# So You Think You Know What An F-Number Is

Most of us have heard, and probably used, the term **f-number**. Most of us have also probably used the term interchangeably with “f-stop” or “aperture”. What are all these things, really? Yes, they have to do with the size of the hole allowing light to pass through the lens, and they affect depth of field and light intensity. But I’m talking about what these things really *are*.

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First, let’s start with a few definitions. An **aperture** is simply a hole which allows light to pass through it. A **diaphragm** is the mechanism inside your lens that forms an aperture, and most modern lenses have an* iris diaphragm* made up of several interlocking blades. An **f-stop** is a discrete step in the f-number, and it refers to the physical stops in the diaphragm adjustment. So how are all these things different from an f-number?

An f-number is a measure of lens speed and it is defined by the focal length of the lens divided by the diameter of the aperture — f/# = f/D where f = focal length and D = aperture diameter. So if the focal length of the lens is equal to the diameter of the aperture, you’d have an f/1. If the focal length of the lens is 8 times longer than the diameter of the aperture, you’d have an f/8.

**F-Number = f/D = (Focal Length)/(Aperture Diameter)**

Here’s an example with one of my fixed focal length lenses (zooms are a little more complicated so I’ll hit that in a moment). I have a 50mm f/1.4 lens. The f/1.4 designation means that it has a *maximum* f-number of 1.4 — so that’s as big as it gets. The minimum f-number on this lens is f/16, so it can vary from f/1.4 to f/16. So using the formula for f-number: at a 50mm focal length and an f-number of 1.4, the equation states 1.4(f/#) = 50mm(f)/(D). Do the algebra, and we get 50mm/1.4 = 35.7mm. That’s physically how big the aperture is at it’s maximum. If I had a f/1.2 lens, the max aperture would be 41.7mm. Now to the other end of the scale, the aperture on this lens has a minimum diameter of 50mm/16 = 3.1mm. Similarly, my 105mm f/2.8 lens has a maximum f-number of f/2.8, an aperture diameter of 37.5mm — which is about the same size as my 50mm lens at f/1.4, which is two stops up from f/2.8.

for a 50mm lens… | ||

F-NUMBER | APERTUREDIAMETER | APERTUREAREA |

1/# | mm | sqmm |

1.4 | 35.7 | 1002 |

2 | 25.0 | 491 |

2.8 | 17.9 | 250 |

4 | 12.5 | 123 |

5.6 | 8.9 | 63 |

8 | 6.3 | 31 |

11 | 4.5 | 16 |

16 | 3.1 | 8 |

On the 50mm lens, including the minimum and maximum f-numbers, there are a total of 8 full f-stops: f/1.4, 2, 2.8, 4, 5.6, 8, 11, and 16, with half-stops between everything but 1.4 and 2 (things like f/1.7, f/6.7, and f/9.5 are half stops — f/1.8, f/3.5, and f/6.3 are third stops found in most modern lenses). **Each full stop lets half as much light in as the last full stop**. This is because the *area* of the aperture is reduced by half with each stop. The values in the table represent the f-numbers, aperture diameters, and aperture areas for this lens. Note the reduction of area as the f-numbers increase. Each full stop down lets half as much light into the camera, and you can see that the area of the aperture for each stop is also cut in half. This is where a lot of people end up confusing themselves over f-numbers. **Higher f-numbers mean smaller apertures** — just remember that. To help explain the numbers in the table a little better, the image below shows the 50mm lens at each full stop from f/1.4 to f/16 from left to right.

**Zoom lenses** are a bit more complicated, and they generally fall into two groups: constant f-number and variable f-number. **Variable f-number zooms** are most common because they are simpler and cheaper. You can spot these lenses by their markings — f/3.5-6.3 means that the lens has a maximum f-number of f/3.5 at the shorter focal length and f/6.3 at the longer focal length. This doesn’t mean that the aperture changes as you zoom; it actually means that it doesn’t change. Remember that f-number is the quotient of focal length and aperture diameter, so as you zoom to a higher focal length (and keep the aperture constant) you allow less light into the camera and the f-number changes. On the other hand, the really spendy zoom lenses can maintain a **constant f-number** at all focal lengths. To achieve this, they must increase the effective aperture diameter as the focal length increases to keep the same f-number ratio.

**F-numbers in zoom lenses aren’t quite as simple as I’ve made them out to be**. That’s basically how they work, but truthfully, I don’t know exactly how they work. If you run the numbers on a zoom lens, it turns out that you don’t get a constant aperture diameter as the focal length increases and the f-number changes. Physically, I’m pretty sure the aperture diameter stays the same. But when you zoom a lens, you shift the location of lens elements, the diaphragm, focal planes, inflection points, etc., and some of these things are factors for the ** effective aperture diameter**. I’m not an optics expert, so I’ll leave it at that.

Basically, **the major take-away** from this should be that the **f-number is a measure of lens speed** — regardless of the camera, regardless of the lens, and regardless of the conditions. If you and a friend are out shooting, you should be able to get the same exposure of a particular subject if you shoot using the same f-number, shutter speed, and ISO value (assuming ISO’s between cameras is somewhat comparable). It takes the focal length and aperture diameter into account in order to give a value of how much light will be allowed into the camera.

