Shutter speed, f/stop and ISO goal values

**Camera settings are marked with Nominal values, but they use their actual precise goal values**

See below for the computed charts of all camera Nominal and Precise setting values. Details of the computing methods are on another math page.

A previous page here mentioned how cameras mark their settings dials with rounded approximate numbers (that I call **Nominal** numbers (Nominal in Merriam-Webster dictionary: *Existing or being something in name or form only*). The synonyms in this case are approximate or imprecise, perhaps close, so-called but not actually real). The marked nominal numbers are intended to be convenient for humans to handle, who mostly care about the 2x intervals, but we really don't much care much about knowing the exact precise number target goals. And the marked nominal numbers are close enough for human interest. They do their job, and serve their purpose. The cameras do instead aim for the precise target goal values, so this is not important when using the camera. However, any exposure calculations (like say EV) do need the precise actual values, when this becomes more important.

Syntax used here about the camera settings:

**“Nominal” values**are the f/stop, shutter speed and ISO values you see marked on your camera, and which it reports to you. These are approximate values established by convention from an older time (earlier technology), but camera design today can use similar but more precise values. For two examples of Nominal, we see shutter speeds marked 1/60 second or 30 seconds, but those actual precise design targets are actually 1/64 second and 32 seconds, because 2x exposure steps must be in the Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 ... (and reciprocals of those, like 1/64).**“Precise” values**are the more precise corresponding target value goals based on the Powers of Two that the camera designers must actually try to implement, to better ensure full stops are exactly 2x exposure, or one EV apart.By “precise”, I don’t imply that the physical accuracy of a Nominal 1/500 second shutter is precisely the exact calculated 0.001953125 seconds. The point is that the modern goal that design does seek is necessarily 1/512 second, 0.001953125 second, implemented as best as modern technology can actually achieve it. Accuracy is quite good today, but not necessarily to as many decimal places as calculations of the goal can show. The point is, 1/512 second is the power of 2 computed as 2

^{-9}(see Stop Number next below) of that actual goal of what we humans still call 1/500 second.**So my term "precise" means the "precise design goal", implemented as well as possible.**

There’s not a great numerical difference, but the Nominal numbers are just what we’ve always been used to (many of the fractional nominal numbers date back 100 years), and they are still seen because we're used to them, but the Precise numbers are the cameras actual goal plan. Users are OK with the Nominal values (because the camera design will handle the precision), but design and math and calculation need the precise goal values.

In the camera, the overwhelming goal for photography is that each full stop must be exactly 2x or 1/2 exposure of the adjacent stop. These are necessarily and explicitly the sequence of the powers of two (or for f/stops, powers of √2), which I call **Precise** numbers, obviously meaning the theoretical precise goal numbers that the camera designer's math certainly aims for (the physical camera mechanisms may not necessarily be as precisely accurate to as many extended decimal places as I show here... but the camera does get very close). But the camera's target goal is certainly these precise calculations (instead of the rounded Nominal numbers).

So the Precise goal values are not info that humans must normally know, except when doing math calculations such as EV or f/stops or Guide Number, then we get better precise results if we know the right numbers to use. Computing method is detailed following the charts below. The camera markings show humans the nominal numbers, but the camera design is always working with the precise values.

We all surely have wondered about the irregular nominal shutter speed value sequences, but knowing this now will explain those sequences of shutter speed full stops...

The precise goal value for **shutter speed is 2 ^{Stop Number}** (which numerical steps are the powers of 2).

S.S. Nominal | 30 | 15 | 8 | 4 | 2 | 1 | 1/2 | 1/4 | 1/8 | 1/15 | 1/30 | 1/60 | 1/125 | 1/250 | 1/500 | 1/1000 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Precise Goal | 32 | 16 | 8 | 4 | 2 | 1 | 1/2 | 1/4 | 1/8 | 1/16 | 1/32 | 1/64 | 1/128 | 1/256 | 1/512 | 1/1024 |

Stop Number | 5 | 4 | 3 | 2 | 1 | 0 | -1 | -2 | -3 | -4 | -5 | -6 | -7 | -8 | -9 | -10 |

The precise goal value for **f/stop is √2 ^{Stop Number}** (which numerical steps are the powers of √2).

f/stop Nominal | f/1 | f/1.4 | f/2 | f/2.8 | f/4 | f/5.6 | f/8 | f/11 | f/16 | f/22 | f/32 |
---|---|---|---|---|---|---|---|---|---|---|---|

Precise Goal | 1 | 1.414 | 2 | 2.828 | 4 | 5.657 | 8 | 11.31 | 16 | 22.6 | 32 |

Stop Number | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

The math of computing with Stop Number is covered in detail on the next page. But first, it likely is a question that if shutter speed seconds x 2 = 1 EV, why is fstop number x √2 = 1 EV?

