The calculation of lens angle (field of view, FOV) primarily depends on the lens focal length, the size of the image sensor, and the shooting distance. Depending on the specific known conditions and application scenarios, the commonly used calculation methods are as follows:

I. Calculation Based on Focal Length and Sensor Size (Theoretical Calculation)
This is the most commonly used calculation method, which derives the field of view angle by using the lens’s focal length and the image sensor’s dimensions.

• Calculation formula: FOV = 2 × arctan(sensor size / (2 × focal length))

• Parameter Description:

  • FOV: Field of View (horizontal, vertical, or diagonal, depending on the sensor size used).

  • Sensor size: The width, height, or diagonal length of the image sensor (such as CCD/CMOS), with the unit consistent with the focal length—typically in millimeters.

  • Focal length: The actual focal length of the lens (unit: millimeters).

• Calculation logic: The shorter the focal length, the wider the field of view (wide-angle); the longer the focal length, the narrower the field of view (telephoto). The larger the sensor size, the wider the field of view at the same focal length.

II. Calculation Based on Focal Length and Shooting Distance (Actual Scene Calculation)
When the focal length of the lens, the shooting distance, and the range of the scene to be covered are known, the field of view angle can be calculated using trigonometric functions.

• Calculation formula: FOV = 2 × arctan(Actual width of the object / (2 × Shooting distance))

• Parameter Description:

  • FOV: Field of View (typically the horizontal field of view).

  • Actual width of the scene: The actual width of the scene that needs to be fully captured by the lens (unit: meters or millimeters; must be consistent with the distance unit).

  • Shooting distance: The distance from the lens to the subject (unit: meters or millimeters).

• Computational logic: The farther the shooting distance, the wider the field of view; the greater the actual width of the scene, the wider the field of view.

3. Calculate the range of objects based on a known field of view (reverse calculation)
When the focal length of a lens, the shooting distance, and the field of view are known, it is possible to retroactively determine the range of objects that the lens can cover. This method is often used to verify whether a lens meets the requirements for surveillance or photography.

• Calculation formula: Actual width of the scene = 2 × Shooting distance × tan(FOV / 2)

• Parameter description: The meanings of each parameter are the same as above; the actual coverage area is derived by reversing the calculation from the known field of view angle.

Precautions:

1. When performing actual calculations, pay attention to the consistency of units (e.g., use millimeters for both focal length and sensor size, and meters for both distance and object width).

2. The actual field of view of a lens can be affected by factors such as lens distortion and the aspect ratio of the sensor (e.g., 4:3 or 16:9). Therefore, there may be slight discrepancies between theoretical calculations and actual values. The parameter tables provided by professional optical designers or lens manufacturers should be used as the final reference.