Equivalent Focal Length and Field of View

When it comes to focal lengths, it seems that many photographers get very confused by “equivalent focal length” and “field of view” jargon that is often used to describe lens attributes on different camera sensors. To help fully understand these terms, I decided to write a quick article, explaining what they truly mean in very simple terms.

1) True Focal Length

What is the true focal length of a lens? This one is extremely important to understand. Focal length is an optical attribute of a lens, which has nothing to do with the camera or the type of sensor it uses. The true focal length of a lens is typically what manufacturer says it is on the lens. For example, the Nikon 50mm f/1.4G lens (below) has a true focal length of 50mm, irrespective of what camera you use it on.

2) Field of View

The “field of view” (which is sometimes wrongfully called “angle of view”, as explained below) is simply what your lens together with the camera can see and capture from left to right, to top to bottom. If you are shooting with a DSLR camera, the field of view is typically what you see inside the viewfinder. Some DSLR cameras, have less than 100% viewfinder coverage, which means that what you see inside the viewfinder is actually less in size than what the final image will be. For example, if you shoot with the Nikon D90 DSLR that has 96% viewfinder coverage, what you see inside the viewfinder is going to be about 4% less than what the camera actually captures. Hence, the actual field of view is always what the camera captures, not necessarily what you see inside the viewfinder.

Here is an example of differences in field of view between 70 and 400mm:

The top-left 70mm image looks almost “wide”, while the 400mm image shows a much greater magnification with a much narrower field of view.

3) Angle of View

Lens manufacturers often publish the term “angle of view” or “maximum angle of view” in lens specifications, because they define what the lens is capable of seeing in degrees. For example, the Nikon 24mm f/1.4G lens has a maximum angle of view of 84°, while Nikon 300mm f/2.8G telephoto lens has a maximum angle of view of only 8°10′ when used on film or full-frame cameras. Take a look at the following illustration:

As you can see, 84 degrees is very wide when compared to 8 degrees. That’s why you can fit a lot of the scene when shooting with a 24mm lens, while a 300mm lens allows you to capture a narrower, but much more magnified portion of the scene.

The main difference between the angle of view and field of view, is that the former is an attribute of the lens, while the latter is the result of both the lens and the camera. For example, the above angle of view of 84° for the 24mm f/1.4G is only for a full-frame camera. Once mounted on a camera with a cropped/APS-C sensor, the field of view, or what you see through the camera actually gets narrower to 61°. Nikon publishes two different numbers for angle of view for lenses – “Maximum Angle of View (DX-format)” and “Maximum Angle of View (FX-format)”. In reality, the actual physical characteristic of the lens (what it sees) does not change. As explained below, the size of the sensor simply crops part of the frame, which results in a narrower “field of view”.

4) Equivalent Focal Length

Let’s now move on to the term “equivalent focal length”, which like I stated in the beginning, is a term that many photographers misunderstand. The word “equivalent” is typically in relation to 35mm film. You see, back in the 35mm film days, the focal length of the lens was always whatever the lens said on the label. With the invention of digital SLRs, the camera sensor (the device that captures images) is often much smaller than the 35mm film, primarily because of high cost. This reduction in size of the sensor results in cutting of the image corners, the process that photographers call “cropping”. The interesting thing, is that the image is actually not cut by the sensor or the camera – parts of the image are simply ignored. Take a look at the following illustration (red arrows represent light entering the camera):

As you can see from the above illustrations, the 35mm film/sensor cameras capture a large area of the lens, while the smaller sensors (also known as “cropped sensors”) capture mostly the center. Note how the light enters the camera chamber in exactly the same way in both illustrations, but the smaller sensor is only able to capture a certain portion of it, while the rest of the light falls outside of the sensor. The term “cropped sensor” can be confusing, since “cropping” an image is often associated with cutting it. Once again, in this case, there is no cutting – the light rays from the edges of the lens just overshoot and do not make it to the sensor.

