# Understanding Camera Numbers and their Origin.Stop Calculator for f/stop, Shutter Speed, ISO

The f/stop numbers are explained on the previous page. There is also another Exposure calculator to compare two "total" exposures determined by including all three f/stop, shutter speed, and ISO parameters combined. The calculator below computes difference in individual values, in all three modes, f/stop, shutter speed, and ISO.

## How Many Stops?

It may not be obvious that the difference between f/1 to f/2 is 2 stops, and f/4 to f/5 is 2/3 stop, while f/9 to f/10 is 1/3 stop, so the calculator purpose is to help with the math, for f/stops, shutter speed or ISO. The calculator options below provide finding differences of the possible settings of your camera.

Other 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). See more detail about Nominal and Precise values (next page).
• “Precise” values are the more precise corresponding goal target values 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 shutter is precisely the exact calculated 0.00015625 seconds of 1/64, but that certainly is the modern goal that design does seek, as best as modern technology can actually achieve it. Which is quite good today, but maybe not necessarily to as many decimal places as calculations can show.
There’s not a great numerical difference, but the Nominal numbers are just what we’ve always been used to, and still assume will be seen, but the Precise numbers are the plan now. Users are OK with the Nominal values (because the camera design will handle the precision), but design and math and calculation need the precise values.

## Compute Stops Difference

Mode:
f/stop values
Shutter Speed values
ISO values

Show nearest nominal Thirds   Halves

1. Precise results of nominal values
from A: to B:

2. Difference in any two numeric values
from A: to B:

3. Add ± EV Exposure to a value
(Add formats like ± 1, 2.333, 2/3, 1 1/2 EV)

4. Compare metered Tenths and nominals
from A: plus EV

compared to B:

Half stops are marked with *½ (to aid avoiding them, because your modern camera surely uses third stops).

The Range of the Nominals here is large, but not quite infinite. The “nearest nominal” shown has limits, but precise calculations can go further.

• f/stop range is f/0.5 to f/256, 18 EV (f/0.5 is considered a limit for the lens to still properly focus colors).
• Shutter speed range is 1/16000 to 512 seconds, 22 EV (the Nikon D1 camera had a 1/16000 second shutter speed and 1/500 second sync, but they discontinued offering that)
• ISO range is from 1.56 to 3276800, 21 EV. Starting at 1.56 is the industry kludge to make ISO 100 and multiples be even full stops, and makes third stops be relative to them, since that's what our cameras do now (math page).

Range here just meaning, it computes further, but the suggested nearest third nominals hold at those limits.

Option 1 selects the marked camera nominal numbers, but it computes with the corresponding precise values that the camera actually uses (better accuracy than the nominal marked numbers). The next page has a chart of the actual precise values that the camera uses, and this calculator matches that internally here.

Option 2 can be any numbers, assumed to be exact or precise numbers (But NOT nominal, so use Option 1 for nominal numbers, it understands nominals). Comparing results of calculated values would use this Option 2, however not sure there is much use for this option, since the only numbers we can select on the camera are the marked nominal numbers (computed in Option 1). But for the reasons stated, in Option 2, the numbers of nominal f/8 to f/11, or from 1/125 to 1/60 second, does Not compute exactly 1.00 EV. In Option 1, it does. And again, the camera always knows how to do it right.

Option 3 assumes that adding corrective +EV exposure compensation adds more shutter time, or causes a lower and wider f/stop number, or a higher ISO number (increasing exposure like the camera compensation does).
The EV increment entered can be any numeric value, like 1.5 EV, but 1/3 stop is 0.3333 EV, 2/3 stop is 0.6667 EV, and 1/2 stop is 0.5 EV (or you can enter easier formats 1/3, 1/2, or 2/3 there, or 1/6 or 1/10, etc, which are calculated precisely).

Option 4 compares the difference of metered tenth stop values to the values we see on the camera. Tenth f/stop values are very popularly used to meter individual flashes in the studio, and there's also a detailed tenths chart just below (but see that down there, differences in tenth stops are extremely easy to compute in our heads).

There are confusion factors here about exposure numbers. As Shutter speed reaches longer time duration and as ISO reaches higher speed sensitivity numbers, exposure increases. But as f/stop reach higher numbers, exposure decreases.

There are also differences in light brightness and exposure. In terms of exposure or compensation, we think of metered f/4 as being more exposure than f/5.6. And it is, when actually metering each light, metering f/5.6 saw a brighter light that needs stopping down to f/5.6 (less exposure), as compared to a dimmer light that meters f/4 (requiring that additional exposure). So (arguably) to reduce any confusion with the signs, the A > B comparisons here try to refer to exposure of the setting values.

