Please can you explain Horizontal Field of View?

I have been playing around with Litchi Mission Hub and Google Earth Pro, but am getting confused. When I look at the spec for my Mavic Pro, I see that the FOV is 78.8 degrees. Is that the horizontal field of view?

When I use Chrome Virtual Litchi Mission, with the drone model set to Mavic Pro, it generates a litchi_mission.kml file with gx:horizFov71.1992828798343</gx:horizFov>. Why the difference? Furthermore, if I look at the “DJI Cameras - Field of View.kml” file it lists the Mavic Pro’s gx:horizFov63.97</gx:horizFov>. Why the three different values?

None of the drones in “DJI Cameras - Field of View.kml” file have the gx:horizFov the same as the nominal (spec) FOV, and it isn’t even the same scaling factor from drone to drone.

Help. My brain hurts.

Welcome @peterwfraser

Simply put … Yes. The area across which your camera can image is known as the field of view or FOV, the larger the FOV the more of your sample you can see.

As for the discrepancies or variations in Google Earth, I havent a clue. I’m not sure it will make much difference when flying a virtual tour. Google Earth Pro is a useful tool to find potential issues with a mission before flight.

Rest your brain and just enjoy the usefulness of Google Earth Pro.

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The FOV mentioned in the specifications of your drone is the diagonal FOV for a 4:3 photo.
It depends on the focal length, aspect ratio of the produced image and the section/part of the image sensor used to produce that immage.
This means that the FOV of a 16:9 video is smaller than the FOV of a 4:3 photo.

When a smaller (cropped) part of the sensor is used to produce an image, the FOV also gets smaller (the Mavic 2 Pro uses a smaller part of the sensor with certain video settings/profile).

For instance with the Mini 3 the FOV for photo is about 81.5° and the FOV for video is about 75° (both diagonal).

Using the Pythagorean theorem you can calculate the 16:9 FOV from the 4:3 FOV.
16:9 FOV = 4:3 FOV / 20 x 18.36

I deleted the four formulas for calculating the horizontal and vertical FOV because they are incorrect (I went too far simplifying them).
Thanks @Sam_G for pointing this out.
I asume you will post the correct ones.


Thank you so much. That makes sense now.

Horizontal and Vertical FOV can be calculated using these formulas:

4:3 aspect:
b = √(c²/1.5625)
hFOV = √(FOV²/1.5625)
vFOV = hFOV x 0.75

Thanks. I like that you got c² in there somewhere.

These equations assume that FOV space is equivalent to aspect-ratio space. I’m not an expert in this but I don’t think you can combine both FOV (degrees) and linear measurements (1.0 + (3/4)**2) like this. Instead, you have to convert between the two spaces (degrees vs linear measurements).

Here is a page that describes the conversion between diagonal FOV and horizontal FOV. I’ve compared the results of the equations you show and the ones outlined in this page and they yield different results.

And I will openly admit that I am not an expert either in the field of FOV, just math.
I didnt combine degrees and linear measurements, only the ratios of the two sides of the 4:3 aspect ratio. Like this image depicts. I think its safe to assume that FOV space is equivalent to aspect ratio


My calculations were based on a right triangle where one side a (the vertical side) is 3/4ths b (the horizontal side).
If a² + b² = c²
and a = .75 of b (4:3 aspect ratio of the image)
then (.75b)² + b² = c²
simplifying gives you .5625 b² + b² = c²
or 1.5625b² = c²
so divide both sides by 1.5625 and you get b² = c²/1.5625
the square root will equal b (horizontal)

How different were the results using the equations from the website you quoted?


  • If Df is the diagonal field of view and Ha:Va is the horizontal to vertical aspect ratio, we can find the corresponding diagonal size in the same units as the aspect ratio:

Da = sqrt(HaHa + VaVa)**

Pythagorean’s theory. No need to figure angles.

Me too. I’m just trying to figure out the “correct” solution to this question.

I think you did. The aspect ratio is a linear measurement. That is where the 1.5625 comes from (1.0 + 0.75**2). The FOV is measured in degrees. When the change in degrees is mapped onto a flat surface, the resulting increments on that flat surface are not linear. A one-degree angular increment results in a longer linear increment as you travel further from the center.

I wrote a program to compare the two methods. Here are the results for the Mini 2 (FOV = 81.5):

Diagonal FOV 4x3 (photo): 81.5°
Vertical FOV 4x3 (trig only): 48.9°
Vertical FOV 4x3 (conv FOV to aspect ratio space): 54.7°
Horizontal FOV 4x3 (trig only): 65.2°
Horizontal FOV 4x3 (conv FOV to aspect ratio space): 69.2°

So are you just ignoring from this statement and down?

