They do say 1/2" sensor, but it means as compared to an old glass video tube, round tube with rounded corners, which doesn't leave much room for the flat rectangular sensor area. The TV video cameras in the old days.
The Wikipedia link says:
[h=3]Table of sensor formats and sizes[/h] Sensor formats of digital cameras are mostly expressed in the non-standardized "inch" system as approximately 1.5 times the length of the diagonal of the sensor. This "optical format" measure goes back to the way image sizes of video cameras used until the late 1980s were expressed, referring to the outside diameter of the glass envelope of the video camera tube. David Pogue of The New York Times states that "the actual sensor size is much smaller than what the camera companies publish – about one-third smaller." For example, a camera advertising a 1/2.7" sensor does not have a sensor with a diagonal of 0.37"; instead, the diagonal is closer to 0.26". Instead of "formats", these sensor sizes are often called types, as in "1/2-inch-type CCD."
So it means 6.4 mm wide. All compact cameras do that. A Nikon Coolpix P340 and a Canon PowerShot S110 both say 1/1.7" sensor. That is 0.58 inches, but it means 7.6 mm wide... about 0.3 inch.
This is easily verified by the published crop factor.
Coolpix P340 says lens is "5.1-25.5 mm (angle of view equivalent to that of 24-120 mm lens in 35mm [135] format)"
Therefore 24/5.1 is crop factor 4.7
Wikipedia 1/1.7" diagonal says 9.5mm. 35mm film diagonal is 43.26 mm.
43.26 / 9.5 = 4.55 crop.
That as close as the details computed.
Widths of 36 / 6.4 is 5.625, which is closer, but crop normally uses the diagonal, because the frames are 4:3 and 3:2. Not same shape, and we are talking about equivalent field of view.
The Fuji HS25 says lens is
"f=4.2–126.0 mm, equivalent to 24–720 mm on a 35 mm camera"
So that is crop 24/4.2 = 5.71, so we could compute the sensor width (from 35mm film) as 36mm / 5.71 = 6.3 mm.
We only know rounded nominal data, but this is pretty close.
But there is no way to use 1/2" for anything (other than to look it up in the Wikipedia table). It is a meaningless number, a false way to represent digital sensors.
It makes no sense, but they all do it. Probably because 1/2" sounds better than 6.4mm width or 9.5mm diagonal.
We could not care less now about old TV camera glass video tubes,
but computing crop factor and magnification still seems important.
We need exact sensor dimensions for that.
Thankfully, the larger cameras do this.