are sized by gauge/gage, the higher the number, the smaller the size.** Is there a formula to determine the gauge or is gauge measure an arbitrary standard in each case ?**

Dunno about the other two, but **shotgun gauge = number of lead balls the diameter of the bore it takes to make a pound**, i.e., a lead ball the same diameter as a 16-gauge shotgun’s barrel weighs one ounce.

Here’s a quote from my McMaster-Carr catalog.

“Many people are familiar with the term ‘gauge’ as used in describing wire diameters and metal thicknesses. Fewer people are aware that 8-gauge sheet steel, 8-gauge stainless steel, the diameter of 8-gauge steel wire and the diameter of 8-gauge copper wire all represent different sizes. In fact, these and a few other materials have different specifications for a given gauge, as shown below”

Take 8 gauge for example:

US Standard (uncoated sheet steel, iron plate and wrought iron) 0.1719 inch

Manufacturers’ Standard (Tin Plate and Stainless steel) 0.1644 inch

Washburn & Moen (Steel wire) 0.1620 inch

American Standard (Wire w/o insulation as well as sheet thickness, use for copper, aluminum and brass) 0.12849 inch

The smaller the (gauge) number the thicker the material. But no consistancy between materials.

Drill bits are measures by various methods:

Fractions, Letter size, Wire size, not to mention Metric.

A number 8 wire size drill bit is 0.1990 inch diameter.

That’s why they publish tables!