The short answer is – the smaller the number the larger the diameter. 30/3 is a good middle of the road diameter for traditional books. 18/3 is suitable for artist books. At the extreme ends, 10/3 is large enough to show off complicated sewing patterns (think Coptic) and 60/3 is perfect for books with many pages of thin paper.
Since thread is a soft material, it’s impossible to accurately measure the diameter. The diameter is relative represented by a number based on the weight of a specific length of fibre. For example, in the 18/3 linen thread, it takes eighteen 300 yard lengths of fibre to equal 1 pound. In comparison, the 10/3 linen thread only takes ten lengths…therefore it must be heavier and thus thicker. This is why the diameter numbers run in the reverse direction.
The “3” in 18/3 represents how many of these size 18 fibres are spun together to make the thread. A 18/2 thread will be 2/3 the diameter of the 18/3. Keep an eye on this second number when comparing threads.
Now to complicate things further…in the above example the diameter is 18 NeL (linen count or Lea). There is a common metric measurement of Nm with is the same principle but based on 1000m per 1 kg. Often you will see this being used by European sources - 1 NeL = 1.6535 Nm.
Just to make your head spin, there are also other units used – tex (grams per km), denier (grams per 9000m), NeS (wool), NeC (English cotton count), Gunze (Japanese), # (cord - pounds), etc.
A couple a final notes…since the source fibres have different weight, you can’t assume that the actual diameter of a cotton and linen thread will be the same, even if they both have the same diameter number and fibre count. Also, thread also comes with a S or Z spin direction, so pay attention when you are trying to roll the end for needle threading as you may end up unravelling the thread.