Shutter speed, f/stop and ISO setting 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.

**Camera settings are marked with Nominal values, but cameras actually use their actual precise design goal values.**

A previous page here mentioned how cameras mark their settings dials with rounded approximate numbers called **Nominal** numbers (Nominal in Merriam-Webster dictionary: *Existing or being something in name or form only*). A convenience maybe, but not necessarily actually existing. The synonyms in this case are approximate or so-called or imprecise, perhaps close, but not actually real. But 1/250 second is friendlier and easier handled than 1/256 second, or at least it was thought so in the past before digital computers arrived. The marked nominal numbers are intended to be convenient for humans to handle, who mostly just 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 camera design does instead aim for the precise target goal values, so this difference is not important when using the camera, it knows how to do it. However, any exposure calculations (like say EV) do need the precise actual values, when this becomes 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 (generally more than 100 years ago), 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 exact 2x exposure steps must be in the binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 — (and reciprocals of those, like 1/64). Think about that, it surely becomes obvious. Binary and Digital actually refer to having only the two possible states of zero and one, but that then in turn requires the base 2 rules.**“Precise” values**are the more precise corresponding**target value design 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 1/512 second goal calculated to be 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 manufacturing 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, maybe not even the number of decimal digits I show. 😊 The point is, Nominal 1/500 second (as we humans call it) is actually 1/512 second, which is the power of 2 computed as 2

^{-9}(see Stop Number next below).

There’s not a great numerical difference, but the Nominal numbers are just the rounding that we’ve always been used to (many of the nominal numbers date back 100 years), and they are still seen because we're used to them (and might question any difference), but the Precise goal numbers are the cameras actual design plan. Users are OK with the Nominal values (because the camera design will aim for the precision), **but design and any math and calculation need to use the actual power of 2 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 today's camera can get pretty close). But the camera's target design 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 or Inverse Square Law, then we get better precise results if we know the right numbers to use. Computing method is detailed on the following page. 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 those irregular nominal shutter speed value sequences, but knowing this now will explain those sequences of shutter speed full stops we see in Nominal numbers. **Both EV and Stop Number are an exponent of 2**, to compute setting values of powers of 2, which are full stops 1 EV apart. Origins of the "EV starting base" are that f/1 at 1 second computes EV 0, and also 2^{Stop Number 0} is either f/1.4 or 1 second (technically, f/stops are exponents of √2, so that the exposures of the circular aperture area are powers of 2 more detail below). EV is computed with both f/stop and shutter speed, so its not exactly the same thing as Stop Number, but both are exponents of 2. It is just the math of the powers of 2.

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

Shutter Speed (duration, seconds) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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 |

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 |

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

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:** √2^{1} is f/1.4. √2^{-1} is f/0.7.

f/stop (aperture) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Nominal | f/0.7 | 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 | 0.707 | 1 | 1.414 | 2 | 2.828 | 4 | 5.657 | 8 | 11.31 | 16 | 22.63 | 32 |

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

The math of computing with Stop Number is covered in a little more detail on the next page.

But the first question is likely 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.

**ISO Numbers are different** (but this box is reasonably skipped)

Before, ISO was the same as shutter speed, in that 2^{StopNumber 5} = ISO 32, just like 2^{5} is 32 seconds or √2^{5} is f/5.657. But ISO numbers changed around 1960, related to starting to build light meters into cameras, when it was decided by somebody that ISO 100 would be a more convenient full stop number, whereas before, ISO 101.6 was a third stop less exposure than the previous full stop at ISO 128, nominal 125 (that's also why we then had film speeds of 64 and 32, which were the standard binary numbers). But 1960 was very early for much computer work, so binary numbers were not yet generally considered round numbers. Film was getting faster too, bigger numbers, but nearing a limit. But the later ISO numbering change was just the thought that a round decimal number would be a convenience, regardless of details, so to speak.

