The Mathematics of the f/stop

The mathematics of the f/stop can be very confusing, but if you can remember just this, then you can get by.  The f/stop is a ratio--a ratio of the focal length of the lens that you are using, to the stop number of your choice. The f, representing focal length, is in the numerator of this ratio (fraction), and the stop number is in the denominator.  Dividing f by the stop number gives the diameter of the aperture opening and determines the amount of light entering the camera through the lens.  We remember that circles with larger diameters are bigger, right?  So, an aperture opening with a large diameter will let in a large amount of light.  You with me?

Now, let's think about the math.  When you divide a fixed quantity, say f = 70 mm, by a small stop number like 2.8, then the quotient is 70/2.8 = 25 mm.  This indicates that the diameter of the roughly circular opening of the aperture is 25 mm (a relatively large diameter letting in a large amount of light).

If you divide the fixed quantity, 70 mm, by a larger stop number like 5, then the quotient is 70/5 = 14.  The stop number of 5 makes the diameter of the aperture opening smaller, now 14 mm (a smaller diameter letting in a smaller amount of light than the 2.8 stop mentioned above).  Can you see that increasing the stop number in the denominator of the f/stop ratio decreases the diameter of the aperture opening when the focal length is fixed?  

So, the f/stop provides you with the length of the diameter of the aperture.  And, the stop number and this diameter are inversely proportional.  When you increase the stop number, the aperture diameter decreases and when you decrease the stop number, the aperture diameter increases.  

My main problem understanding the f/stop has been its name-- f/stop.  This fraction tells me to divide, yet on my camera, I choose only the denominator of this ratio.  I would like for us to stop using the term f/stop and simply say something like "aperture stop".  This requires two more syllables, though, so maybe not.

For more information on the f/stop, you might like the article at the following link.

A Tedious Explanation of the f/stop