Video sensor size measurement originates from the first tube cameras where the size designation would have related to the outside diameter of the glass tube. The area of the face of the tube used to create the actual image would have been much smaller, typically about 2/3rds of the tubes outside diameter. So a 1″ tube would give a 2/3″ diameter active area, within which you would have a 4:3 frame with a 16mm diagonal.
An old 2/3″ Tube camera would have had a 4:3 active area of about 8.8mm x 6.6mm giving an 11mm diagonal. This 4:3 11mm diagonal is the size now used to denote a modern 2/3″ sensor. A 1/2″ sensor has a 8mm diagonal and a 1″ sensor a 16mm diagonal.
Yes, it’s confusing, but the same 2/3″ lenses as designed for tube cameras in the 1950’s can still be used today on a modern 2/3″ video camera and will give the same field of view today as they did back then. So the sizes have stuck, even though they have little relationship with the physical size of a modern sensor. A modern 2/3″ sensor is nowhere near 2/3 of an inch across the diagonal.
This is why some manufacturers are now using the term “1 inch type”, as this is the active area that would be the equivalent to the active area of an old 1″ diameter Vidicon/Saticon/Plumbicon Tube from the 1950’s.
1/3″ = 6mm diag.
1/2″ = 8mm
2/3″ = 11mm
1″ = 16mm
4/3″ = 22mm
A camera with a Super35mm sensor would be the equivalent of approx 35-40mm
APS-C would be approx 30mm