Possibly not related, but at about the same time (1960), Kodak doubled all black&white film speed ratings (the films themselves were still the same, just a different number was printed on the boxes). Since we were then using more light meters, this real purpose was that it removed some of the excessive safety factor that was previously in the rating. Many users then were already doubling the ISO because it metered better results. We were largely using light meters then anyway.

StopNum + offset | ISO 2^SN | Old ISO SN 2^SN | |
---|---|---|---|

1.643856 | 3.125 | 0 | 1 |

2.643856 | 6.25 | 1 | 2 |

3.643856 | 12.5 | 2 | 4 |

4.643856 | 25 | 3 | 8 |

5.643856 | 50 | 4 | 16 |

6.643856 | 100 | 5 | 32 |

7.643856 | 200 | 6 | 64 |

8.643856 | 400 | 7 | 128 |

9.643856 | 800 | 8 | 256 |

10.643856 | 1600 | 9 | 512 |

11.643856 | 3200 | 10 | 1024 |

12.643856 | 6400 | 11 | 2048 |

It's probably a confusion to mention it here, but if you were wondering about ISO, this is just mentioning that ISO has been different for many years. ISO still starts at Stop Number 0, 1, 2, 3, 4, 5, etc, except an 1.643856 offset is also added to each one, like at right. And of course thirds have 0.3333 and 0.6667 added to them. See the large chart below.

These are a different starting point and different shifted numbers. The 1.643856 offset is like log₂(100/32) which is 1.645856, but many divisors like 8, 16, 32, 64 work (to make ISO 100 be a full stop). Each full stop's Stop Number adds that same number (but still increments full stops by +1, which are still powers of 2 so doubling ISO is still 1 EV). The purpose is that ISO 100 is now a full stop (at Stop Number 6.644). It seems a shifted scale, but **it is still powers of 2, and No ISO is changed. ISO 100 is still ISO 100, unchanged, about Stop Number 6.64 on either scale.** And 100 is a good round number base for higher multiples of ISO numbers, and above ISO 100, higher ISO numbers do even continue the 1, 2, 4, 8, 16 multiples of 100. Apparently decimal numbers are more pleasant. 😊 I have wondered why ISO was not simply just marked with nominal numbers too, but I am Not suggesting we should be concerned about the previous system, but just am mentioning that ISO is set up a little differently than f/stop or shutter speed. See
more detail about ISO (toward bottom of that next page).

So it's not as simple as before, but it works, and it seems not really a complication, because the ISO rules can largely be ignored. Because ISO is not computed into EV except in the light meter. Our EV is computed to match the settings (f/stop and shutter speed) for the ISO we are using. So the light meter needs it, but our EV calculations have no real need to compute ISO numbers. That doubling ISO is 1 EV seems all we need to know unless we are building light meters.

**Nominals:** The Nominal numbers for **shutter speed** are three different sequences (marked in three colors above). **We of course know that can't really be right, because we expect each stop to be an exact factor of 2, which is of course the only acceptable answer.** We can see that in a few cases (for example 3 and 6 seconds, or 10 and 20 seconds, and their reciprocals), the camera adjacent half stops and third stops are both marked with the same convenient nominal number, but of course both the half and third stop cannot be the same precise value. Nominals are reasonably assumed just to be approximate rounded numbers (rounded casually, to the nearest 5 or 10 or 100 or something). These markings are just easier approximations of the actual precise numbers that the camera designer knows it must actually use. We are long used to seeing these nominal numbers, which seem close enough for human concerns, but both the camera and any computing must use the actual precise values. And the camera does necessarily use the precise goals, as accurately as possible as the camera can do it.

**Again, the necessary major goal of photography exposure is that each full stop must precisely be a exposure factor of 2x**. 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 some Nominal shutter speed sequences like 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, etc. However, the camera design does know to instead use the precise design goals, of 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, etc, so that each step is precisely 2x or 1/2 values.

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 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, 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.

These charts show the camera's usual approximate Nominal marked values that are shown to us, and their corresponding computed target design goals (that I call Precise Goals) 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 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.

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 binary Powers of Two sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 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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