The precise goal value for f/stop is √2^{Stop Number}

The numerical steps of the f/stop Numbers are the powers of √2, but those steps do give Exposure steps of the powers of 2 (1 EV).
Examples: √2¹ is f/1.4.   √2^-1 is f/0.7.

The math of computing with Stop Number is covered in a little more detail on the next page. And if any trouble making you a believer about this actual system, see a section below how it seriously affects interval timers used in photography.

But one big likely question is that if shutter speed seconds x 2 = 1 EV change, why is fstop Number x √2 = 1 EV? (speaking of the fstop Number itself). That's because, the Area of a circular aperture is Pi × r². Doubled area is 2 (Pi × r²) = Pi × (√2 × r)². So increasing the aperture radius by √2 doubles its area which doubles its exposure which is 1 EV. Doubled aperture areas increment exposure in steps of EV 1.0 (2x), but the f/stop Number (= focal length / aperture diameter) increments 2x area in steps of √2. Stop Number is an exponent of 2, but f/stop Number increments as √2 × Stop Number. The beginning point is √2 × 0 = f/1. √2 is 1.414, so each full f/stop number is 1.414 x the previous f/stop number, each of which is a 2x stop of EV exposure change.

The marked Nominal numbers are more or less rounded values. A few nominal f/stop values like f/1.2, f/3.5, f/5.6, f/6.3, f/22 are exceptions, truncated instead of rounded. So there is no hard rule, these Nominals are simply convenient but approximate "names" from 100 years of history, but not necessarily actual existing precise numbers. The shutter half and third stop markings of 10 and 20 seconds and the marked 1/10 and 1/20 seconds would seem about 10% off, near 2/10 stop. And some f/stop values too, at least if less than f/1.4, but they do round to the same value down there. Most nominal markings have no more than about 2% or 6% numeric discrepancy. Which is a tiny difference, not more than 1/10 stop. But not to worry, do realize that any such error is Not At All Real, any such "error" exists only in our own minds. Because, the nominal numbers generally don't actually even exist (at least are not literal — a definition of "nominal" is "existing in name only"). The modern camera is designed to try to use the correct precise goal numbers instead (and digital technology certainly does help to do that). The nominal markings are just conventionally convenient to show, simpler for humans. We don't normally care about the exact number, we just expect each stop to be 2x or 1/2x value, which they certainly are.

Old time mechanical shutters (timed with a system of springs and gears) were not so precisely accurate, and design was rarely attempted faster than 1/500 second, or longer than one second, if even that. But we have digital precision today. What the digital camera timing actually uses is these precise steps, precise 2x steps called stops (1 stop is 1 EV). The shutters now use a quartz clock crystal and computer chips, and we have precise half and third stops now too. The numbers are not actually much different than human notions, at least for the full stops, but the marked values are still the old approximate conventional nominal numbers that were always shown. The real value that will be used is not actually shown, but it is not so different.

The Precise goal values are the numeric binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, which are a special system, powers of 2, each exactly double the previous. That 2x is the basis of "binary", and it is how our cameras work. Those powers of 2 are exact 2x multiples, critical to our concept of "stops". But to make it easy on humans, on the camera, these are "marked" with rounded nominal values (easy approximations, for example 1/102 second is marked 1/100, and 1/1024 is marked 1/1000). The digital camera still uses the exact values internally, to make stops be always exact 2x or 1/2x steps. The camera always aims for the exact precise goal, trying to be perfectly accurate, as accurate as the physical mechanical mechanisms can respond. The physical settings are greatly more accurate than in the old days.

Stop Number is a mathematical numbering system, not arbitrary, because shutter speed 1 second, and aperture f/1 and ISO 1 were assigned as the base as Stop Number 0, because 2⁰ = 1. ISO 1 was the first classical try, but around 1960 (when light meters were added to cameras) ISO was shifted to ensure that ISO 100 (popular in film and cameras) came out as an exact full stop, instead of ISO 101.6 as a third stop. Before, ISO 128 was the full stop.

This is simple indeed, and is the least complicated, and yet most precise way it could be. The actual shutter speed sequence 1, 1/2, 1/4, 1/8 doesn't suddenly shift to 1/15, 1/30, 1/60, and then suddenly shift again to 1/125, 1/250, 1/500. The Nominal approximations did that when someone decided rounded decimal numbers looked better, but nevertheless, the modern camera necessarily tries to do it right. The Nominals were thought to be more helpful for humans to handle. 32 and 64 and 128 and 256 may seem nice round numbers in today's digital, but it may not have always been so obvious. 😊 This nominal nomenclature was adopted maybe 100 years ago, before the computer and the digital era, when was before mechanical shutters with springs and gears could be very accurate anyway. If invented today, we would probably have no issue with seeing the real binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 — however the third stop markings, like 1/102 or 1/323 or 1/406 second would still look odd to us. We humans like rounded numbers, and we are used to this old system now with its nice rounded numbers, and it is convenient for humans. But one stop should be exactly 2x exposure, and modern camera are designed to do it right regardless of our perception of the numbers. Nominal does have a certain beauty, and it serves our purpose fine. The exact markings we see are not very important to humans, but the important need is for each full stop (and each three third stops, or any one stop change) to be exactly 2x the light from previous stop — which is easy work for today's crystal timed shutter.

