Lenses: focal length, angle of view and framing

Learn to estimate the framing that you will obtain with a specific objective (field of view) at a certain distance from the scene.

As we saw in the article on the focal length of the lenses, in photography, the focal length is a synonym for the angle of view.

The angle of view depends on the focal length of the objective and the size of the surface where the image is projected (photographic film or sensor).

For historical reasons, 35mm film is used as a reference (which corresponds to Full Frame sensors in digital cameras).

What is the angle of view?

The angle, the portion of the scene, that we can frame in our sensor (or film) using a lens with a specific focal length.

Basic rules:

  • Distances short focal: viewing angle very wide
  • Distances focal lengths: viewing angle very narrow
  • Large pickup surface (large sensor ) – increased viewing angle.

Small surface area (remote sensor ): lower angle of view (crop)
angle view

The angle of view vs. Focal length

As we have commented, in photography, the 35mm film or the Full Frame sensor (36 × 24 mm) is taken as a reference.

Knowing the focal length and the sensor’s size, the angle of view can be calculated by trigonometry but

I have never seen a photographer with a calculator in hand to know the exact grade that he will achieve with his equipment.

The angle of view is something that is internalized.

Intuitively, with experience, you get an idea of ​​the framing that each lens will give you (its focal length) in certain situations.

  • With the angular and wide-angle, you get a wide viewing angle.
  • Medium focal length lenses (regular) give a rise of view that closely resembles the perception we have when looking at that scene with our own eyes.
  • Long-focal lenses ( telephoto lenses ) give us an increasingly narrow-angle, which we often associate with the ‘reach’ of that lens to photograph distant objects.

The equivalent angle of view and focal length

The angle of view depends on the size of the sensor.

If we had to consider all sensor and film sizes, we would go crazy with the viewing angles.

In photography, it is spoken in the language of 35mm film.

All photographers know how a specific focal length would behave (approximately what angle of view it would have) in a 35mm frame or a Full Frame sensor.

We all speak in that language. What you do is ‘ transform ‘ the lens’s focal length, normalize it based on the sensor’s size.

The crop factor and equivalent focal length appear here.

Imagine a camera with a Full Frame sensor and a camera with an APS-C sensor, and a single 50mm lens compatible with both cameras.

A typical APS-C sensor applies a 1.5x crop factor (it’s its size ratio to a Full Frame sensor).

When we place the 50mm lens on the APS-C camera, the angle of view that we obtain in the photo is similar to what we would get in the Full Frame camera with a 75mm lens (1.5 x 50 = 75).

So we say that this lens (in our camera) has an equivalent focal length of 75mm.

The focal length is an optical characteristic of the lens, and it does not change. The lens will have the same visual elements in any camera or in whatever use we give it.

The equivalent focal length is simply a gimmick, a normalization, which allows us to intuitively estimate from the head what kind of frames we will achieve with that lens in that camera.

Here’s an example of viewing angles on cameras with an APS-C sensor for lenses of different focal lengths. In black is the real focal length of the lens, and in parentheses, the equivalent focal length in that particular camera.

angle view 2

What is the field of view?

The field of view tells us how much of a scene fits within the frame (occupies the entire structure) for a given focal length (and camera).

It is measured in units of length, in meters, for example.

How is the field of view related to the angle of view?

The view depends on the angle of view and the distance between the camera and the scene.

We are going to see it with an example.

Let’s assume a certain equivalent focal length: 400mm.

Now we find ourselves a good friend (one of those who have much patience), and we tell him to place himself at a certain distance from our camera: first at 25m, then at 50m … and so on.

Our equipment has the same angle of view, which corresponds to the equivalent focal length of 400m.

However, the field of view in each photo is different.

At 25m, the view field is about 2m (horizontal), and our friend looks very large in the frame.

At 400m, the view field is about 35m wide, and comparatively, the person looks much smaller.

If we now test with a 200mm lens, the angle of view will change (now it will be more comprehensive).

Comparatively, placing the person at the same distances, the field of view will also be wider concerning the 400mm lens.

Then below, we will see how to estimate the field of view and its use.

So, summarizing:

  • Viewing angle (in English Angle of View – AOV ) refers to the angle covering our combination of lens and camera. It is measured in degrees.
  • FOV (Field of View English – FOV ) refers to the scene’s actual size that fits within our framework. It is measured in meters.

In practice, everyone swaps names, and you will find the term FOV much more to refer to the angle of view.

So when you hear and read FOV, they are almost certainly referring to an angle.

Why do we want to know the field of view?

In general, we rarely need to know the field of vision for typical day-to-day situations, especially in photography.

When could we be interested?

  • When we are going to buy a new lens, and we are evaluating which focal length interests us the most.
  • When we plan a photographic outing, we want to know what equipment we are interested in bringing and what frames we will have from different locations.
  • In professional film and video productions, all scenes need to be planned very well. In many cases, it is essential to know in detail the field of view of each shot. For example, imagine that you have a set for a scene, or you are looking for a particular frame that includes several elements, etc.

Below we see some real examples so that you can get an idea of ​​use.

field of view

How to estimate the field of view

This calculation is only valid for straight lenses; it would not be accurate for fisheye lenses.

And it is only valid when the subject is at a certain distance from the camera, such that that distance is considerably more significant than the focal length of the lens itself.