The screen height and width are proportional to the tangent of the half angle. We use this to convert between field-of-view space and aspect-ratio space:

Post deleted - my apologies to the community

Thanks. That makes sense to me. It seems like longer focal lengths approximate to the Pythagorean approach, but the results diverge more the shorter the focal length becomes.

Thanks for that. I agree; you’ve got to use the arctans. Are you explicitly entering the focal length, or are you inferring it from the sensor size and the FOV number?

That is what I gather as I dig into this.

The web page that I found is starting from the diagonal FOV in degrees and the aspect ratio.

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I’ve spent more time figuring this stuff out. I’m sorry but this post is going to become complicated and is not intended for “light reading”. Here are my findings. I welcome any corrections or other insights.

The aspect ratio, while unit-less in measurements, are measured using linear quantities. When I use the term “linear” I don’t necessarily mean “in a straight line”. Instead, I am referring to a consistent unit of measure no matter where it occurs along a line.

Field of view (FOV) is a linear measure but only in “degree space”. When the FOV is projected onto a flat surface, a linear change in the FOV degrees corresponds to a non-linear change when measured on that flat surface. Here is diagram to help describe this:

What this means is that one cannot use the Pythagorean Theorem to convert between the diagonal and horizontal FOV quantities because while the aspect ratio quantities of the sensor are linear, FOV values are not linear when projected onto that flat surface.

This concept is touched on in this description of the issue:

I have created this diagram to help describe how the ratio of tangents of the FOVs are equal to the ratios of horizontal to diagonal aspects. Remember, tangent is “opposite over adjacent” where, in this case, the “adjacent” length is the same for all aspect ratios and therefore not included in the equation.

Rearranging that equation to solve for FOVhoriz we get:

Using what I’ve learned, I have created a web application to compute the horizontal and vertical FOV values based on a 4x3 aspect ratio and a diagonal FOV. Using another rearrangement of the above equation I can compute the equivalent 16x9 diagonal FOV. Let me know if there is interest in this.

Using this application I have created a table comparing the FOV computations using the above equations to those using FOV values directly in the Pythagorean Theorem. You will notice that for small FOVs, there is not much difference between the two methods (which is expected). However, as the FOV becomes larger, the difference between the two methods becomes larger.

FOVdiag FOVhoriz FOVvert FOVhoriz(linear) FOVvert(linear)
20 16.1 12.1 16 12
30 24.2 18.3 24 18
40 32.5 24.6 32 24
50 40.9 31.3 40 30
60 49.6 38.2 48 36
70 58.5 45.6 56 42
80 67.7 53.4 64 48
90 77.3 61.9 72 54
100 87.3 71.1 80 60
![image 398x201](upload://rVqfryfAY2M3qCB6sOsQ5xS035U.png)

Note: The last two columns in this table are those computed assuming FOV values can be used directly in the Pythagorean Theorem. As a result, these values are not correct but shown here for comparison purposes only.

In your formula, what numerical value are you using for ‘aspectHoriz’ and ‘aspectDiag’?
Horiz = 4 (from the diagram), Vert = 3 (assumption), then is the aspectDiag = 5?

From the quoted website, the define aspect ratio this way:
Assuming square pixels, the aspect ratio is the horizontal resolution divided by the vertical resolution.

I, too have struggled to understand the calculations and I agree … Pythagoras was brilliant to figure out the relationship of opposite sides, adjacent sides and hypotenuse(s). But his basic formula is not the way to calculate H-FOV and V-FOV based on a given FOV (typically given as diagonal, to make it look bigger like a TV screen size). I apologize to anyone that used my erroneous calculations.

Do not use the figures in the last 2 columns

Très bon travail. Merci pour votre investissement.

Yes. Because it is a 4x3 sensor, the values are aspectHoriz=4, aspectVert=3, aspectHoriz=5.

Like most others, I started doing these calculations using the Pythagorean Theorem directly. However, when I couldn’t match what I had found online, I started digging deeper into it.

What is still perplexing, I cannot match the values in the original post. eg. gx:horizFov71.1992828798343 or gx:horizFov63.97.

However, using a rearrangement of the formulas I showed above, I can correctly compute the 16x9 diagonal aspect of a 4x3 sensor when used in video mode.