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What Is Equivalence in Photography?

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When it comes to different-sized sensors, you have an issue known as ‘equivalence’ that needs to be taken into account.
If you don’t know about different sensor sizes, then this article is for you. You will find all the information needed for when you plan to use the same lens on two different camera systems.
This is helpful if you plan on upgrading your system while keeping the same lenses.
Orange flowers in a vase, with grids overlayed to indicate full frame lens projection, full frame lens sensor and crop sensor - equivalence in photography
[Note: ExpertPhotography is supported by readers. Product links on ExpertPhotography are referral links. If you use one of these and buy something, we make a little bit of money. Need more info? See how it all works here.Ed.]

What Is Equivalence?

Equivalence, in its most basic meaning, is how we compare lenses across cameras with different formats (sensor sizes).
This has become a complicated matter since the birth of the digital camera. It’s not always clearly understood, which is what this article is for.
When we look at a lens, we get a few pieces of information from its name. For example, the Canon EF 24-70 mm f/2.8L II USM lets us know what the lens can do, in its title.
The two main reasons we go for one lens over another are the focal length and the aperture. For the Canon EF 24-70 mm f/2.8L II USM, the focal length has a range of 24-70mm. The aperture, across the entire focal length range, is f/2.8.
The make and type of a lens is also important to make sure the lens works with your camera. Here, we see Canon and the letters EF.
What we often misunderstand, or perhaps don’t know, is these two pieces of information are based on ‘equivalent’ camera systems. When photographers worked with film, there were only a handful of sizes. Every SLR or TLR was the same size, even if the manufacturer differed.
These cameras had to work with predesignated sizes of film, namely large format, medium format and 35 mm. The 35 mm bit is very important. When we talk about ‘equivalent’, we are really talking about how close a camera is to that original 35 mm camera.
A diagram showing various crop factors and full frame - equivalence in photography

35mm & Digital SLRs

As we pointed out, every 35 mm film camera used the same film size. It didn’t matter if the camera was a Nikon, Canon, Olympus, Pentax, Leica or Smena. This made it easy to choose which film was needed.
With the birth of the DSLR, film was no longer needed. Everything happened internally. Camera companies had to create affordable systems for a broad market. Due to this, they invented the ‘crop sensor’.
The camera sensor is the most complicated and therefore most expensive part of the camera. The size and quality of the sensor directly influences the resolution and quality of the image. The bigger the sensor, the more expensive the system.
Many photographers couldn’t afford the expensive ‘full frame’ cameras, so the camera manufacturers developed smaller ‘crop sensors’. The price difference can be very different indeed, but there are disadvantages to having a crop sensor camera system.
The ‘full frame‘ systems were also known as ’35mm equivalent’. Their sensor size (36 mm × 24 mm) matched the size of the negative film used in old 35mm cameras. The crop sensors are also knows as APS-C or Micro Four-Thirds systems.
When using the Canon 24-70 mm lens on a full frame system, you received a true 24-70 mm focal length. But, when the same lens is used on a ‘crop sensor’ system, things become complicated. You don’t get the true 24-70 mm range.
Each camera company has a different crop sensor ratio. Nikon has 1.5x, Canon uses 1.6x, and the Micro Four-Thirds systems have a ratio of 2x. This changes your lens substantially.

CameraSensor FormatSensor DiagonalCrop FactorFocal LengthDiagonal Angle of View
Canon EOS 5D Mark iVFull Frame (864mm2)43.3mm1100mm24.4deg
Olympus OM-D E-M10Four Thirds (224mm2)21.6mm250mm24.4deg

The lens’ focal length is affected by this ratio. A 24-70 mm lens on a Canon crop sensor becomes a 38-112 mm (24*1.6-70*1.6).
If you plan on achieving a 24 mm field of view using a crop sensor camera, then this lens is not the answer.
It doesn’t end there. The focal length range of the lens is not the only thing that is affected by the crop sensor. Apertures also interact differently when compared to 35 mm equivalent ‘full frame’ or ‘crop’ sensor cameras.
A nikon dslr camera resting on a pavement

F/Stops and Apertures

You might know that different sensor sizes affect the focal length of a lens already. But what you might not know is that apertures are affected in the same way. It is the physical size of the aperture that affects the depth of field, not the lens’ f/stop number.
Two lenses with equal 50 mm focal lengths will give the same depth of field, as long as they have the same aperture diameters.
They are the same as long as they are used from the same position and viewed at the same output size.
Consider the following table:

CameraFocal LengthAperture DiameterF- NumberDepth of FieldEquiv.
F-number
Canon EOS 5D Mark IV100mm25mmF/4Near 16.1m
Far 26.3m
Total 10.1m
F/4
Olympus OM-D E-M1050mm25mmF/2Near 16.1m
Far 26.3m
Total 10.1m
F/4

We find the f/stop by dividing the focal length by the aperture diameter. We would summarise that the aperture of the 100 mm lens would be f/4 (100 mm/25 mm). The same size aperture diameter in the 50 mm lens would be f/2 (50 mm/25 mm).
As you can see, although the lenses are quite different, the sensors used with them make them similar. The 50 mm f/2 lens gives the same framing and depth of field as the 100 mm f/ lens.
Because of these changes, we can say that the 50 mm f/2 Micro Four-Thirds lens is equivalent to the 100 mm f/4 full frame lens.
The equivalent aperture not only tells you the depth of field you will achieve, but also how much light you can pull from your scene. The bigger the sensor, the more light is captured, meaning you can use a lower ISO.
A lower ISO means a better quality image. With film cameras, you needed to use a camera system that used bigger film if you wanted to increase your quality. With digital photography, you can go from a crop sensor to full frame, without having to jump to medium or large formats.

