Wheel axle thread size What size nut does it take to fit the rear wheel with a nexus Shimano rear axle? I measured the axle size and I'm getting 9.2mm. or .360 in.
Most likely you need:
3/8" diameter
26 tpi (thread per inch)

On the website below there is a list off all Shimano gear hubs which use this size nut:
https://www.sjscycles.co.uk/hub-spares/shimano-nexus-brim40-cap-nut-38-inch/

Please check if your hub is listed to ensure compatibility.

Source: https://forum.cyclinguk.org/viewtopic.php?t=98948