*If anybody else out there has a better explanation of how f-numbers on zoom lenses work, feel free to let us know.*

## Karl Schuneman

June 18, 2007I have found one website and one article website that explains the f-stop and it’s use with digtial cameras.

http://www.slrgear.com Very important information on the sharpness of lens. Checkout their test on “blur”. They show that DSLR and SLR lens are their sharpest F8 to F11 and the faster the lens the sharper the lens becomes in that range.

http://www.cambridgeincolour.com/tutorials.htm These tutorials are very well done. Under “Advance Tutorials” read about “Understanding Diffraction: Pixel Size, Aperture and Airy Disks” Limits on Digital cameras f-stop. Sure you can use smaller opening, but sharpness of the image will fall off.

## Andrew Ferguson

June 18, 2007Thanks for jumping in on this, Brian. I was vaguely aware of the relationship between focal length and aperture. What I wasn’t aware of was the mechanics of the relationship and how that affected variable f-number zooms:

“This doesnâ€™t mean that the aperture changes as you zoom; it actually means that it doesnâ€™t change.”

I think I need to spend some more time learning the physics and optics once I finish my current batch of photography books.

## Brian Auer

June 18, 2007Be careful what you jump into — optics is a HUGE topic. I’d like to learn more about it, but I focused on other topics when I went to school for mechanical engineering. All I know is that I don’t know the least of what really goes on with optics. If you find any good books on the subject, let me know. I wouldn’t mind diving into it a little bit.

## photography tips

June 21, 2007Good article! This table and all these tips are very helpful in most cases, though sometimes you should more rely on your intuition and experience. Photography requires practice, practice and practice!

## The Dino

July 8, 2007I am happy that I found this blog. I had idea about F but after this I become expert.

## Alan Cook

January 27, 2008Awesome. You make my understanding of F-number look like a joke.

Thanks for the great information.

## burun

February 5, 2008Great blog page. Thanks a lot for the information.

## göğüs büyütme

April 2, 2008Very informative article about F-stop and aperture relations. This is the basics of photography everybody should memorize.

## Mirko CRO

May 4, 2008Great article!

I have one question regarding aperture: How does all this relate with crop factors of an DSLR camera?

If i have camera with crop factor of 1.5 and a 50mm f/1.4 lens. Does that mean that my f number isn’t 35.7mm (50/1.4) but 53.6mm (50*1.5/1.4)?

“the f-number is a measure of lens speed — regardless of the camera, regardless of the lens, and regardless of the conditions.”

Would that mean that this statement isn’t true?

## Brian Auer

May 4, 2008Good Question!!! The crop factor on a digital camera has nothing to do with the lens’ f-number, real focal length, and aperture diameter. The increase in focal length is only an equivalent value — it’s not actually giving you any more magnification (check out this article where I did a comparison between a digital and film SLR equipped with 50mm lenses).

So if you have a 50mm lens (for a film or digital camera) and you set the f-number at f/1.4, your aperture diameter is 35.7mm.

## Mirko CRO

May 4, 2008Thanks!

I get it. Just one more thing – does the crop factor affect depth of field (and how if it does)?

## Brian Auer

May 4, 2008The crop factor does change the depth of field. Here’s an online DOF calculator that you can use to see the differences between digital and film cameras. I couldn’t really tell you why though without doing a little more research on the subject.

## Victoria

July 22, 2008I came across this blog and the post title grabbed my eye, so I started reading. My answer to the question in the title would be – yes, I do know what an f-number is and will be glad to share this with those interested.

The actual definition for the f-number is the focal length divided by the entrance pupil diameter.

When you look at the entrance of your lens what you see is not the actual diaphragm, but its image, formed by preceding surfaces. This image of the diaphragm is called the entrance pupil and its apparent size and position are determined by those preceding lenses you’re looking through.

In variable f-number zooms with fixed diaphragm diameter changing the focal length also changes the entrance pupil diameter and position due to the necessary shift of the lens elements. So even if the diaphragm size is constant, as Brian suspected, in reality the entrance pupil diameter varies.

Moreover, there are cases in variable f-number zooms when the iris diameter is changed as you zoom along with the f-number, but it’s a different story…

Thanks for reading my boring comment :)

## Denise

August 1, 2008Photography is so very calculative and involves a lot of technique. This shows how much mastery is needed to be an ace photgrapher.

## estetik

September 25, 2008Great post. Every photographer knows the importance of F-number.

## izlekop

November 4, 2008In variable f-number zooms with fixed diaphragm diameter changing the focal length also changes the entrance pupil diameter and position due to the necessary shift of the lens elements. So even if the diaphragm size is constant, as Brian suspected, in reality the entrance pupil diameter varies.

## Burun Estetiği

December 3, 2008When you look at the entrance of your lens what you see is not the actual diaphragm, but its image, formed by preceding surfaces. This image of the diaphragm is called the entrance pupil and its apparent size and position are determined by those preceding lenses you’re looking through.

## Joel

April 5, 2009That was a pretty good explanation of focal numbers. very well explained. There are a lot of technical aspects in photography which makes picture a perfect one.

## Продажа Электродвигателей

May 14, 2009When you look at the entrance of your lens what you see is not the actual diaphragm, but its image, formed by preceding surfaces. This image of the diaphragm is called the entrance pupil and its apparent size and position are determined by those preceding lenses you’re looking through.

In variable f-number zooms with fixed diaphragm diameter changing the focal length also changes the entrance pupil diameter and position due to the necessary shift of the lens elements. So even if the diaphragm size is constant, as Brian suspected, in reality the entrance pupil diameter varies.

Moreover, there are cases in variable f-number zooms when the iris diameter is changed as you zoom along with the f-number, but it’s a different story…

## kurye

January 18, 2010