If you know the distance to the subject and the size of a subject that will exactly fill the frame, it is simple geometry.

Sensor_Width / Focal_Length = Subject_Width / Distance_to_Subject

or

Sensor_Width = Focal_Length * Subject_Width / Distance_to_Subject

Where the subject exactly fills the frame.

Here is a test on my camera, a Canon 7D:

Sensor Width = 50mm * 32.5"/72" = 22.57 mm

My actual sensor width is 22.3 mm, an error of about 1%

Note that this method is only valid for "normal" rectilinear lenses. It is not valid for fisheye or macro lenses.

For a compound lens, you will need to estimate the equivalent simple lens position, the "nodal" point. It is usually about in the middle of the lens. However, it can be outside the lens in some cases.

Note that the units of the distance to subject and subject width can be anything (as long as they are the same), they will cancel, it is the ratio that is important.