Focal length – lens for 1/2 "sensors, mounted on a 1/3" sensor

https://en.wikipedia.org/wiki/Image_sensor_format#Table_of_sensor_formats_and_sizes provides a table to determine the approximate sensor size from the descriptions "1 / x inch". It may not be accurate because some sensors may all use the same description. Should be ballpark, close enough.

Crop Factor is (43.266 / diagonal) The 43.266mm is the 35mm film diagonal used as the default reference.

My website has some crop factor calculator
https://www.scantips.com/lights/cropfactor.html#crop doing it all.

For example, a 1 / 2.3 "sensor has about 5.65 times the crop factor.
A smaller 1/3 "sensor has about 7.2 times the crop factor.
These cut factors are standard for 35 mm films.

If you need to consider these two sensors in this case, the relative crop factor of the smaller sensor (larger crop factor) is 7.2 / 5.65 = 1.27x (relative to this larger sensor instead of 35mm film). This is also the inverse ratio of the equivalent focal length (to get the same field of view). This larger sensor requires a 1.27x longer focal length than the smaller one. Or the other way around.