Although there is a worldwide trend to the International System (SI) or Metric measurement, the current practice in wire measurement in the United States is generally the use of the customary English Units. The current practice of the NAtional Bureau of Standards (NBS), the Institute of Electrical and Electronic Engineers (IEEE), and the The American Society of Testing Materials (ASTM) is to reflect American Wire Gauge in parallel with metric units of measurement.
The American Wire Gauge, like some other gauge systems, does generally represent steps in the wire drawing process. In addition to that, the numbers are retrogressive to the wire size  that is, the larger the number the smaller the wire. These gauge sizes are not arbitrary, but are a geometric progression. With the definition of two sizes in the series of gauge sizes, all size related properties of any gauge in the series is defined by that relationship. With AWG 0000 as 0.4600 inch and AWG 36 as 0.0050 and 38 gauge sizes between these two, the ratio of any diameter to the next larger diameter can be determined as follows:

= 

= 1.1229322 
The square of this ratio is: 1.2610
This Square of the ratio between sizes can be used as a means of obtaining the resistance, mass and cross section of any wire size if one is memorized these values for only one size. This conversion number can easily remembered as 1 1/4. 
Therefore:
Knowing 20 AWG has a crosssection of 1020 circular mils tell us 19 AWG will have 1 1/4 x 1020 or approximately 1250 circular mils. If we had memorized the resistance of 20 AWG as 10 ohms/1000 feet, 19 AWG would have less resistance by 10 ÷ 1 1/4 or approximately 8 ohms/1000 feet.
Since the function os geometric, the cube of this 1 1/4 is approximately 2. This allows you to easily calculate the dimensional functions in 3 gauge increments. Every 3 gauge sizes the resistance, mass per unit, and cross section will double or halve.
Then with a 20 AWG Cross section of 1020 circular mils, 17 AWG will be approximately 2040 mils and 23 AWG will be approximately 510 circular mils.
Using this relationship, with the commitment to memory of the crosssectional area, resistance and mass per unit for any one size, you can quickly move to the value for any other wire size.
For diameter calculation, remembering one diameter, the diameter will double or halve every size gauges and for each gauge the next larger gauge diameter is 120% or 1.2 times the smaller gauge. If you remember six contiguous gauges in mils e.g. 39  44 AWG, you would know all diameters by this rule. Actually, if you just remember 39 AWG as 3.5 mils and the spread between these gauges is 0.3 mil except between 39 and 40 where it is 0.4 mil and 23 and 44 is 0.2 mil, you will have quick access to all gauge diameters. 