physical aperture inside the camera. There's a magnification factor due to the optical elements in front of the aperture. It's constant for any given lens, but varies from lens to lens depending on the design.

3/20/2006 03:40:00 PM  
Anonymous Anonymous said...

There has been many faster lenses than f/1.0, but most of them are for smaller size than 35 mm: 16 mm or 8 mm film, video cameras etc.

4/10/2006 12:28:00 AM  
Anonymous Anonymous said...

How about f stops as it relates to depth of focus? And how most lens dont preform their best when opened up all the way.

4/13/2006 11:03:00 PM  
Anonymous Anonymous said...

Awesome site! I just received the Nikon D50 for my Birthday. Can you recommend any good books for this newbie? Thanks so much! Janice Campbell

7/30/2006 11:05:00 PM  
Blogger saanga said...

Hello Janice,

I do not have any book recommendations for you. However, here are a few recommendations on "How to learn basic skills of photography?"

There are three very basic lessons.

1. Exposure: How photography works

Try to understand the basic concept of "Exposure". There are many good articles on the web including an article on this site : Cooking and Photography.

2. Composition: What makes pictures look good

Next important thing is composition i.e. how to identify and emphasize the subject in a frame. A good starting point is the article "The Rule of Thirds" on this site.

3. Technical Skills : How to make the camera do what you want

The third important thing to learn is basic technical skills. This includes knowing your camera, its various modes and manipulation of various dials to get desired results. The best source for this is the product manual. Please Read the Manual. Also read "F Number - Demystified" and "Depth of Field - The Third Dimension" on this site.

Once you understand exposure(How Photgraphy works), composition(What makes pictures look Good) and develop technical skills(How to get the camera to do what you want), you will not look for any books.

I personally have not read any books on photography. But I do read a bunch of articles on the web and forums on dpreview.com.

The best way is to take a lot of pictures of the same scene with different settings and then compare them.

Good Luck.

8/02/2006 08:02:00 AM  
Blogger Matthew Bamberg said...

Great technical info. Good math applications for a high school or college math class.

1/28/2007 01:43:00 PM  
Anonymous Anonymous said...

there's just one problem with this, if diameter=focal length/F# then it should give you the true lens diameter of a zoom lens, once you know the F# as a function of focal length. That would mean the Canon 70-200mm F2.8 IS would have a lens diameter of 71mm at 200mm which is not too much less than the 77mm filters that it takes. But what about the 17-55 F2.8 IS? It takes the same filters. This would mean that Canon has made the lens 4x as wide as it has to be, and of course, 60% of the cost of the 70-200 F2.8 IS. Is it, perchance, actually the "back end" of a 70-200 that just has been aperture-limited to 1/4th the aperture of the 70-200 F2.8?

8/09/2007 03:42:00 PM  
Anonymous Anonymous said...

...this would explain why the 24-105 F4 is the same size as the 17-55 F2.8, though. And only slightly more expensive. Though you might as well just get the 17-55 F2.8 and a 2x teleconverter.

8/09/2007 03:48:00 PM  

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