F-Stop Numbers Explained, Left Brain Thinking!

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Have you ever wondered how the aperture numbers work? Probably not right. Well, I did. It’s how my mind works. So for all of you left brained thinkers out there…..here you go.


Let me quickly explain aperture for those who don’t know. Simply put it is the size of the opening on your lens that allows light into your camera. This opening is adjustable if you have a manual operating camera. I think aperture is the hardest thing for most photographers to understand because intuitively it is backwards. The larger the aperture number the smaller the opening in the lens. Completely backwards and confusing….I know. We can blame the math for that. If you want to know more about the basics of aperture visit our article here.


Now, the most simple way to define the math to calculate the aperture number is the focal length of your lens divided by the diameter of the opening in your lens. The equation looks like this: S=F/D where S=f/stop number, F=focal length & D=diameter of the opening. Now lets dig into the details.


First, let’s talk about the most common aperture numbers you see on lenses: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32. Thats about as far as most lenses get. These numbers are in full stop increments. Most DSLR’s will show 2 numbers between each of these increments. Can you see any rhyme or reason to these numbers? Check out every other number……1.4, 2.8, 5.6, 11, 22 and 2, 4, 8, 16, 32…..they double with the exception of 5.6 to 11 but thats only because of the change from a fraction to a whole number. Technically it is 11.2. Doesn’t that makes things a bit easier to remember?


Lets go back to the math now. To start lets say you have a 50mm prime lens. This means you get 50mm focal length and that is all….no zoom. If you set that lens to f/2.8 the opening of the lens will adjust to 17.86mm when you press the shutter. If you are shooting with a DSLR the lens is wide open until you press the shutter then the lens aperture blades adjust to the aperture you have selected. How did I get to that number? I switched the equation around a bit. Now I wanted to solve for the diameter of the opening so this is the proper equation: D=F/S. So D=50/2.8 and therefore D=17.86. If you were to use the same lens at f/22 then your opening would be 2.27mm…..tiny.


Lastly, lets talk about why lenses cost so much. Have you ever seen those really big lenses at sporting events? They’re massive, why? Let’s do the math. If you have a 400mm lens and you want to be able to shoot at f/2.8 how big of an opening do you need to let all that light go that far? Math time again….D=400/2.8. The answer is 142.86mm. To all of our North American friends thats 5.6 inches of diameter needed. That doesn’t include the lens housing that this opening has to live in either. What does this mean? A ton of high quality glass and materials to make this massive lens and a $10,000 price tag.



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