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# Camera Field of View Calculator

What is a camera field of view?The angle of viewHow to calculate the angle of view of a cameraThe field of viewHow to calculate the camera field of viewA quick summary: angle of view vs. field of view...and some examples!Does the sensor size of a DSLR matter?FAQs

Whether you are planning a photoshoot or just a photography enthusiast, our camera field of view calculator will help you learn the whole picture.

With our tool, you will be able to calculate the camera's field of view (any camera!), and not only that, there is more to it. Keep reading to discover:

• What is the field of view of a camera?
• What is the difference between the angle of view and the field of view of a camera?
• How to calculate the angle of view.
• How to determine the field of view of a camera.
• Some focused examples.

Refine your photographic knowledge with our dedicated tools like the depth of field calculator and our magnification of a lens calculator. Cheese! 📸

## What is a camera field of view?

📷 Cameras are our way to create memories — instants preserved forever — from what we can see. However, their electronic eyes have some limitations when it comes to how much of those memories they record. We may need to think beforehand about what we want to include in our pictures, and many photographers find it helpful to know their cameras' field of view.

The concept of field of view is not unique to photography: check how it differs for astronomers at our telescope field of view calculator. 🔭

⚠️ There is quite a bit of confusion online (and not only) on the matter, with various definitions and interpretations. Here we gave the one that makes the most sense for us, but feel free to disagree and let us know!

The basic concept underlying the entire matter is that cameras can capture a single, defined portion of the real-world at once. How significant this portion depends on the camera set-up, particularly on the type of lens and camera body used by the photographer.

Imagine drawing a rectangle in front of you. How would you tell someone how big it is? You have two ways of saying so:

• Using angles to specify in absolute terms the dimensions; or
• Using a pair of length measurements: you can't say only "1 meter", but you have to specify "1 meter at 4 meters of distance" (this is a relative measurement).

The concepts are used almost interchangeably, as they define the same concept. However, their definitions are different. Let's discover them in detail.

## The angle of view

When we use angles to define the dimensions of a picture, we talk of the angle of view. The angle of view is pretty easy to visualize: your camera lies at the center of a sphere, and connecting the angles of the scene you are capturing to its center gives you a set of three angles:

• A horizontal angle;
• A vertical angle; and
• A diagonal angle.

The two first ones define the width and height of the rectangle corresponding to our sensor. Notice that these quantities are absolute: you can place the "sphere" as far as you like (even at an infinite distance), and the angle of view will still be the same.

## How to calculate the angle of view of a camera

To calculate the angle of view, you need to know two parameters of your set-up; one easy, the other one not so much:

• The focal length of the lens you are using; and
• The dimensions of the sensor of your camera.

🙋 To find the size of your sensor, search on Google "[your camera model] sensor size": you will easily find the correct values!

The formula for the angle of view (in degrees) is:

$\footnotesize \text{aov}_i = 2 \arctan{\left(\frac{\text{sensors size}_i}{2\times \text{focal length}} \right)}$

Why the tiny $i$, you ask? This formula holds for all the three possible directions on the sensor: horizontal, vertical, and diagonal.

As a rule of thumb, the higher the magnification of the lens is, the smaller the angle of view. If you manage to fit the Moon in your picture, the vertical angle of view would be around half a degree, but this feat requires a pretty high magnification. On the other hand, a $55\ \text{mm}$ lens on an SLR (single-lens reflex) camera will give you a horizontal angle of view of about $20\degree$.

Think about the Moon for a second more. You managed to fit it into your picture — your sensor! We are talking of a $3,500\ \text{km}$ body. You can take a picture of a plane passing between you and our satellite with some luck and good timing. A B747 flying at $6.5\ \text{km}$ would almost eclipse the Moon, fitting perfectly in the picture together. Does it mean the jumbo jet is really that jumbo, or that the field of view can be a relative concept, too?

## The field of view

Even if angles are easy to visualize, they can be hard to estimate (how wide is $5\degree$?). The field of view comes in handy to complement the idea of the angle of view.

Take the diverging lines from the sphere's center to the corner of the scene, and stop them at a certain distance $d$. Now, draw the corresponding rectangle: you will obtain a set of measurements we call the field of view at a distance $d$.

Here is the lack of absoluteness of the field of view: its value varies with the distance between the camera and the subject. That's why in the same angle of view, you can fit both the Moon and a passenger airplane.

## How to calculate the camera field of view

As for the angle of view, you can identify three quantities associated with the field of view: a horizontal length, a vertical length, and a diagonal length. To calculate the field of view $\text{fov}_i$ of a camera in each of the three possible directions, use the following formula:

$\footnotesize \text{fov}_i = 2\tan{\left(\frac{\text{aov}_i}{2}\right)}\times d$

You already know what the $i$ means and $d$ is the distance at which the field of view is measured. Remember to use the correct dimension of your sensor: you want to use its length to calculate the horizontal field of view of your camera, not the vertical one... unless you are taking a portrait picture.

## A quick summary: angle of view vs. field of view

A camera captures a rectangular portion of the real world, projecting it onto its sensor. We identified two possible ways to measure the size of that portion:

• The angle of view; and
• The field of view.

We define both quantities for three spatial directions, which allows us to calculate a vertical, diagonal, and horizontal field of view for a camera set-up, alongside the respective angles of view.

The field of view is a function of both the angle of view and the distance between the sensor and the object.

