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Here's the formula for converting American (or Brown and Sharpe) wire gauge to millimeters:

dn = 0.005 mm x 25.4 x 92 36-n/39

With this formula, you can convert a wire gauge size to the diameter of the wire in millimeters. The dn is the diameter of the wire in millimeters, as you might have guessed, and the n in the exponent is the gauge of the wire you wish to find the diameter of.

Wikipedia has a fine article on this. They have the formula for converting wire gauge to diameter as well as one for calculating cross-sectional area. They also explain where the formula comes from, if you're interested. The formula for converting from diameter to the wire gauge, the inverse of this formula, is also listed, as is a chart. A link is provided for you convenience. Another link is also provided to an online calculator that will let you just put in a diameter or a wire gauge and will do all the work for you. (Note that this calculator works in inches and not millimeters, so you'll have to make a conversion.)

Improved Answer By Sandip Vikma :"Above original formula is difficult to calculate. So, you may use bellow derived formula to convert Gauge into MM".

dn = 0.127 x 92 [0.9230769-0.025641026n]

Where,

dn = Thickness in MM.

n = Thickness in Gauge.

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