Tables for F/stop, Shutter Speed, ISO, and EV

The number for lens f/stop in photography (for example, f/8) is the ratio of lens focal length divided by the effective lens aperture. Aperture is not the obvious physical diameter (shown by black vertical lines below), but instead is the apparent "working" diameter as seen through the magnification of the front lens element.

That is math and physics, but still, the very useful purpose of f/stop numbers is the grand concept that f/8 will the same exposure in any lens, regardless of focal length, or physical size of construction. OK, yes, there can be slight minor variations, especially in the old days in lenses without modern coatings (losing a lot of light), and even today in fancy lenses containing many glass elements (losing a slight amount of light). Slight variations, but which are important in professional movie cameras, visible variations when switching lenses on the same scene. So their lenses can use T-stops, which are calibrated to the actual amount of light the lens transmits, instead of the theoretical amount. This is relatively unimportant for still cameras.

Is f/stop written f/stop or f-stop? The lens manufacturers properly write f/8. But the term f-stop has become popular on-line, so we see both. My habit is still to write f/stop, because we write f/8, to be remindful of the division defining it:

f/stop = focal length / aperture diameter.

So, f/8 denotes "focal length / 8", which represents the "effective" aperture diameter of the lens, and this exposure value can be compared with other lenses in this way. Then a series of multiple f/stop steps is designed, called "stops". Each full stop towards larger numbers gives half the light exposure of the previous step (called stopping down, which also increases depth of field).

The tables below are the computed f/stop numbers of the camera aperture. The first table is the fractional steps in tenth stops. These charts show the actual numbers, and the relationships, and one purpose is to aid determining span in stops between two values.

F/stop Table, in Tenth-stops

Notes: f/stop = sqrt(2)^(stop number + fraction)

Usage: If you set your light meter to read in tenth stops, the format of the result value shown is (for example):

This is NOT f/8.7. It is 7/10 of the way between f/8 and f/11 - or about f/10. If you set the flash meter to read in third stops, the same light will read f/10.

By definition, both of these equivalent values are 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 is 0.1 stop. The fraction 1/3 stop is 0.33 stops, and 2/3 stop is 0.67 stops, so a reading around 0.3 is one third stop, and one around 0.7 is two third stops. The lens can only be set to third stops, so just pick the nearest third stop: 0, 1/3, 2/3, or 1 stop.

There would seem no point of 1/10 stop meter readings for daylight, since we can only set the camera to third stops. But one good reason to use tenth stops 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 is when pondering fill level for that lighting ratio - how much is 1.3 stop less than f/10? It is about f/6.3, but who knows that? But if we read this as f/5.6 plus 3/10 stop vs. f/8 plus 6/10 stop, then we easily know 1.3 stops in our heads, immediately. Or, the chart above can determine it too.

Rounding: (values are more often truncated, or even approximated).

We say it as f/11, but f/11.3 is the correct actual calculated value. Most other values are closer, but Guide Number calculations for speedlights ought to use 11.3 instead of 11.
To make that fact be obvious, note that progressions arranged into rows of every-other doubled aperture values are also defined as:

Marked shutter speed numbers are also approximated. For example, the standard shutter speed chart below shows 1/20 second and 1/10 second (and 10 and 20 seconds) to be both third stop values and half stop values. Same value cannot be both, and the camera does compute the actual value closer (half stop 20 seconds will be 22.6 seconds, and 30 seconds will be 32 seconds), but we humans are frequently shown easier rounded or even "equivalents".

How the Stops are Numbered (Origin of these numbers)

f/stop

Shutter speed and ISO

ISO speed was a film sensitivity concept. Digital speed is a gain factor, multiplied after the digital sensor does what it does, but the same ISO numbering scheme is used, still an apparent "sensitivity" indication.

Shutter speed is of course the time duration when the shutter is open, exposing the sensor or film to the light from the aperture. On many cameras, numerical values for shutter speed are marked on the camera using two methods with different meanings - for example, marked as 4 or 4". Just the number alone, like 4, is an implied fraction (1 over the number), meaning 1/4 second. The same number written 4" means four whole seconds, not a fraction. A slow shutter is a longer duration, and a fast shutter is a shorter duration.

A flash, especially a speedlight flash, is typically a much shorter duration than the shutter. The flash simply must occur while the shutter is open (sync), but the faster flash exposure is not affected by the slower shutter speed. Keeping the shutter open longer does increase the continuous ambient light seen, but shutter speed does not change what the fast flash does.

There are two shutter speed charts below, the camera's normal rounded marked values, and the theoretical computed value goals that are actually used.

Each "Theoretical Actual" shutter speed at right below is just the simple progression (starting at one second), showing third stop times in sequential multiples of cube root of 2 (1.2599), and half stop times as sequential multiples of square root of 2 (1.4142). This insures that every interval of three third-stops, or two half-stops, is exactly 2x or 1/2x value (i.e., exactly one stop). These are the "Actual" shutter speed goals the camera uses. I am not implying practical accuracy is within a microsecond, my goal was merely to show four significant digits for 1/1000 to 1/8000 second values. The goal of precision here is to show that any and every third value of third stops is exactly double or half value (one stop).

The other "Shutter Speed" chart is the camera's normal marked numbers for same shutter speeds. These marked values take liberties to show even or round values for convenient human use. This is just a marking, which does not affect what the shutter does. It is difficult to verify the fast 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). It must do that, because the basis of the system is that one stop is 2x the light. The markings only have about 2% or 6% numeric discrepancy (the 10 and 20 half-stop values are a little worse), which is insignificant, and really, only in our own minds, not in what the shutter actually does. Cameras could mark the actual values, but we are used to this system (and it is convenient). The precise marking is not very important, the important need is for each stop to be 2x the light from previous stop - easy work for today's electronically timed shutter. So the point is NOT that there is a marking discrepancy, but instead is that you need not be concerned about it. The shutter does the right thing, and it really is a pretty neat system, better than our learning a sequence of numbers like 1/813 second shutter speed. All we need to know is that double or half is one stop, and these marked rounded numbers make it easy to know the next one.

EV (Exposure Value)

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