# Re: Wire gauge calc?

```Tesla List wrote:

> Were did this definition of the exact diameter come from? It must also
> include a temperature at which it is true. It is interesting that many
> charts have different values for a given gauge.

>From my other post some time ago:

I plotted some gauge-diameter pairs with logarithmic scale for the
diameter, and obtained a straight line.
Such a line must correspond to a relation Ln(d)=a*g+b (d=diameter;
g=gauge).
If I pick two pairs, and solve the system of two linear equations:
Ln(d1)=a*g1+b
Ln(d2)=a*g2+b
The solution is:
a=-Ln(d1/d2)/(g2-g1)
b=(g2*ln(d1)-g1*ln(d2))/(g2-g1)

The scale is defined so 0000 (gauge=-3 in the formula) has a
diameter of 460 mils and 36 has a diameter of 5 mils.
Using the definition above, the exact expressions for the two
coefficients, and so the "official formula" would be:

a = -Ln(460/5)/39 = 0.115943296847
b = (36*ln(460)+3*ln(5))/39 = 5.78339659892
and diameter in mils = exp(a*gauge+b)

The different tables are a bit different because many old tables
were computed by hand, with low precision and different rounding
criteria. The values are for 20 degrees Celsius (68 F).

Antonio Carlos M. de Queiroz

```