Manufacturers knew about this “overshooting” process when they designed smaller sensors, so they started producing lenses specifically designed for cropped sensor cameras to make them cheaper. Nikon calls them “DX”, while Canon calls them “EF-S”. Basically, the lens itself passes through a smaller image circle and by the time it gets to the sensor, not much of the circle is actually wasted. Think of it as the right part of the above illustration, except the circle is much smaller. Obviously, lenses like these do not function as they should on full-frame/35mm cameras – only half of the scene will actually make it to the sensor. Nikon full-frame cameras are programmed to recognize DX lenses and will automatically decrease the image resolution, while the Canon EF-S lenses will not function on full-frame cameras at all.

How do two cameras with different sensor sizes have the same image resolution? For example, both full-frame Nikon D700 and cropped sensor Nikon D300s have 12.1 Megapixels while having different size sensors. This is because the Nikon D300s camera has much smaller pixels (and hence, higher pixel density) compared to Nikon D700 – that’s how 12.1 million pixels are able to fit on a smaller sensor. What this essentially means, is that the smaller sensors with smaller pixels enlarge the center area of the lens more in this case. If a lens is not of very high quality and is not able to resolve fine details, the images might appear less sharp on cropped sensors.

Let’s now get back to the term “equivalent focal length”. I’m sure you have seen manufacturers claim something like “The 28-300mm lens has a field of view equivalent to a focal length of 42-450mm in 35mm format”, which is a correct way of saying it. Others may say something like “the lens focal length is equivalent to 42-450mm on DX sensor”, which is an incorrect way of saying it. As I have shown above, in relation to the camera sensor, the focal length of the lens never changes – only the field of view does. Saying something like “my 28-300mm lens on my Nikon D90 is like a 42-450mm lens” is incorrect for this reason.

Where do these larger numbers such as 42-450mm come from? Let’s now look into the crop factor and how these “equivalent” numbers are actually computed.

5) The Crop Factor

By now you understand what “equivalent focal length” truly stands for and how the smaller sensors ignore the larger circle area. Let’s now talk about the crop factor – the term that manufacturers and photographers often use to describe camera sensors and to calculate the “equivalent focal length”. You might have heard people say something like “Nikon D90 camera has a 1.5x crop factor” or “Canon 60D has a 1.6x crop factor”. The term “crop factor” came up after smaller sensors were invented to make it easier for people to understand how much narrower the field of view gets when a lens is used on a camera with a small sensor. Manufacturers had to somehow explain how an image on a smaller sensor camera looks enlarged or “zoomed in” compared to 35mm film.

If you take the sensor area of a full-frame sensor or 35mm film and compare it to a cropped sensor, you will be surprised to see that the former is at least twice larger than the latter. For example, the Nikon full-frame cameras approximately have a sensor size of 36mm x 24mm which gives us a surface area of 864. Cropped-sensor cameras like the Nikon D90, on the other hand, have an approximate sensor size of 24mm x 16mm, which is around 384 in surface area – a whopping 2.3 times smaller compared to Nikon D3s! But when it comes to focal lengths, you do not use the surface area of the lens. The crop ratio is computed by taking the diagonal of the full-frame sensor, divided by the diagonal of the cropped sensor.

Now you will have to remember some math. Remember how to compute the diagonal? Here is the formula in case you forgot it: √(X² + Y²). The full frame camera has a diagonal of 43.26 (square root of 1296+576), while the cropped sensor cameras have an approximate diagonal of 28.84 (square root of 576 + 256). If you take 43.26 and divide it by 28.84, you get 1.5 – the ratio of the full-frame sensor diagonal to the cropped sensor diagonal (these numbers are rounded – the actual ratio is a little bit higher, around 1.52).

What do you do with this ratio? You multiply it to get the “equivalent focal length”. For example, the Nikon 24mm f/1.4G lens has an field of view equivalent to approximately 36mm when mounted on a cropped sensor camera like Nikon D90. What this means, is that if you took a 24mm lens and mounted it on a cropped sensor camera, then took a 36mm lens and mounted it on a full-frame camera, you would get about the same view. If you put it the other way, to have the same field of view as the 24mm mounted on a full-frame camera, you would need a 16mm lens on a cropped sensor camera. For example, if you were standing from one spot and could fit a house in your frame using a 24mm lens on a full-frame/35mm camera, to be able to fit that same house on a cropped sensor camera, you would need to have a much wider lens with a focal length of 16mm.

Hope this clears up the true definition of the above terms for those who do not understand them well. If you have any questions or comments, please post them in the comments section below.

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