## ...and some examples!

It's impossible to define a typical field of view of a camera: it depends on the lens you are mounting at the moment. However, we can give you some practical examples.

Canon produces a rectilinear $\text{11-24 mm}$ lens — which is insane — that allows capturing sharp wide-angle images. How wide? Let's mount the lens on a Canon EOS 550D and calculate this camera field of view!

A rectilinear lens is a lens that preserves orthogonality: two straight, perpendicular lines in the real world are depicted as straight, perpendicular eyes by a rectilinear lens. A fisheye lens, on the other hand, distorts them — a small price to pay for an extremely wide field of view!

The Canon EOS 550D has a sensor size $22.3\times14.9\ \text{mm}$, which allows us to calculate both the horizontal and the vertical angle of view. Let's not be extreme and use the $24\ \text{mm}$ focal length.

For the horizontal angle of view we have:

\footnotesize \begin{align*} \text{aov}_{\text{h}} &= 2\times \arctan{\left(\frac{22.3\ \text{mm}}{2\times 24 \text{ mm}} \right)}\\\\ &=0.87\ \text{rad} = 50\degree \end{align*}

And for the horizontal direction we calculate:

\footnotesize \begin{align*} \text{aov}_{\text{v}} &= 2\times \arctan{\left(\frac{14.9\ \text{mm}}{2\times 24 \text{ mm}} \right)}\\\\ &=0.60\ \text{rad} = 34\degree \end{align*}

That is an extremely wide angle of view: it covers $1700$ square degrees! However, you need almost 20 of these fields to capture a true $260\degree$ picture.

What can you capture with this lens? For a distance $d=200\ \text{m}$, the angle of view converts into the respective linear field of views:

\footnotesize \begin{align*} &\text{fov}_{\text{h}} = 2\tan{\left(\frac{50\degree}{2}\right)}\times 200= 186\ \text{m}\\\\ &\text{fov}_{\text{v}} = 2\tan{\left(\frac{34\degree}{2}\right)}\times 200= 122\ \text{m}\\ \end{align*}

That is more than enough to fit the whole Colosseum in Rome in a single picture. And all of this standing barely more than the diameter of the arena itself away!

On the other hand, let's calculate the camera field of view for a typical telephoto lens set-up. We keep the same camera but mount a $200\ \text{mm}$ lens. Insert the values in the appropriate fields of our camera field of view calculator and calculate the angles of view in this case:

\footnotesize \begin{align*} \text{aov}_{\text{v}} &= 2\times \arctan{\left(\frac{14.9\ \text{mm}}{2\times 200 \text{ mm}} \right)}\\\\ &=0.11\ \text{rad} = 6.4\degree \end{align*}

For the horizontal one, and:

\footnotesize \begin{align*} \text{aov}_{\text{v}} &= 2\times \arctan{\left(\frac{14.9\ \text{mm}}{2\times 200 \text{ mm}} \right)}\\\\ &=0.074\ \text{rad} = 4.3\degree \end{align*}

The solid angle covered by this set-up is about $27$ square degrees for the vertical one! If you want to take a $360\degree$ picture, you'll need more than $1500$ shots! But at a distance of $200\ \text{m}$ you would be able to picture an area of $45\ \text{m}\times 30\ \text{m}$: good enough to take some exciting wildlife pictures without disturbing anyone!

🙋 You can use our camera field of view calculator to find the values of the angles and fields of view and to calculate the needed focal length of the lens you need to mount to obtain a particular field of view. We locked the variables associated with the sensor's size: it's unlikely you will change it instead of the lens!

Do you want to learn more about the fundamental of photography with a slight technical twist? We made the right calculators for you: the aspect ratio calculator and the crop factor calculator!

## Does the sensor size of a DSLR matter?

The sensor size of your camera significantly affects the quality of your pictures. A camera with a larger sensor will give you a wider field of view for the same lens, maintaining the same magnification: your subject will be surrounded by more background. The advantages are relative, though: when printing the photograph in the same format, a larger field of view will necessarily translate to a lower magnification.

FAQs

### What is the angle field of view of a camera with a 23.5 x 15.6 mm sensor and 50 mm lens?

Using angles, it is 26.5° × 17.7°, vertical and horizontal angle of view, respectively. To calculate these values, input them in the angle of view formula:

aovᵢ = 2 × arctan(sᵢ/(2 × f))

where:

• sᵢ is either the width w or the height h of the sensor; and
• f the focal length of the lens.

To find the result, substitute these values:
aovᵥ = 2 × arctan(23.5/(2 × 50)) = 26.5°
aovh = 2 × arctan(15.6/(2 × 50)) = 17.7°

### What is the difference between camera angle of view and camera field of view?

The angle of view of a camera is an absolute measure of the horizontal and vertical angles captured by a combination of camera and lens. The field of view measures the same concept but uses lengths. Since the angles don't change, the field of view depends on the distance: specifically, it increases alongside it.

### How do I determine the camera field of view?

To calculate the camera field of view, you need to know three parameters:

1. The focal length f of the lens.
2. The camera sensor's size (w × l).
3. The distance d from the camera to the subject.

1. Calculate the angle of view for each side of the sensor sᵢ with the formula:

aovᵢ = 2 × arctan(sᵢ/(2 × f))

2. Input each result in the camera field of view equation:

fovᵢ = 2 × tan(aov/2) × d