About

The field of view (FOV) is the angle between the edges of a frame in one dimension (horizontal, vertical, or diagonal). Usually, we are talking about diagonal FOV, because in rectangular frames, the diagonal is larger than both the width and the height (the Pythagorean theorem states that d = √( h² + w² ))

FOV [°] = 2 * arctan ( d [mm] / (2 * f [mm]) )

^{FOV is our field of view in degrees, d is one of the dimensions of the sensor (height/width/diagonal) in millimeters and f is the focal length in millimeters.}

Because the focal-length is a fixed value that is determined by the lens's properties, and because the sensor-size influences the FOV (see crop-factor), it is common to talk about "focal length equivalent to 35mm".

e [mm] = f [mm] * c

^{e is the equivalent focal length in millimeters, f is the focal length in millimeters, and c is the crop factor (c = A_35mm[mm²] / A_{Cropped sensor}[mm²], where A is the sensor area in square millimeters) )}

While the focal length does not change, because the smaller sensor sees less of the image circle, it has a smaller FOV, for which you would have to use a longer focal length lens on a 35mm (full frame) camera.

Further reading:

• Does my crop sensor camera actually turn my lenses into a longer focal length?
• Why do Full Frame lenses and crop body lenses exhibit the same crop factor when used on a crop body camera?
• How can I calculate vertical field of view from horizontal field of view?
• What is crop factor and how does it relate to focal length?