The Area of a circle 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 doing it increments in steps of √2. Stop Number is the exponent, and 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.

**Again, the necessary major goal of photography exposure is that each full stop must precisely be a exposure factor of 2**. It has to be, so that the light meters can compute correct stops, and so humans can visualize Equivalent Exposure values. Again, that simply is not exactly true for many Nominal shutter speeds like 1/15, 1/30, 1/60, 1/125, 1/250, etc. However, the camera knows to instead use the precise goals.

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. There is no hard rule, these Nominals are simply convenient but approximate "names" from 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 13% off, near 2/10 stop. And some f/stop values too. Most nominal markings have no more than about 2% or 6% or 10% 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 real, any error exists only in our own minds.** Because, the nominal numbers generally don't actually 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 numbers instead (and digital technology certainly does help). The nominal markings seem convenient to show, just to be simpler for humans.

Old time mechanical shutters (timed with a system of springs and gears) were not so 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 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. The real value that will be used is not actually shown, but it is not so different.

The **Precise** goal values are the numeric values 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 digital fractions 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 2^{0} = 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 1/2, 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 camera tries to do it right, and only the nominal markings change, many years ago thought to be more helpful for humans to handle. 32 and 64 and 128 may seem nice round numbers today, but it may not have always been so obvious. :) This nominal nomenclature was adopted maybe 100 years ago, before the computer era, and 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 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 numbers — 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, and it is convenient for humans, but the camera is designed to do it right. Nominal does have a certain beauty, and it serves our purpose. 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) to be exactly 2x the light from previous stop — easy work for today's crystal timed shutter.

Camera settings design is very concerned with the exact values. Humans normally don't much care about exact specifics. We do want 2x stops, but 7.8125 milliseconds 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. 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.

These charts show the camera's usual approximate Nominal marked values that are shown to us, and their corresponding theoretical computed target goals (that I call Precise) that the camera instead does actually attempt to perform. Shutter speed abbreviations of ms and sec are milliseconds and seconds. Since we use third stops today, the half stops are specially marked in the charts.

There is also an option to show sixth stops. Of course, 1/3, 1/2, and 2/3 stops are already 2/6, 3/6, and 4/6 values, so this option only adds 1/6 and 5/6. Which is probably only of interest for Auto ISO, since some camera automation does use 1/6 stops for Auto ISO values. Or tenth stops can be also shown (some light meters can read in tenth stops).

There is a two page printable PDF file of these values (6 digits, thirds and half stops, fits Letter or A4 paper).

which is Very Important to Interval Timers

Nikon manuals say the interval timer duration must be longer than the shutter speed. But Nikon users using the cameras 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 sequence 1, 2, 4, 8, 16, 32 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 likely does correctly time any exact duration that you specify, but the internal timer instead uses camera shutter speeds, and the interval must be long enough to hold that duration. Many timer instructions say interval should be one second longer, some say two seconds longer, likely related to 32 seconds. Camera processing should not the issue, as the camera memory will buffer shots, but the shutter must complete before another attempt to start it again. If the goal is minimum delay, you might instead try the Continuous shutter option. Zero timer delay might be an unsafe try (because the manual says interval must be longer than the shutter), but since timer units are normally full seconds, one more second should be enough. But if using the cameras 30 second shutter, that will be 32 seconds, and the interval must be a bit longer, 33 seconds. Run an extended test in a rather dark closet 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 the camera actually implemented 30 seconds, but when doing math, the numbers come out right for 32 seconds, eliminating that 1/10 stop error. In the old days of mechanically timed shutters, camera shutter speeds could not do more than one second (if that), so it was not an issue then.

The 2x stop concept is quite sacred. Nikon DSLR do 32 seconds for 30 nominal, which makes the full stops be correct. 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 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 1, 2, 4, 8, 16, 32 numbers (which I call Precise). The Nominal numbers 15 and 30 are simply easier conventional rounded approximations shown to humans.

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

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