Camera design settings are very concerned with the exact values. Humans normally don't much care about exact specifics. We do want 2x stops, but 7.8125 milliseconds (1/128 seconds) is not a number we want to think about. So unless we're doing precise math calculations, we just choose things in terms of nominal third stops, and the camera tends to it, correctly (as accurately as technology permits). We could easily compute the percentage difference between nominal and the actual precise goals, but it seems quite unimportant, since nominal speeds are not real, do not exist, and are not used. Nominal is just a rough abbreviation for the actual precise goal. The point is NOT that there is a marking discrepancy, but that it's not important, that we need not be concerned about it. The important thing is that the actual stops are all exactly 2x steps, as precise as possible. Any "error" of Nominal exists only in our own mind, because the camera knows to do the right thing. We might miss out knowing how neat a system it is, but knowing the detail is not required to operate the camera. But if involved in calculating numbers, you will be very interested in using the precise values.

Nominal stops are more or less rounded, somewhat arbitrarily. Nominal is simply based on past convention (dating to the early days of cameras). Nominal settings are just rounded approximations that have been marked over the years to look nice. But to create the 2x stops of 1.0 EV difference, the modern camera design must actually use the precise target goal values.

Nominal 30 seconds is actually 32 seconds,
which is Very Important to camera Interval Timers

Nikon manuals say the interval timer duration must be longer than the shutter speed. But Nikon users using the camera's interval timer to record multiple 30 second shots will have a problem if they set the interval timer to 31 second intervals, thinking it is longer than the 30 second shutter speed. This sounds very reasonable, but this cannot work, because the camera 30 second setting actually does 32 second exposures (because the binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 seconds must each be 2x full stops). The interval timer will miss many exposures if mistimed, and/or will stop when it gets behind. But 33 second intervals would work well for "30 second" shutters which actually are 32 seconds. Similarly, "15 seconds" is 16, and needs 17 second intervals.

If using an external interval timer with camera Bulb shutter mode, the external timer (when it offers any value, like 30 seconds) likely does correctly time any exact duration that you specify. But the camera's internal timer instead uses camera shutter speeds, and the interval must be long enough to hold that duration. Many camera timer instructions say interval should be one second longer than shutter speed, and some say two seconds longer, likely related to 32 seconds but they don't explain why or when.

Camera processing should not be the issue, as the camera memory will buffer shots (up to a limit), but the shutter must complete before another attempt to start it again. If the goal is many frames with minimum delay, you might instead try the Continuous shutter option with "30 seconds". Zero timer delay might be an unsafe try (because the manual says interval must be longer than the shutter), but one more second should be enough. Except if using the cameras 30 second shutter, that special case will be 32 seconds, and the interval must be a bit longer, 33 seconds. Run an extended test at home to be sure your numbers will work before you go out on your trip. If 8 or 10 shots all work as expected (without missing any shots), you should be good to go.

The difference between nominal and precise does exist. The difference in 30 and 32 seconds is only about a 1/10 stop, not very important to us even if an old camera's mechanical shutter actually implemented 30 seconds, but when doing math, the numbers come out right for 32 seconds, eliminating that 1/10 stop error. And in the old days of mechanically timed shutters, camera shutter speeds could not do more than one second (if even that), so it was not an issue then. In 1960, even the shutter of the first Nikon F SLR did from 1 second to 1/1000 second, in full stops.

The 2x stop concept is quite sacred. Now Nikon DSLR do 32 seconds for 30 nominal. A Canon compact does 16 seconds for 15 nominal. And a Sekonic meter reading tenth stops will show exactly 2.0 EV difference between 8 seconds and "30" seconds, which is computing for 32 seconds, which is the expected right thing to do, because that's what the camera will do (the ISO specs have specified that the correct action is the exact powers of two).

It is not a debate. You can easily verify by timing your modern shutter yourself (15 or 30 seconds will be 16 and 32 seconds). It's difficult to verify the fast shutter numbers, but at the 30 second end, we can easily measure and confirm the camera shutter in fact does use the computed theoretical numbers (32 seconds actual instead of the marked 30 seconds). The basis of "stops" in photography is that one stop is 2x the light, so it is very important that cameras honor the binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 numbers (which I call the Precise Goals that the hardware tries to do). The Nominal numbers 15 and 30 are simply easier conventional rounded approximations shown to humans by convention for 100 years.

Lots more about the Math of calculating these precise numbers is covered on its own page, next.