f-stop is a term or a measurement [or just call it a setting on your camera for easier understanding] that defines how wide the aperture is open and how much light will pass through it. Some of the most commonly used f/stop numbers are,

f/1.0, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, f/44

This is one of the most confusing aspects of photography and a mystery to many people, even to the ones who are deep into photography and use it all the time. To understand how this calculation works and what these numbers represent, we will have to go a little into high school mathematics but a simple explanation first. If you do not wish to know all the math behind it, just remember that each of the f/stops numbers specify a certain amount of opening in the aperture. Each of the f/stop number would either double the amount of light entering into the sensor or cut it in half than the previous f/stop setting. It means that at f/8, the opening in aperture will be smaller than that of f/5.6 and the amount of light entering the sensor will be half of f/5.6. Further at f/11, the opening will be narrower and it will be half of the light entering at f/8. Lets refer to the picture below to help us understand this a little better.

As you can see, every-time you change the f/stop number, the overlapping blades close in and and the hole keeps getting smaller. This is the hole that light passes through from the lens to to the sensor and hence larger the hole means more the light.

F/1.0 though the smallest number is the largest of these stops and you are shooting “wide open” when you have this number selected on your camera because the aperture is completely open. As you switch to a higher number, you are reducing the size of the opening and each f/stop after is half as much the light as the previous one.

And that is it. f/stop is nothing more than a preset on your camera dial which tells you how much the aperture is open.

Now this is all you need to know from a photographer’s point of view in order to take pictures. If you have no intention of going into the technical and mathematical details, you can stop and move on to the next article. However if you do wish to know how this entire concept of f/stops works, then continue reading.

People often get thrown off by mainly two things, when it comes to f/stops.

Why are these numbers the other way around? Why is 1 here greater than 16? Why not switch it and put f/1 for the setting when the aperture’s opening is smallest?

F/5.6 is not half of f/8 so if the amount light is getting cut into half, where is this calculation coming from? Why are these numbers not half of the previous f/stops?

The variation between these numbers is definitely the most confusing part. For example, switching from f/1.4 to f/2 doesn’t really look like halving the amount of light. f/8 sounds like more light as it is a larger number. Neither does f/11 to f/8 looks like double the amount of light. The explanation of these lies in the “area of aperture” that is derived from these f/stop numbers. Remember, f/stop is a measurement of aperture which directly impacts the depth of field {about which you will read in a later article in this series]. This is where the mathematical explanation comes in and we will have to refer to a few formulas,

Formula for radius which is D/2 where D stands for Diameter

Formula for the area of a circle which is π * radius2, where π represents the value of pi which is 3.14159265.

The inverse-square law of physics which states that a specified physical quantity or intensity is inversely proportional to the square of the distance it travels. In formula, Intensity is proportional to 1/(Distance * Distance)

For these calculations, lets say we have a lens of focal length 50mm.

Camera Setting A : 50mm lens at f/8

Aperture Diameter would be Focal Length divided by f-stop = 6.25

Aperture Radius would be Diameter divided by 2 = 3.125

Area of aperture would be [pi * Radius * Radius] = 9.76pi

Hence the intensity of light passing through would come to [9.76pi/(50 * 50] = 0.012264778

Camera Setting B : 50mm lens at f/11

Aperture Diameter would be Focal Length divided by f-stop = 4.54

Aperture Radius would be Diameter divided by 2 = 2.27

Area of aperture would be [pi * Radius * Radius] = 5.15pi

Hence the intensity of light passing through would come to [5.15pi/(50 * 50] = 0.006471681

Camera Setting C : 50mm lens at f/stop f/16

Aperture Diameter would be Focal Length divided by f-stop = 3.12

Aperture Radius would be Diameter divided by 2 = 1.56

Area of aperture would be [pi * Radius * Radius] = 2.43pi

Hence the intensity of light passing through would come to [5.15pi/(50 * 50] = 0.00289026

5

As you can tell from these calculations, the amount of the light entering the sensor is getting either gets almost doubled or cut in half with every different aperture setting. The reason why the stop numbers are not always double of the previous number is because f/stop is a ratio between the focal length of the lens and the aperture in it.

Apart from the light, another thing that either gets cuts in half or doubled with every f/stop number is the area of aperture. To understand this, we will again have to go into mathematical calculations based on the above mentioned formulas.

Camera Setting A : 100mm lens at f/2.8

Aperture Diameter would be Focal Length divided by f-stop = 35.71

Aperture Radius would be Diameter divided by 2 = 17.86

Area of aperture would be [pi * Radius * Radius] = 1001.78 Sq mm

Camera Setting B : 100mm lens at f/4

Aperture Diameter would be Focal Length divided by f-stop = 25

Aperture Radius would be Diameter divided by 2 = 12.5

Area of aperture would be [pi * Radius * Radius] = 490.87 Sq mm

Camera Setting C : 100mm lens at f/5.6

Aperture Diameter would be Focal Length divided by f-stop = 17.85

Aperture Radius would be Diameter divided by 2 = 8.93

Area of aperture would be [pi * Radius * Radius] = 250.45 Sq mm

So we notice, every-time there is a change in f/stop, the area of aperture either doubles or halves.

All this mathematical explanation is just good to know information, to give you a better understanding of what you are working with. The only few things you really need to know about f/stops from a photographer’s point of view are,

- f/stops controls the amount of light that enters the sensor
- It affects depth of field in a photo
- Low f-stop number means larger lens opening and hence more light
- High f-stop numbers means smaller lens opening and hence less light

Another good to know information that we can discuss here is about the origin of the word “f/stop” and why the f is in lower case. While many belove that the letter “f” stands for focal, it actually is not the case. The idea of f/stops was introduced in early days of the cameras when photography had just been introduced to the world. Cameras were a new invention back then and were going through a lot of changes and modifications. How the overlapping blades can widen or narrow the aperture opening is something that was invented by a well known photographer of those days, Ansel Adams. He with a other few photographers had formed a group called f.64. Members of this group were all famous photographers and pillars of the world of photography. Initially the group thought to name itself as US256 but the idea was later scrapped and they decided on f.64. The dot later got replaced with a slash and the group got named as f/64. Later when the entire concept of controlling the aperture opening was bought in by the group, it got named the lower case f with a slash mark followed by the measurement, solely to name this innovation after the group’s name.