Lens Angle of View

When shopping for a new lens, most photographers focus on a lens’s focal length. But what is focal length exactly? And how does it relate to the angle of view? Also, how does the angle of view differ from the field of view? Then, ultimately, how do these descriptive terms affect our photos? In this post, we’ll demystify all of these terms and help you better understand how these affect our final images.

Define “Focal Length”

Focal length is a basic description of a lens, usually expressed in millimeters (mm). While many think it measures the actual length of the lens, it doesn’t. Instead, it describes the object forming distance or the calculated point where the light rays converge onto the camera sensor to form a sharp image. We also refer to this phenomenon as the “Nodal Point.”

Common focal lengths include 35mm, 50mm, 24-70mm, and 70-200mm. The first two examples, being fixed focal lengths, are called primes, and the latter being variable focal lengths, are called zooms.

But, that’s a brief definition of focal length. We’ll come back to it later in the post to discuss how it affects the final image. However, two important terms get thrown around when describing a lens’s “angle of view.” And those terms are Angle of View and Field of View. Some use the terms interchangeably, but they’re different things. So we’re going to cover each below.

Define “Angle of View”

The standard definition of Angle of View (AOV) describes the amount of a scene a lens captures onto the sensor, expressed as an angle in degrees. And we can calculate the AOV in several ways using either the horizontal width, vertical height, or diagonal. However, most lens manufacturers will specify the AOV by measuring the diagonal of the image. And they calculate AOV by using a combination of the lens’ focal length and the camera’s sensor size.

Below is the most common equation for calculating AOV in degrees instead of radians.

Angle of view = 2 × (ArcTan (sensor width / (2 × focal length))) × (180/π)

Ultimately, though, the AOV expresses whether the lens shows more of the scene or less of it. Or, put another way, it captures a wide view or a narrow view. An example, imagine turning your head 90º left and right, creating a 180º panorama, versus putting on a pair of binoculars or using a telescope and staring forward off in the distance. You’d have entirely different views of the landscape ahead. And that’s the difference we’re talking about.

Wide-angle lenses below 35mm capture a larger AOV and more of the scene ahead. While longer focal lengths say those above 70mm, offer a smaller AOV and a smaller area of the scene ahead.

Below, I’ve included a chart with the most common full-frame lenses and corresponding AOV measurements based on the attached camera’s sensor size. Please refer to the notes below to better understand the nuances of this chart.

Define “Field of View”

Now that we’ve defined Angle of View let’s describe Field of View, as the two are different.

The standard definition of Field of View (FOV) is the calculated field size based on your focal length and sensor size. Field size means how large the subject appears in the frame. And this calculation also includes an added dimensional variable like the subject or background distance. But, this dimensional variable can be any distance, so long as it’s known and specific. And any point you select will be where the calculated field size is referenced.

However, it’s essential that if you want to calculate a lens’ FOV at a set distance, that you have the proper dimensions of the camera’s sensor and the accurate focal length. It’s also essential to know the nodal point of the lens. But, as mentioned previously, it’s difficult for us photographers to know the specific focal length or nodal points as manufactured. Only the manufacturer knows the measurements through computer simulation and their lens tables. So for us, this calculation is only helpful as a starting point, not for accuracy. Below is the equation from Edmunds Optics that measures FOV horizontally. And if desired, you can also do some added math that considers the Aspect ratio to calculate the Diagonal FOV.

FOV = 2 × (Subject Distance × tan(AOV/2))

Field of View vs. Angle of View

As you can tell by the formulas, FOV and AOV are two separate calculations. But, unlike FOV, AOV is independent of a specific distance. Meaning, it’s not calculated at a set distance from the lens, be it meters or feet. And, as far as we can tell, AOV, being unformed across all distances and unspecific, seems to be the standard for that reason. It could easily be the case that camera lens manufacturers could use FOV and display this specification on their product pages using a set distance, say 10m. But, that isn’t the case. And, instead, they all use AOV. So, really, when most people describe Field of View in photography, they’re actually describing Angle of View. And it’s merely a case of confusion.

Focal Length vs. Angle of View

It’s important to highlight an essential relationship between focal length and AOV. And the focal length used directly impacts the AOV and the image magnification the lens produces. Again, AOV being how much of the scene a lens captures.

Short focal lengths, like those below 35mm, capture more of the scene ahead since they have a larger AOV, often exceeding angles greater than 75º. They also have a lower image magnification. While longer focal lengths, like those above 70mm, provide a much more narrow view of the scene ahead, often providing an angle below 50º. And subsequently, they have a higher image magnification, so the subject in the frame appears larger, and their apparent size increases.

If you’re unfamiliar with the term image magnification, it describes the relative size of individual elements in the foreground compared to those in the background. It’s also referred to as Lens Compression. But, it’s a phenomenon that happens due to the relative distance between you, the subject, and the background. And it’s an apparent perspective change that’s a function of distance.

It goes like this: with a telephoto lens, you have a larger magnification ratio, which means it requires less proximity to fill the frame with an average-sized subject. But, to get the proper framing means you’re also further away from them. Doing so causes the distance between the subject and background to shrink, effectively enlarging the subject itself. In contrast, wide-angle lenses, having lower magnifications, force you to get closer to the subject to fill the frame. And doing so emphasizes the difference between them and background objects, making the background look further away.

Below is a diagram of this in practice by shooting at the same distance.

Of course, you can sometimes physically move closer or further to the subject, mimicking the effect of altering the focal length. But, even so, the focal length of the lens and its subsequent AOV don’t change—instead, only the relationship between the subject and background changes. And it’s merely a fact that subjects taken with a long telephoto lens will always occupy more area on the sensor than the same subject taken with a wide-angle lens, assuming the distance remains equal. So if you’re looking for the unique focal magnification effect of a telephoto lens, it’s always your best option.

So Why Does This Matter?

Ultimately, these definitions and terms help photographers select the right lens. When choosing a specific lens, we usually do so based on focal length alone. However, this decision also means we’re selecting a specific angle of view. And the angle of view is essential here, as it genuinely determines our framing. So it’s essential to pick the right AOV for the type of subject you’re shooting. Do you want a large angle to cover, say, a vast landscape or a narrow-angle to capture distant wildlife in close detail? Knowing this information beforehand is key.

Otherwise, you’ll run into difficulties when framing and composing your images, like not being able to zoom out wide enough or being too zoomed in and close. Of course, you can also physically move closer to the subject to create a tighter frame or move away. But, that’s not always possible. And it also doesn’t produce the same effect as altering the AOV itself. As such, consider your use case beforehand and the subject matter.

But, besides that, this information is mostly technical jargon that’s usually hidden amongst the forums. But, it does provide some insight into how we can control what shows up in our images. Granted, most photographers could care less about the mathematics, instead they care about what our cameras capture and how that translates to the final image.

Conclusion

Now that we’ve covered the definitions of Angle of View and Field of View, you should clearly understand this terminology. Again Angle of View (AOV) determines your framing and composition. Field of View is more of a technical calculation to describe the subject’s size within the frame. But, for most of us, this information is not a necessity. It’s only more helpful to merely select the appropriate lens that gives you the desired framing.

So in the end, does focal length and angle of view really matter? No. Neither matters. The only thing that’s important is we have a large enough angle of view to capture what’s important in our frame. But, the idea of using focal length to define how much we can capture is much easier than thinking about angle of view. And that’s the key takeaway from this particular post, in my opinion.