Let say that we have the following values, as an example:
Shutter speed: 1/40
Aperture: 2
ISO: 1000
How can I get the EV number for this exposure, extract (or add) an EV value (0.33, 0.66 etc.) and calculate back the new shutter speed (or ISO) value?
In fact I want to calculate how the Exposure Compensation will affect my values.
The Exposure value can be calculated with the given Aperture and shutter speed using the following formula:
(src: wikipedia)
where,
N: Aperture value
t: Shutter Speed
The above EV is for ISO 100 called as EV100. EV For subsequent ISO values is calulated with help of EV100 using the following formula:
where,
EV100: EV from the first formula
S : required ISO value
The Exposure compensation works by adding or subtracting the required Exposure compensation value with the current EV to get the new EV.
This new EV can be reverse engineered with the above formulas to get the Aperture and Shutter speeds.
Applying the values you have given:
EV100 = 7.32 //At ISO 100
EV1000 = 7.32 + 3.32 = 10.64 //At ISO 1000
On applying Exposure Compensation of 0.33:
EV(new) = 10.62 +0.33 = 10.95
Now reverse engineer this value to get N and t accordingly.
[I can neither comment nor vote (missing rep), but both the other answers with calculations are wrong]
Exposure Value (EV) is desribed as:
where N is the relative aperture, t the exposure time (shutter speed) and S the ISO speed.
An aperture N=f/1.0, a shutter speed of t=1s and an ISO speed of S=100 corresponds to EV=0. An EV of +1 means half the light, and EV of -1 means double the light of EV=0 will be exposed to the recording medium.
Source: Wikipedia
[Note: This seems counterintuitive, but a brighter scene requires a higher EV to be correctly exposed, while a darker scene requires a smaller EV to be correctly exposed. ]
Given your numbers your total EV will be:
Now exposure compensation works the opposite as EV. A positive exposure compensation (brighten up picture) will decrease EV, a negative exposure compensation (darken picture) will increase EV. So you need to subtract your compensation from the EV.
Source: Wikipedia
Applying your exposure compensation of +0.33:
EV = 4 - (+0.33) = 3.66
You can reverse engineer this value in order to get either a new N, t or S. For example applying an exposure compensation of +0.33 (brighten up picture) will have the same effect as increasing your exposure time to t=1/32.
EV=0 is a very dark scene. By exposure compensation of +0.33 let more light in (t=1/32 is longer than t=1/40)
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0 EV = f/1 at ISO 100 for shutter speed of 1 sec. See here.
So total EV for Shutter speed of 1/40, Aperture f/2 and ISO 1000
= 2 EV - 3 1/3 EV + 5 1/3 EV
= 4 EV
To add 1/3 EV for shutter speed, you just add 1/3 of a stop after 1/40 sec i.e. 1/50 sec.
To add 1/3 EV for ISO 1000, it becomes ISO 1250
The entire "EV" system is designed to remove the need to do real calculation while shooting. A change of one stop in EV compensation means that one of the exposure factors — aperture, shutter, or ISO — will be doubled (to let in more light, for positive EV adjustments) or halved (do darken the exposure with a negative EV adjustment).
For shutter and ISO, that's a straightforward doubling or halving, for aperture, since the opening is a two-dimensional area, the change is by the square root of two, which you also don't need to calculate because there's a basic sequence that we all just memorize– f/1.4, f/2.0, f/2.8, f/4, f/5.6, f/8, f/11, f16.
So, if you have shutter speed 1/40, aperture f/2, and ISO 1000 and you dial in +1 EV compensation, one of these happens: shutter speed drops to 1/20, aperture opens to f/1.4, or ISO increases to 2000.
If you dial in -1 EV, one of these happens: shutter speed increases to 1/80, aperture closes to f/2.8, or ISO drops to 500.
If you use fractional EV compensation, like the 1/3rd or 2/3rd stops given in your example, it's slightly more complicated because the change is less than a full doubling or halving, but rather than worrying about the exact math, I think it's most helpful to just think of it as "okay, less than a full stop of change". That way, you don't have to fill your mind with arithmetic and can concentrate on your photograph and the actual impact of changing the exposure.
More on the EV scale at: What is the EV scale? and What is one "stop"?
Although the implementation of many features such as this is likely different across manufacturers, market classes and even generations of equivalent models:
As observed on a Nikon D3100, assuming that ISO is fixed:
In semi-auto modes (A and S) there is only one variable, which will be adjusted as requested.
In P mode, the program diagram shown in the manual will be followed, just with an adjusted EV.
In M mode, compensation can only be set from the menu, and it shifts the meter scale normally.
When auto ISO is enabled, it will behave as if the difference in final EV was due to an actual difference in subject brightness. Therefore, it can be assumed that exposure compensation is applied directly to the meter reading, not influencing the camera any differently from a variation in the physical LV being metered.