Steps we are going to follow:

1. What is the equivalent focal length of the lens in our camera?

For example, if we used 50mm on a Nikon APS-C sensor camera, the equivalent focal length would be 75mm.

2.What angle of view corresponds to that equivalent focal length?

We would have to calculate the tangent (of the half of said angle). But we have it already figured in this table:

The multiplication factor that appears in the table is the result of this formula: 2 * tan (ang / 2)

The displayed angle corresponds to the horizontal viewing angle.

For the example that we are following, the equivalent focal length of 75mm corresponds to a factor of 0.5

3.We estimate the distance to the subject

The more precise the distance from which we are going to use the camera, the better. In many cases, it would be worth a rough estimate.

Imagine, for example, that we will stand 5 meters from the person to take a portrait.

4.We calculate the field of vision at that distance

We multiply the factor by the distance.

In the example: 5m x 0.5 = 2.5m

The horizontal field of view of the scene would be 2.5m wide. Since the sensor has a 3: 2 form factor, the height of the vertical field of view would be approximately 1.7m.


Example 1: Telephoto lens for bird photography

Imagine we are looking for a telephoto lens for bird photography.

Let’s suppose we want to photograph the lesser kestrel, which is about 35cm long. And we want to have an idea of ​​the framing that we are going to achieve with different focal lengths depending on the distance we can approach.

We have a Canon APS-C camera: 1.6x crop factor.

Let’s see first with a 300mm telephoto lens.

1. Equivalent focal length: 1.6 x 300 = 480mm

2.We do not have the exact focal length in the table, but we can estimate that the factor would be an intermediate value, for example, 0.08

3.We will observe the lesser from the ground, and the bird will be in a tower about 30 meters high. We will also estimate 100 meters for when we try to track in flight.

4. We calculate:
30m -> 0.08 * 30 = 2.4 meters wide

Approximate field of view height: 2.4 * 2/3 = 1.6 meters high (160cm).

The lesser (about 35cm) would cover about 1/4 of our frame.

It would not be wrong.

For in-flight photography:
100m -> 0.08 * 100 = 8 meters wide

Assuming a wingspan of about 70 cm (0.7 m), this time horizontal, the lesser would cover about 9% of our frame.

How about a 400mm?

The equivalent focal length in our camera would be 640mm.

The multiplication factor would be 0.06
30m -> 0.06 * 30 = 1.8 meters wide

Frame height (since we are going to photograph it posed, vertically): 1.8 * 2/3 = 1.2 meters (120cm).

The lesser would occupy approximately 30% of the frame.

Photography in flight:

100m -> 0.06 * 100 = 6 meters (horizontal width of our field of view at that distance)

The lesser would occupy approximately 12% of our horizontal frame.

self video recording

Example 2:  Home recording studio for youtube

We want to set up a small recording studio for YouTube in one of our house rooms.

We are looking for a fixed lens to improve our videos’ quality, for shots in which we appear in front of the camera talking.

The room is relatively small, so we want to know if we would be more interested in a 50mm or a 35mm.

The room is about 5 meters long, but we have to leave a margin with the back wall and a small margin for the tripod’s camera.

The actual distance between the camera and the person will be about 3
Our camera is a Sony with an APS-C sensor: 1.5x crop factor.

Let’s go there with the 50mm :

  • Equivalent Focal: 50 * 1.5 = 75mm
  • Multiplication factor: 0.5
  • Distance: 3.5m
  • Horizontal field of view: 3.5 * 0.5 = 1.75 meters
  • Vertical field of view: 1.75 * 2/3 = 1.16 meters

It would be suitable for a medium shot: from the head, with a little air above, to the hips. Perfect for

images in which we appear seated.

We now see with the 35mm :

  • Equivalent Focal: 35 * 1.5 = 52.5mm (approx. 50mm)
  • Multiplication factor: 0.7
  • Distance: 3.5m
  • Horizontal field of view: 3.5 * 0.7 = 2.45 meters
  • Vertical field of view: 2.45 * 2/3 = 1.63 meters

It would be very fair for full-body shots depending on our height. We would have to assess whether we interested in having that extra margin that the 35mm provides us (giving up a little perhaps part of the background blur) or if we prefer the 50mm, although it limits us a bit the type of shots that we are going to do in that study.

photography planning

Example 3: Planning photographic outings

The idea here is the following:

We want to take a series of photos in a natural environment, and we are going to look for particular frames for our composition.

Imagine, for example, that you want to take several characteristic elements of the area in the same frame.

You have to plan from which points you can take the photo (viewpoints, trails, etc.), at what distances the landscape elements will be concerning your camera and the distances between them, to get an idea of ​​the frames and focal points need.

This planning is more complex or more complicated. It would be a bit tedious to do it by hand.

You can use Google Maps, with its utility of measuring distances, which will give you a pretty good approximation.

Usually, you want to estimate the angle you need to cover a landscape (minimum focal length) with all those elements from your observation point.

Or also, if you are looking for detail photography (a distant landmark, for example) to get an idea of ​​how that element would appear in your frame with the focal length you are going to use.

For example, if your maximum focal length is 200mm, what frame can you get from point A and point B to get the full detail of that landmark you want to photograph.

In practice, mobile applications such as PhotoPills allow you to plan your outings in great detail, including the sun’s trajectories and the moon, the Milky Way, etc., for the location where you are going to be, schedules …

And their tools also include field of view estimators.