Aren’t All F/Stops the Same?

Yes, they are, but they aren’t equivalent across different systems. The sensor size doesn’t physically change the aperture, nor does it change the actual focal length of the camera.
If you put a 50 mm lens on any system smaller than full frame, the focal length doesn’t change. It stays a 50 mm lens. But, you will get a narrower angle of view.
This is because you are not using the lens to its fullest capacity. The narrow angle of view doesn’t hit the entire circle of light you get from the lens. For this reason, the 50 mm lens on a Micro Four-Thirds is equivalent to a 100 mm lens.
Similarly, the actual f-number tells you the amount of light on each square mm on the sensor. This doesn’t change across different sensor sizes.
The equivalent apertures take into account how many square mm of sensor you have behind the lens.
A diagram showing aperture and depth of field - equivalence in photography

ISO and Its Confusing Involvement

As if it wasn’t confusing already, ISO steps in to add to the complication. ISO ensures that if you expose a sensor for a given amount of time at a given intensity, you will get a certain brightness in your image.
ISO is based around the intensity of light you are capturing in any given scene. This means that ISO depends on the f-number, not the equivalent aperture.
A camera with a Four-Thirds sensor paired with a 50 mm f/2 lens will produce a jpeg at the same brightness as a jpeg taken with a full-frame sensor with a 100 mm f/2 lens.
That is, assuming the camera is using the same ISO, shutter speed and f-stop. The smaller sensor will be receiving 1/4 more light than it’s counterpart.
ISO is a useful setting, as the same set of exposures will work across all cameras. But, it does disguise how much light the sensor gets.
A full frame sensor will receive four times more light that the Four-Thirds camera as it has four times the surface area. It is important to know the intensity doesn’t change.
The larger sensor will always receive more light as long as the other settings are set to the same value. Unless the full-frame sensor is worse in quality than the Four Thirds system, it will use this light to produce noiseless image.
There is a flip side. You can attach a faster lens to a smaller format sensor to match the total light available to the larger sensor systems. You can also use a slower shutter speed.
This really only works in low light situation, where you light is limited. In well lit conditions, you need to be careful of highlight clipping. Here, you can’t just open the aperture to match a larger sensor’s total light.

What About Equivalent Sensitivities

If the sensor area affects how much light a sensor is exposed to, doesn’t it make sense to say that this particular ISO on camera A will match that particular ISO on camera B?
In theory, you can work out how much total light one system is receiving, and then calculate the equivalent for the other system.
However, sensors differ greatly. Without having very specific knowledge about each of them, it is difficult to find out that twice the total light equals twice the overall low-light performance.
One format cannot have a ‘depth of field’ advantage over another system. Diffraction depends on the f-number and its impact on an image is proportional to sensor size.
Because of this, diffraction will have the same impact on two images if they were captured using equivalent apertures. If an aperture is small enough to give the desired amount of depth of field, it will show the same amount of diffraction, regardless of sensor size.

Real-World Example

Camera manufacturers have started to produce equivalent lenses for less than full frame sensors. This makes it easier to demonstrate the ways they are and aren’t equivalent.

FormatFocal LengthF-numberCrop Factor Equivalent Focal LengthEquivalent Aperture
Full Frame85 mmf/1.2185 mmf/1.2
APS-C56 mmf/1.21.584 mmf/1.8
Four Thirds42.5 mmf/1.2285 mmf/2.4

Depth of Field Equivalence

Here we used the crop factor ratio of the sensor to work out the equivalent aperture. The crop factor come from the ratio of the sensor diagonal compared to the original 35 mm negative size (36 mm x 24 mm).
[photo f/1.2 full frame]
[photo f/1.2 crop]
[photo f/1.2 four thirds]

Aperture Equivalence

Below, we photographed the same scene, but this time focusing at ‘equivalent’ apertures.

