Camera Field of View Calculator

Field of view is how wide a scene a lens captures, set by sensor size and focal length.

How the Math Works

The Field of View (FOV) formula calculates the angular coverage of a lens using trigonometry. Here, FOV = 2 * atan(sensor / (2 * focal)), where 'sensor' is the dimension of the camera's sensor (e.g., width or height), and 'focal' is the lens's focal length. The arctangent (atan) function determines the angle of a right triangle formed by the sensor half-dimension and the focal length. Doubling this angle gives the full field of view, representing how much of the scene the lens can capture at a given distance. This mathematical relationship ensures precise prediction of a lens's visual range.

Practical Applications

To apply this calculation, first measure or obtain the sensor dimension (e.g., 36mm for a full-frame camera's width) and the lens's focal length (e.g., 50mm). Plug these values into the formula to determine the FOV in radians or degrees. This helps photographers and videographers select lenses for specific shots—wide-angle lenses (low focal length) yield larger FOVs, while telephoto lenses (high focal length) narrow the FOV. It also aids in framing scenes, comparing lenses, or designing camera systems for tasks like surveillance or drone imaging where coverage is critical.

Day-to-Day Use

In everyday life, this calculation empowers smarter camera choices. For instance, when buying a camera, you can estimate how much of a room or landscape a lens will capture, ensuring you don’t need to step back or move objects. It helps content creators frame shots without trial and error, whether filming a vlog, taking group photos, or setting up security cameras. Additionally, understanding FOV enhances storytelling by guiding decisions on lens selection to emphasize perspective, depth, or subject proximity in photos and videos.

Worked example

Full-frame 36 mm sensor with a 50 mm lens gives about 39.6 degrees.

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