Lens aperture, f-stop and why it’s intuitive

There are a lot of beginners in photography who don’t fully understand lens basics. It’s a lot to take in, especially if you aren’t mathematically inclined, so there’s no shame in that. I also think experts in photography get a little confused by the digits and pass that along to beginners. As a demonstration, I typed “explain lenses to me” in Google and one of the top articles I was linked to is published at masterclass.com. It’s a great article, and the majority of it is accurate but I spotted a mistake.

You’ve probably read or seen a million and one articles/videos about lens basics, but I think the way I view it is different to those. Please let me know what you think in the comments below as I don’t want to churn out content exactly the same as everyone else :).

F-stops are counterintuitive, because the larger the number, the smaller the opening

This is a quote from the article, and you might think it’s accurate, right? That’s actually wrong; the bigger the aperture, the bigger the number. Aperture values aren’t expressed like ISO with a simple number e.g. 100, 200, 400, etc. They’re a calculation/ratio/equation: f/x. F (the focal length of the lens you have mounted e.g. 100mm) divided by (the slash) a value (e.g. 1.4). If you don’t complete the calculation and you only take digits from an equation, it will seem counter-intuitive.

Aperture values are expressed as a calculation/ratio/equation

A bigger aperture gives you more background blur when all else is equal; consequently, a bigger aperture number gives you more background blur as well. They are one and the same but not if you misunderstand the calculation. It’s intuitive when you realise you’re given a calculation and not a number.

Using two example apertures, both with a 100mm lens, we can calculate dimensions… For my first two examples, I will use f/1.4 and f/2.8, where f = 100mm:

  • 100mm / 1.4 = 71.4285714286mm (this is your aperture when expressed as a number i.e. a dimension, NOT 1.4; 1.4 is simply a VALUE from the equation).
  • 100mm / 2.8 = 35.7142857143mm.

As you can see, the bigger diameter/number (71.4285714286mm) is the wider aperture and gives more background blur (all else being equal).

Why have aperture expressed as an equation rather than a dimension/number?

A number on its own would soon become confusing. Let’s pretend we have a 35mm lens mounted; f = 35mm:

  • 35mm / 1.4 = 25mm.
  • 35mm / 2.8 = 12.5mm.

A 12.5mm aperture on a 35mm lens is the same as 35.7142857143mm on a 100mm lens. As you can see, it’s awfully confusing. So it’s a lot easier to have f/2.8 shown in camera. The bigger number is f/1.4 — not f/2.8.

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