Understanding Aperture And F/Stops

By Gary Gray

Something I’ve encountered over the years of teaching photography is a lack of basic understanding by many students and even experienced photographers of what is referred to as the exposure triangle.

The exposure triangle refers to the relationship of aperture, shutter speed and ISO settings when setting exposure on a camera.

Many photographers I’ve encountered rely on the camera to make the necessary exposure calculations when they take photographs. Some will set the camera for shutter priority, which allows the operator to set a fixed shutter speed and the camera will adjust the aperture and in some configurations the ISO, automatically for what the camera believes to be a proper exposure. Or, they may use aperture priority, which means the operator sets the desired aperture and the camera adjusts the shutter speed and in some cases the ISO for proper exposure.

In photography, the basic exposure values (EV) are most often referred to as f/stops.  Most digital cameras I’ve worked with will default to making f/stops operate in 1/3 increments. This allows for fine tuning of exposure and gives plenty of wiggle room in most situations. A typical example would be to modify a camera’s exposure for shooting in snow by adding a little positive exposure compensation, say .3 or .6 stops to compensate for the camera metering being affected by an over abundance of white in a scene.

An f/stop is basically a logarithmic mathematical function. If you took high school algebra, you probably studied logarithms at some point and the same mathematical principles apply to the exposure triangle.  Myself, I used to work as a radio engineer and we used this same logarithmic relationship when calculating signal strengths of a radio wave, only we called these values db, or decibels. This is different terminology to describe the same thing. Signal strength. In the case of photography, the signal is light. In radio engineering the signal is a radio frequency wave. The mathematical relationships are based on the same logarithmic principles.

In photography 1 full f/stop is the same thing as 3 db (decibels)

I’ll spare you having to understand how decibels and f/stops are calculated from signal strength as I’m not teaching an algebra class here; however, I will give you the basic starting points for understanding what this means for setting exposure in a camera. Think of the power of the signal, in our case the amount of light reaching the sensor and you can use f/stops as the method of calculating the light power needed to make a proper exposure.

Logarithmically and Photographically speaking, 1 f/stop is equal to 3 db of gain or loss in signal. Simplifying the mathematics of this, we have…

1db = 1/3 of an f/stop: In terms of increasing exposure, a 1/3 f/stop would increase the amount of light by a multiplier of 1.259 and a decrease in f/stop would decrease the amount of light by a multiplier of .794

2db = 2/3 of an f/stop: In terms of increasing exposure, a 2/3 f/stop would increase the amount of light by a multiplier of 1.585 and a decrease in f/stop would reduce the amount of light my a multiplier of .631

3db = 1 full f/stop; In terms of increasing exposure, a full f/stop would increase the amount of light by a multiplier of 1.995 and a decrease in f/stop would reduce the amount of light my a multiplier of .501

This is all about logarithmic relationship.

So, when we talk about one f/stop, we are describing either doubling or halving the amount of light. Pretty simple stuff (I think.)

Transferring this mathematical relationship to your camera and we have something like this.

If you have a shutter speed of 1/100 of a second and change that speed by one f/stop, you end up with either 1/200 of a second (faster speed) or 1/50 of a second (slower speed)  Faster shutter speeds reduce the amount of collected light by half, and a 1 stop slower shutter speed increases the amount of light by doubling it.

The same mathematical formula applies to the ISO value. A one full stop increase or decrease in ISO will either double or halve the power of the light. A change in ISO from 100 to 200 is one full f/stop. A change in ISO value from 100 to 400 is 2 stops. A change in ISO value from ISO 100 to ISO 800 is 3 stops. Just double or halve the value to get one full f/stop.

Aperture works the same way only it’s different. This is where a lot of people get confused, because apertures in the camera are generally denoted in fractional numbers and those fractional numbers aren’t following the same apparent rule of halving or doubling.  That means a one f/stop increase in aperture from say f/4 does not equate to f/8 and likewise a one f/stop decrease in aperture from f/16 is not f/8. I’ll explain.

Aperture is an expression representing a fraction of the lens focal length. The loss or gain of light moving through a lens is represented by the inverse square law.  Light power is inversely proportional to the square of the distance the light travels.

In photography, full aperture stops are denoted as follows.

Contrary to the math used to calculated an f/stop for shutter speed or ISO, a full stop of aperture change isn’t denoted in camera by halving or doubling the f number of the aperture. Why? Because the f number of aperture is calculated and denoted by the actual physical characteristics of the amount of light traveling through a particular lens and all lenses of different focal lengths are different. The f number of an aperture setting is still using a logarithmic function, but that actual value doesn’t remain constant across the board. Therefore, when you want to double the amount of light hitting the sensor by decreasing the f number using aperture, you have to remember this fact. To achieve a full stop of light gain from a lens set to f/11, you don’t divide it by 2, you adjust to f/8 (one full stop.)

By using f/stops, it’s quick and easy to understand the amount of light you either gain or loose by your settings, just keep in mind, aperture has to be calculated a little differently when adjusting your camera. It’s always a good idea to know and understand the full f/stop values of your camera and to not make the mistake of using the same quick math to calculate an f setting on the lens as you use to calculate the shutter speed or ISO.

For your viewing pleasure I’ve included a link to a aperture table on the phototraces website.

And there you have it.