Converting Diagonal Field of View (FOV) to Horizontal FOV

Aspect Ratios and FOVs

As is commonly done with cameras, DJI advertises the Field of View (FOV) of their lenses using the diagonal angle. This FOV value corresponds to an aspect ratio of 4x3 which is typically used for photos.

Pythagorean's Theorem Incorrectly Applied

It is sometimes desired to know either the horizontal FOV or vertical FOV or both. To compute either the horizontal or vertical FOV, it is tempting to use the Pythagorean Theorem to compute the ratio of aspect-horizontal to aspect-diagonal and then multiply the diagonal FOV by that ratio to obtain the horizontal FOV but that would be incorrect. This method is summarized in the figure to the right.

The reason the above method would be incorrect is because the FOV angle, when projected onto a flat plane has a non-linear relationship with distances along that plane. For example, a one-degree change of FOV when the FOV is small results in a relatively small linear change on that flat plane. However, a one-degree change of FOV when the FOV is large (closer to 180) yields a massive change on that same flat plane.

Comparing Aspect Ratio to Tangents of FOVs

Referring to the figure to the right, one can see that the tangent of the half-FOV angle would be equal to half the aspect over the adjacent side. Applying this rule to both the diagonal and the horizontal yields two equations that can be combined to form one equation relating the FOV angles to the aspect ratios.

This equation can be re-arranged to solve for FOVhoriz, given FOVdiag and the aspect ratio information as shown in the figure to the right.

A similar method can be used to convert between the diagonal FOV of a 4x3 aspect ratio typically used to capture photos to the equivalent diagonal FOV of a 16x9 aspect ratio typically used in video capture. In this conversion, the horizontal FOV would be the same for both a 4x3 photo and 16x9 video.

More Information on FOV

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