There is an unthreaded section at the top of the lug, as well as an unthreaded section at the top of the nut, so I had to device a method to accurately get these measurements.
Here is what I did. First I put the nut on the stud to where the first thread would catch. Then I measured the depth of the hole.
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The first place I can catch a thread is at 13mm.
Then I put the tire on and measured again.
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The depth at .3mm means I have 12.7mm of thread engagement.
Now I need to know what the full thread depth is, so I put a bolt in reverse to where it would catch a thread and measured again from the bottom.
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14.8mm is the total thread depth of the nut.
12.7/14.8 = .858 or about ~%85.