Chapter 12. How ƒ/Calc Handles Aperture Values

The aperture numbers 1, 1.4, 2, 2.8, 4, 5.6... are the integer powers of the square root of 2: ƒ/1 is the square root of 2 to the zero'th power, ƒ/1.4 is the square root of 2 to the first power, ƒ/2 is the square root of 2 squared, and so on. Fractional stops are fractional powers instead. See the ƒ number formulas section for more detail on all this.

The even integer powers are all exact values (1, 2, 4, 8...), but all the other common ƒ stop values are approximations of varying accuracy.

All this is just trivia most of the time, but when doing calculations with ƒ numbers, it makes sense to use the most accurate values possible. ƒ/Calc's drop-down aperture lists show the common approximations, but internally it always uses the accurate value instead. For example, ƒ/5.6 is actually ƒ/5.656..., so it's not even rounded correctly, much less very accurate as computer math goes. But, few care about this trivial detail, so ƒ/Calc juggles things internally so it can show you ƒ/5.6 while it goes and uses the “real” value in its calculations.

If you want to see what values ƒ/Calc is using for these aperture values, the easiest way is to:

  1. change the ƒ stop rounding rule to “3 decimal places”

  2. go into the ƒ Number tab and tell it you want to calculate ƒ2 as ƒ1 plus stops

  3. put 0 in the ƒ1 field, then put odd integer values in the stops field

Note that if you type in one of the common approximations, like 5.6, ƒ/Calc will not second-guess you and substitute 5.656854.... It will assume you really want to use the value 5.6. You can again use the ƒ Numbers tab profitably here. Tell it to calculate stops as ƒ2 minus ƒ1, then pick one of the odd ƒ numbers from the ƒ1 drop-down list and type the “same” value in the ƒ2 field. The calculated stops difference tells you how far apart the idealized and actual values are.