Converting Diagonal Field of View (FOV) to Horizontal FOV
What is a Camera's Field of View (FOV)?
A camera's field of view (FOV) is the extent of the scene visible through the camera lens. It is measured as an angle (in degrees) and can be described in three ways:
- Diagonal FOV: The angle measured from one corner of the image to the opposite corner (most often used by manufacturers).
- Horizontal FOV: The width of the scene visible from left to right.
- Vertial FOV: The height of the scene visible from top to bottom.
Because cameras capture rectangular images, the horizontal FOV is always smaller than the diagonal FOV.
What Determines Field of View?
The FOV depends on two factors:
- Focal length of the lens: (how "zoomed in" the camera is)
- Short focal length (wide-angle lens) = wider FOV
- Long focal length (telophoto lens) = narrower FOV
- Sensor size (the physical size of the camer's imageing sensor)
- Larger sensor = captures wider angle
- Smaller sensor = narrower view
- The relationship can be expressed mathematicaly as: tan(hFOV/2) = 0.5*sensor_width/focal_length, where hFOV is the horizontal FOV
Why Field of View Matters (for drones)
For drone pilots, the FOV determines how much ground area is visible in each photo or video frame. It directly affects:
- Framing and composition for photography and videography
- Mapping accuracy (when calculating Ground Sample Distance, or GSD)
- Coverage area per flight path in waypoint missions
- Overlap settings when planning photogrammetry missions
Example:
A DJI Mini 4 Pro has a diagonal FOV of 82.1°, meaning it captures a fairly wide scene suitable for mapping or inspection.
Converting Between FOV Types
DJI, like most camera manufacturers, specifies the Field of View (FOV) of its lenses using the diagonal angle. This value corresponds to a 4:3 (or occasionally 3:2) aspect ratio, which is the format typically used for still photos.
However, it is often useful to know the horizontal and/or vertical FOV instead of the diagonal. A tempting, but incorrect approach, is to use the Pythagorean Theorem to determine the ratio between the horizontal and diagonal aspects, and then multiply the diagonal FOV by that ratio to estimate the horizontal FOV. This simplified method, illustrated in the figure to the right, produces inaccurate results.
The reason this approach fails is because FOV angles do not scale linearly when projected onto a flat plane. The relationship between the FOV angle and the corresponding distance on the projection plane is non-linear. For example, increasing the FOV by one degree at a narrow angle produces a small change in projected width, while the same one-degree increase at a wide FOV (approaching 180°) produces a dramatically larger change.
As shown in the figure to the right, the tangent of half the FOV angle equals half of the image dimension (width, height, or diagonal) divided by the adjacent side of the projection triangle. Applying this relationship to both the diagonal and horizontal directions yields two equations that can be combined into one expression relating the FOV angles to the aspect ratio.
This equation can then be rearranged to solve for horizontal FOV (FOVhoriz) given the diagonal FOV (FOVdiag) and the aspect ratio parameters, as demonstrated in the figure.
A similar process can be used to convert between the diagonal FOV of a 4:3 (or 3:2) photo format and the equivalent diagonal FOV of a 16:9 video format. In this conversion, the horizontal FOV remains constant, while the vertical FOV and diagonal FOV adjust to match the new aspect ratio used in video capture.
Horizontal/Vertical FOV Calculation Tools
- Horizontal and Vertical FOV/GSD Calculator for DJI Drones
- Converting diagonal field of view and aspect ratio to horizontal and vertical field of view