Wire size, length vs resistance

Here's an easy way to calculate approximate wire diameter and resistance if you don't have a wire gauge table handy (but are familiar with decibels):

Wire gauge calculations and decibel calculations are closely related, because both are based on logarithms. If you are familiar with a few "rules of thumb" for decibels (such as 20dB being a ratio of 10 in voltage and 100 in power), you can calculate approximate wire characteristics in your head.

Start with 10 gauge wire. It is approximately 0.1 inch in diameter and has a resistance of about 1 ohm per thousand feet - nice round numbers, easy to remember. From there, wire diameter ratios for other gauges work like voltage ratios expressed in decibels. For example, 20 dB is a voltage ratio of 10, and changing wire gauge by 20 numbers should change the diameter by that same factor of 10. So going from AWG 10 to AWG 30 should reduce the diameter by a factor of 10, which would be 0.01 inches. The exact diameter of AWG 30 from a wire table is 0.01002 inches, so our quick calculation was pretty close. If you also remember the voltage ratios for 3dB, 6dB and 10 dB, you can work your way up and down the wire gauges.

Wire resistance works like decibel power ratios, so 20 gauges is like 20dB, which is a power ratio of 100. Thus 30 gauge wire would calculate to about 100 ohms per thousand feet. The wire table says 103.2, so we are again pretty close, probably closer than the manufacturing tolerance of most wire.

A more practical example would be 16 gauge wire. Six dB is a factor of two in voltage, and a factor of four in power. Again starting from AWG 10, we find that AWG 16 is about 0.050" in diameter, and has a resistance of about 4 ohms per thousand feet. Another 6dB takes you to AWG 22, 6dB more to AWG 28, and so on.

Solid wire is easier to wrap and insert in solder tabs, but stranded is more durable from flexing and better for grounding tuning caps and antennas.

Thanks for this info Cliff. I have printed it off for keeping.
Here another odd question ..When replacing hook-up wire in the old radios do you prefer soild or stranded.
I like solid wire around 22ga because it is so much easier to bend and hook on a terminal. Your thoughts.

American Wire Gages--(AWG)--Sizes--and--Resistances--
1-AWG--wire--size--(solid)--
2-Area-CM*-
3-Resistance--per-1000--ft--(ohms)--@--20--C--
4-Diameter (inches)--
5-Maximum--current**(amperes)--

1-AWG---2-CM----------3-R-------4-D-in---5-A
----------------------------------------------
0000---211600---------0.049-----0.46-----380--
000----167810---------0.0618----0.40965--328--
00-----133080---------0.078-----0.3648---283--
0------105530---------0.0983----0.32485--245--
1-------83694---------0.124-----0.2893---211--
2-------66373---------0.1563----0.25763--181--
3-------52634---------0.197-----0.22942--158--
4-------41742---------0.2485----0.20431--135--
5-------33102---------0.3133----0.18194--118--
6-------26250---------0.3951----0.16202--101--
7-------20816---------0.4982----0.14428---89--
8-------16509---------0.6282----0.12849---73--
9-------13094---------0.7921----0.11443---64--
10------10381---------0.9989----0.10189---55--
11-------8234---------1.26------0.09074---47--
12-------6529---------1.588-----0.0808----41--
13-------5178.4-------2.003-----0.07196---35--
14-------4106.8-------2.525-----0.06408---32--
15-------3256.7-------3.184-----0.05707---28--
16-------2582.9-------4.016-----0.05082---22--
17-------2048.2-------5.064-----0.04526---19--
18-------1624.3-------6.385-----0.0403----16--
19-------1288.1-------8.051-----0.03589---14--
20-------1021.5------10.15------0.03196---11--
21--------810.1------12.8-------0.02846----9--
22--------642.4------16.14------0.02535----7--
23--------509.45-----20.36------0.02257----4.7--
24--------404.01-----25.67------0.0201-----3.5--
25--------320.4------32.37------0.0179-----2.7--
26--------254.1------40.81------0.01594----2.2--
27--------201.5------51.47------0.0142-----1.7--
28--------159.79-----64.9-------0.01264----1.4--
29--------126.72-----81.83------0.01126----1.2--
30--------100.5-----103.2-------0.01002----0.86--
31---------79.7-----130.1-------0.00893----0.7--
32---------63.21----164.1-------0.00795----0.53--
33---------50.13----206.9-------0.00708----0.43--
34---------39.75----260.9-------0.0063-----0.33--
35---------31.52----329---------0.00561----0.27--
36---------25-------414.8-------0.005------0.21--
37---------19.83----523.1-------0.00445----0.17--
38---------15.72----659.6-------0.00396----0.13--
39---------12.47----831.8-------0.00353----0.11--
40----------9.89----1049--------0.00314----0.09--

Wire has a conductive property that depends on the material used such as copper, aluminum, gold or silver.
Wire also has a property called resistance, and that depends on its size and/or length and even temperature.

Some of the rules of a conductor states:
Comparing the usefulness of electrical conductors is by using specific resistance.
Resistance of a material is measured by a specific resistance and that is a cubic centimeter of the material at a temperature of 68 degrees F.

That standard measured is :
copper=(.0000017 ohm)
silver=(.00000163 ohm)
aluminum=(.00000283 ohm)

The DC resistance of a conductor varies inversely with its cross sectional area.
The greater the cross sectional area of a conductor the less resistance.
Area = PI X R squared
So doubling (2 X) the radius or diameter increases the area 2 times and reduces the resistance to 1/4th.
So tripling (3 X) the radius or diameter increases the area 9 times and reduces the resistance to 1/9th.
1D = R = 100 Ohms
2 x D= 1/4 R 100 ohms X 0.25 = 25 ohms
3 x D= 1/9 R 100 ohms X 0.11 = 11.1 ohms
note: D=diameter,R=resistance
So if a wire (A), is twice the area of another wire(B), its resistance is 1/4 that of (B) if the given length is the same.
---------------------------------------------
The resistance of a wire varies and is Directly proportional to its length.

If wire (A) is twice the length of wire (B) having the same cross-sectional area, then the longer wire (A) will have twice the resistance.
So if wire (A) is 1 foot long and is 5 ohms, and the wire (B) measures 2 foot long, Then (wire B) will have a resistance of 10 Ohms.
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Wire sizes
Remember this the diameter of the wire is expressed in mils and
the cross-sectional area is expressed in circular mils.

Another standard of measure is used for wire is the circular mil. which equals 1/1000 of an inch= .001 inch
The area of a circle which is the area proportional to the square of the diameter, or d squared.
So a round wire that has a diameter of 100 mils has a cross-sectional area of d squared or = 100 X 100 = 10,000 circular mils. So 400 mils = d squared or 400 x 400 = 160,000 circular mils.
This is used to express the cross-sectional area.
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The most common wire gage used is the American Wire Gage.
Its sizes range from Number 36 = 5 mils to 0000 (pronounced 4 aught) which equals 460 mils
Note: there are 39 gage sizes.
Reference material used and paraphrased for clarity was from the book series "Basic Radio by M. Tepper. Copyright September, 1961 by John F. Rider Publisher Inc."
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Here is a great link to finding data on wire sizes.

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