Science solutions - Fine-wire diameter formulas

Diameter vs. wire weight

The volume of a length of wire equals:

Where:
V : wire volume [m3, in3]
Ø : wire diameter [mm, in]
L : wire length [m, in]

Calculating the wire diameter of a given measured length of wire with a certain mass is done with

Where:
Ø : wire diameter [mm, in]
m : wire mass [kg, lbs]
ρ : wire density [kg/m3, lbs/in3]
L : wire length [m, in]

Diameter vs. electrical resistance

The resistance of a wire is calculated with

Where
R : electrical resistance [Ω]
ρ : electrical resistivity [Ω·m]
L : wire length [m]
Ø : wire diameter [m]

The resistance per length of wire is:

Calculating the wire diameter of a given measured length of wire with a certain resistivity is done with

Physical properties for common materials

	Density 1)	Melting point	Thermal conductivity 1)	Thermal expansion 2)	Elastic modulus 1)	Shear modulus 1)	Electrical resistivity 1)
Symbol	ρ (rho)		λ (lambda)	α (alpha)	E	G	ρ (rho)
Unit	·10^3 [kg/m^3]	[K]	[W/mK]	·10^-6 [K-1]	·10^9 [Pa]	·10^9 [Pa]	·10^-9 [Ω·m]
Aluminum	2.7	933	237	23.1	70	26	27
Aluminum alloy	2.63 – 2.82	749 – 927	121 – 180	22.0 – 26	79 – 79	26 – 30	50
Copper	8.97	1358	398	16.6	110	48	16.7 – 67.5
Copper alloy	7.47 – 8.94	1128 – 1533	110 – 390	16.3 – 20.2	110 – 120	47	140 – 490
Gold	19.3	1337	315	14.2	83	27	24
Iron	7.86	1811	80	11.8	211	82	98
Steel	6.92 – 9.13	1644 – 1805	11-12	10.0 – 17.3	190 – 210	75 – 80	180
Stainless steel	7.64 – 8.44		7.3 – 26	17.3	195	57 – 97	720 – 765
Lead	11.35	601	35	28.9	16	5.6	210
Lead alloy	7.85 – 11.35	455 – 599	20.2	19.5 – 29.0			150
Molybdenum	10.28	2896	140	4.8	329	126	52
Molybdenum alloy	10.21	2610
Nickel	8.91	1728	90	13.4	210	80	70
Nickel alloy	7.75 – 8.85	1383 – 1727	12.6 – 17.0	0.0 – 14	170 – 200	66	112 – 330
Platinum	21.45	2041	73	8.8	168	61	106
Silver	10.49	1234	427	18.9	83	30	16.1
Titanium	4.51	1941	20	8.6	116	44	430
Titanium alloy	4.43 – 4.70	1822 – 1922		8 – 10	110 – 120	39 – 44
Tungsten	19.29	3695	178	4.5	411	161	55
Zinc	7.14	693	115	30.2	108	43	59
Zinc alloy	6.64 – 7.20	659 – 798	105 – 115	23.3 – 27.4	> 86	34
Ceramic	2.30 – 5.50	4143		0 – 7.5	450
Tungsten carbide		3143	100	3.7	586 – 689	262
ND/SSCD diamond	3.52	3820	900 – 2320	1.3	1050 – 1200	478	10(13)
PCD diamond			500 – 600		827 – 1103

Physical properties for common materials. Source: Wikipedia.com, Efunda.com, CRC handbook of Mechanical Engineering, Element6, Sandvik Hyperion

Notes:
1) T = 293K
2) T = 273-373 K

Quickly convert between units

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