I.Definition
The field of view (FOV) describes the extent of the observable scene captured by an imaging system. In photography, the terms field of view (FOV) and angle of view (AOV) are often used interchangeably to refer to the maximum angular extent of a scene observable by a camera.
Depending on the measurement direction, the field of view may be specified as the horizontal field of view (HFOV), vertical field of view (VFOV), or diagonal field of view (DFOV).

Figure 1. HFOV, VFOV, and DFOV illustration(Image source: https://commons.wikimedia.org/w/index.php?curid=5294848)

From an optical perspective, the angle of view is defined as the angle subtended by the entrance window at the center of the entrance pupil. The field stop limits the field of view, while the entrance window is the image of the field stop formed by the optical system in object space.

Figure 2. Optical definition of field of view (FOV)

II.Impact Factors
The field of view (FOV) of a camera is determined by both the focal length of the lens and the size of the image sensor.
1. Focal Length
The focal length is the distance between the optical center of the lens and the focal plane of the image sensor. For a given sensor size, a longer focal length results in a narrower angle of view, while a shorter focal length produces a wider angle of view.

Figure 3. Field of view with focal lengths of 24 mm, 28 mm, 35 mm, 50 mm, and 72 mm.（Image source: https://commons.wikimedia.org/wiki/File:24-72mm_zoom_demo.jpg)

2. Sensor Size
For a given focal length, a larger sensor produces a wider angle of view because it captures a larger portion of the image projected by the lens. Conversely, a smaller sensor results in a narrower angle of view. This relationship is commonly expressed by the crop factor, which quantifies the difference in field of view between sensor formats.

Figure 4. Field-of-view cropping caused by different sensor sizes.

III.Calculation
The effective focal length of the lens and the size of the image sensor fully determine the field of view (FOV) of a camera. The general formula for the angle of view is:
$$\alpha = 2\arctan\left(\frac{d}{2f}\right)$$ where $d$ is the dimension of the sensor in the measurement direction, and $f$ is the effective focal length.

If the sensor has a horizontal dimension $d_{h}$ for width and a vertical dimension $d_{v}$ for height, the horizontal, vertical, and diagonal fields of view can be calculated as:

$$HFOV=2arctan\frac{d_{h}}{2f}$$

$$VFOV=2arctan\frac{d_{v}}{2f}$$

$$DFOV = 2 \arctan\left( \frac{\sqrt{{d_{h}}^2 + {d_{v}}^2}}{2f} \right)$$ where HFOV, VFOV, and DFOV denote the horizontal, vertical, and diagonal angles of view, respectively.