FormatLensMax. Equivalent ApertureCommon Equivalent AperturesF-numbers equivalent to f/3.2Closest F-numberDifference from Ideal
Full Frame85 mm f/1.2f/1.2f/3.2f/3.3f/3.2+0.1 EV
APS-C56 mm f/1.2f/1.8f/3.2f/2.1f/2+0.2 EV
Four Thirds42.5 mm f/1.2f/2.4f/3.2f/1.6f/1.6+0.1 EV*1

The full frame has the smallest maximum equivalent aperture. We will stop the other lenses down to match it.
In the fourth column, you’ll find the f-number required on each lens to offer that f/3.2 equivalent mount of depth of field.
The fifth column shows the closest available f-number to that target.
[photo f/1.2 full frame]
[photo f/1.2 crop]
[photo f/1.2 four thirds]

Sensitivity Equivalence

Now, we need to address the issue of sensitivity or ISO equivalence.
We have three cameras set to the same f-number, the same ISO and the same shutter speed (f/2, ISO 200 and 1/1.3 sec).
We are using a low light scene. This is where equivalence is most likely to predict the sensors performance.
In good light, the larger the sensor, the more more surface area the camera can commit to each region of the scene. This gives us cleaner images without being dependent on aperture.
[photo f/1.2 full frame]
[photo f/1.2 crop]
[photo f/1.2 four thirds]
As you can see, and to no surprise, the camera with the larger sensor does better in giving us better quality.
The question is, does it do proportionally better in terms of its size?

Exposure Equivalence

Here, we have the cameras set to equivalent apertures. This allows us to compare images in terms of depth-of-field and framing.
We also need to use an ISO setting required to produce an equally bright image from the same amount of total light.
To calculate this, we have used the ratio of the surface areas of the different sensors. To ensure the noise was visible across all final images, we used a higher ISO.

LensSelected Equivalent ApertureF-numbers Equivalent to f/5.6 on Full-FrameClosest Available F-numberISO Required to use 1/1.3 Shutter SpeedNearest Available ISODifference from Ideal
Canon EOS-1D Xf/5.6f/5.6f/5.629753200+0.1EV
Fujifilm X-A1f/5.6f/3.7f/3.612681250+0.1EV
Panasonic GH4f/5.6f/2.8f/2.87748000EV

[photo f/1.2 full frame]
[photo f/1.2 crop]
[photo f/1.2 four thirds]
As you can see, while the noise levels are similar, they’re not quite the same. Noise, at is seems, is not solely related to sensor size.
There are a number of factors at play here. Most are down to the sensor’s performance, but there are other complications, such as the different transmissions between lenses.
Transmissions (or T-stops) show that all lenses absorb some of the light they collect for the sensor. This number is always higher than the f-stop. For example, a lens with an f-stop of 2.8 might have a t-stop of 3.2 (a quarter of the light lost through transmission).
Due to issues such as these, it is impossible to find the exact equivalent lens, system, sensor or settings. It can only serve as a guide, albeit a very good guide.

Why Do I Need To Care?

The idea of equivalence allows you to understand the difference in performance across different camera formats.
It shows you how relatable the f-stop and sensor size is to how much light the camera has access to.
Although we see differences here, equivalence is unlikely to affect our day-to-day shooting. For example, flooding your images with more light isn’t going to improve them, it will just overexpose them.
Equivalence is important in knowing what you are using or buying when considering the size, image quality and depth of field. There is no universally perfect system, but it will help you find the best system for you.
After all, smaller-than-full-frame sensors have their own benefits, and are the cheapest option among all sensor sizes.

Re-Cap

  • To find the equivalent focal length for less-than full-frame cameras, multiply the actual focal length by the crop factor.
  • To find the equivalent aperture for less-than full-frame cameras, multiply the f-number by the crop factor.
  • The equivalent aperture lets you know which aperture on a full frame lens will give you the same depth of field from a less-than full frame camera.
  • F-numbers tell you how much light intensity hits the sensor. A larger sensor means more light.
  • F-numbers and equivalent apertures cannot mix. F-numbers are for exposure calculations. Equivalent apertures are for comparing formats.
  • F-numbers and ISO’s are dependant on the sensor size. ISO 100 on a small sensor will not give you the same quality image as ISO 100 on a larger sensor.
  • Depth-of-Field and background blur are not the same thing.
  • Equivalent aperture will accurately predict depth-of-field (except at very close focus distances).
  • Bokeh isn’t reduced to the amount or shape of aperture blades.
  • In low light situation, equivalent aperture can help you get an idea of noise performance.
  • Equivalence doesn’t provide a precise prediction of camera performance.
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[activeKey]
[activeKey]
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
[type='text']
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[type='password']
[activeKey]
[activeKey]
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[type='password']
[activeKey]
[activeKey]
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[type='password']
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[activeKey]
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[activeKey]
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[activeKey]
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[type='password']
[type='password']
[activeKey]
[activeKey]
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
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[type='password']
[type='password']
[activeKey]
[activeKey]
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]
[type='text']
[type='text']
[type='password']
[type='password']
[activeKey]
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['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
['rmockx.RealPlayer G2 Control', 'rmocx.RealPlayer G2 Control.1', 'RealPlayer.RealPlayer(tm) ActiveX Control (32-bit)', 'RealVideo.RealVideo(tm) ActiveX Control (32-bit)', 'RealPlayer']
[index]
[index]
[i]
[i]