Why Are F/Stop Numbers Backward?

Photographers are always going on about “What f/stop did you give it?”  This may also be expressed as: f-number,  focal ratiof-ratio, or relative aperture.  What are they talking about?

Following on from the previous post about the Color Temperature and why it seems to be a paradox.  Another bit of paradoxical photography terminology is the numbering of f/stops (Aperture).  Many beginners (and not a few professionals) have a hard time reconciling that a small f/stop actually means a wide aperture and vice versa, that the big f/stop numbers mean a smaller aperture size (hole).

All is revealed when you discover that the f/stop number is the ratio result of  focal length of lens / aperture size (Diameter).  Eg.  a 100mm focal length has it’s stop (aperture) set to a size of 20mm – that means the f/stop number is 5,  but if the aperture size was just 4mm then the f/stop number is 25!  (I used easy numbers to avoid fractions of a ratio).

Definition of Focal Ratio as a graphic
Definition of Focal Ratio as a graphic

The numbers you see/use are calculated so that a doubling or halving of light passing through the aperture (iris) occurs as you move “one full stop” in the appropriate direction.  In other words the relationship of the area of the aperture opening to allow light through is the determining factor in exposure.  So different focal lengths will need different aperture areas (sizes) to pass through the same amount of light in a given unit of time.

Standard apertures (f/Stops)
Standard apertures (f/Stops)

But this doesn’t mean that if you have set f/16 then f/8 would be twice the light amount let through.  It actually turns out that the ratio number that halves the light is 11.  Oh no!  f/8 would actually be 2 stops increase which means 4 times the light is allowed to pass.  How can this be?  Easy.  Since it is the diameter of the aperture you are using you are really making use of the area of the aperture, which historically has always been a circle but could be a square or triangle or some other shape.  If you double the diameter you have actually increased the area the aperture circle encloses by 4 times!  So what is one stop (bigger in area) than f/16, turns out that it is f/12 but for other historical reasons f/11 has been used.  The ratio numbers are a little wobbly when you do the maths but it all works out in the end.

If you have heard of a T-Stop that is an f/stop corrected for transmission loss and is typically only applicable in cinematography so that different camera lens will pass exactly the same amount of light rather than the rather loose arrangement that f/stops with still image lenses have been built with.

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