So yes, the Option 4 adjustment might seem backward at first glance, since (if thinking in terms of needed compensation) we think of f/4 as being more exposure than f/5.6. However, Option 4 is not the same as "compensation". When actually metering each flash, note that metering f/5.6 saw a brighter light that needs f/5.6, as compared to a dimmer light that meters f/4, needing that additional exposure. Think of Option 4 as metered "Light levels", which it is. That's a bonafide basic, which is how we set the power level of studio flashes. And when we meter the sum of the two Main and Fill lights together for the camera exposure, the correct exposure sum will likely be around 1/3 EV greater than the brightest.

## Tenth Stop Usage

Cameras today can use third stops. If using a modern camera, I cannot imagine any reason not to choose third stops. Greater precision of adjustment can only be a good thing. When the light meter reads a certain value, the camera can be set to the nearest third stop. That difference is not more than ± 1/6 stop (half a third). So the calculators above try to flag the 1/2 stop values as possibly unintended, but all the numbers work.

But handheld light meters typically can also be set to read tenth stops (advantages for metering multiple flash). If you set your light meter to read in tenth stops, the format of the result value we see is (for example):

f/8 plus 7/10 stop

But this is NOT f/8.7. It is 7/10 of the way between f/8 and f/11, about f/10, and read as "f/8 plus 7/10 stop".

The equivalent value of f/8 plus 7/10 stop rounds to simply two third-clicks past f/8, or one third-click below f/11 (easy to set). The camera dial will indicate f/10 there, but we can instead meter and work in tenth-stop differences from full stops.

Fractions: 1/10 EV is 0.1 stop. The fraction 1/3 stop is 0.333 stops, and 2/3 stop is 0.667 stops, so a reading of 3/10 is around one third stop, and one of 7/10 is about two third stops. The camera can only be set to third stops, so just pick the nearest third stop: 0, 1/3, 2/3, or 1 stop. This is just a more precise exposure reading.

There would not seem much point of 1/10 stop meter readings for daylight (IMO), since we can only set the camera to the nearest third stop. Maybe metering in tenths could give us an indication that the 1/3 stop exposure we set was actually a bit more or less than metered.

However there are two very good reasons to use tenth stops for metering multiple flash. One is for greater precision in adjusting the power level of individual flash units — the actual difference between two lights could be controlled more closely.

But the overwhelming advantage of metering flash in tenth stops is when pondering fill level for that lighting ratio of two lights. If one light is f/10, how much is one and a third stop less than f/10? It is about f/6.3, but who knows that? That math is more difficult. But if we read these two values as f/5.6 plus 3/10 stop vs. f/8 plus 6/10 stop, then we easily see ratio is 1.3 stops difference, immediately, in our head.

For a very practical case, note the above calculators initial default for f/stops Option 4, of f/5.6 plus 4/10 compared to f/4.5. Say that is a main light and fill light for a portrait. F/4.5 is a nominal third stop from f/4 (0.333 EV from f/4). If both were metered in tenths, we would directly see f/5.6 plus 4/10 vs f/4 plus 3/10, and we immediately see in our head the difference is one stop and one tenth for 1.1 EV difference (very slightly less in this case of the 0.033 rounding of 0.333 - 3/10, but precision easily within 1/10 EV). That's really a big deal to know and use, tenths are a really fast and easy and convenient and precise way to set the lighting ratio, precisely, all in our head (see more about actual use of tenths).

The tenths chart below shows the precise calculated values. Light meters reading tenths don't show that calculated number, they just show values of full stops plus tenths, as for example f/4 plus 2/10 EV. And in addition to tenth stops, it was convenient to also show precise third values below too). Half stops are the +0.5 EV value.

## f/stop chart of Tenth Stops, 1/10 EV

Change precision shown below

Notes:   f/stop = √2 (stop number + fraction)   (√2 is 1.4142)

e.g., 2/10 stops past f/11 (stop number 7) is √2 7.2 = f/12.126
Or 1/3 stop past f/11 is √2 7.3333 = f/12.699

If interested, here is a one page printable file of this tenths f/stop table.

Nominal and precise values of all (full and third and half and sixth and tenth) stops for shutter speed, f/stop and ISO are on the next page.

Note that "Stop Number" and "f/stop number" are different things. Stop Number is the exponent of √2 that computes the f/stop number. Example: Stop Number 6 is f/8, this way: √2 6 = f/8.