Wire Resistance Calculator for Copper and Aluminum Conductors

How do you calculate wire resistance?

Multiply the resistivity of the metal by the conductor length and divide by its cross-section, then correct for temperature: R = ρ20 × L / A × [1 + α20 × (T − 20)].

The calculator and both tables use these formulas:

R_T = ρ20 × (k × L) / A × [1 + α20 × (T − 20)]
Copper, annealed (100 % IACS): ρ20 = 0.017241 Ω·mm²/m (= 1/58), α20 = 0.00393 /°C
Aluminum, hard-drawn EC grade (61.0 % IACS): ρ20 = 0.028264 Ω·mm²/m, α20 = 0.00403 /°C
L = route length in m (1 ft = 0.3048 m); k = 1 for one conductor, 2 for go-and-return
A = cross-section in mm²; from AWG: A = π/4 × (25.4 × 0.005 × 92^((36 − n)/39))²; from kcmil: A = 0.506707479 × kcmil
Ω/km = ρ20 × 1000 / A × [1 + α20 × (T − 20)]; Ω/1000 ft = Ω/km × 0.3048

Here ρ20 is the resistivity at 20 °C, α20 is the temperature coefficient referred to 20 °C, and T is the conductor temperature in °C. For 1/0, 2/0, 3/0 and 4/0, the gauge number n is 0, −1, −2 and −3.

The copper constants are the International Annealed Copper Standard (IACS), which the IEC adopted in 1913 and publishes as IEC 60028, International standard of resistance for copper. The aluminum constants are those of hard-drawn EC aluminum, which has 61.0 % of the conductivity of annealed copper.

The figure below shows each symbol in a circuit with a supply, a load and the two conductors between them.

The four worked examples below show intermediate values rounded to four significant figures. The calculator keeps full precision, so recalculating from the rounded values can change the last digit.

Example 1: 2.5 mm² copper, 50 m go-and-return at 70 °C

1. Length counted: k × L = 2 × 50 m = 100 m.
2. Resistance at 20 °C: R20 = 0.017241 × 100 / 2.5 = 0.68964 Ω.
3. Temperature factor: 1 + 0.00393 × (70 − 20) = 1.1965.
4. Result: R70 = 0.68964 × 1.1965 = 0.8252 Ω for the loop, or 8.252 Ω/km per conductor.
5. At 16 A, the voltage across the loop is V = I × R = 16 × 0.8252 = 13.20 V, and the conductors dissipate I² × R = 211.2 W.

Example 2: 12 AWG copper, 100 ft round trip at 75 °C

1. Cross-section: 12 AWG = 3.309 mm².
2. Length counted: 2 × 100 ft = 200 ft = 60.96 m.
3. Resistance at 20 °C: R20 = 0.017241 × 60.96 / 3.309 = 0.3176 Ω.
4. Temperature factor: 1 + 0.00393 × (75 − 20) = 1.21615.
5. Result: R75 = 0.3863 Ω for the loop. Per conductor, that is 6.337 Ω/km, or 1.932 Ω/1000 ft (1.588 Ω/1000 ft at 20 °C).

Example 3: 2 AWG aluminum, 500 ft at 90 °C

1. Cross-section: 2 AWG = 33.63 mm².
2. Length counted: one conductor, k = 1, so L = 500 × 0.3048 = 152.4 m.
3. Resistance at 20 °C: R20 = 0.028264 × 152.4 / 33.63 = 0.1281 Ω.
4. Temperature factor: 1 + 0.00403 × (90 − 20) = 1.2821.
5. Result: R90 = 0.1642 Ω, which is 1.078 Ω/km or 0.3284 Ω/1000 ft.

Example 4: correcting a 20 °C table value to 90 °C

1. Table value: 16 mm² copper has 1.078 Ω/km at 20 °C, or 1.0776 Ω/km before rounding; see the 16 mm² row.
2. Temperature factor: 1 + 0.00393 × (90 − 20) = 1.2751.
3. Result: 1.0776 Ω/km × 1.2751 = 1.374 Ω/km at 90 °C.
4. The inferred-zero form gives the same result: 1.0776 Ω/km × (234.5 + 90)/(234.5 + 20) = 1.0776 × 1.27505, again 1.374 Ω/km. The section on why published coefficients differ explains this form.

Sources: resistivity 0.017241 Ω·mm²/m at 20 °C and α20 = 0.00393 /°C, NBS Handbook 100 (1966), section 1.2 a–b, and appendix 5 (text of the IEC “International Standard of Resistance for Copper”); AWG geometry, the same handbook, section 2.2; aluminum constants, NBS Handbook 109 (1972), table 1; worked examples calculated.

How does temperature change conductor resistance?

Resistance rises almost linearly with conductor temperature: from 20 °C, copper gains 0.393 % per °C and hard-drawn aluminum 0.403 % per °C. At 90 °C, copper has 1.2751 times and aluminum 1.2821 times its 20 °C resistance.

Multiply a 20 °C value by these factors to get the resistance at another conductor temperature:

Enter the conductor temperature, not the air temperature. A cable carrying its full load runs close to the maximum conductor temperature of its insulation, which the cable datasheet gives. Before ordering, ask our engineers to confirm the maximum conductor temperature of the cable you are quoting.

The linear rule holds well over the calculator’s range. NBS Handbook 100 states that the IEC coefficient for copper rests on NBS measurements from 10 to 100 °C. It also cites data showing copper resistance linear to about 500 °C, and its table 11 lists copper resistance with this coefficient up to 200 °C. NBS Handbook 109 tabulates aluminum up to 100 °C; above that, the calculator applies the same linear rule.

Why do published temperature coefficients differ?

Because the coefficient depends on the reference temperature and on the conductivity of the metal. For annealed copper, NBS Handbook 100 table 3 gives 0.00427 at 0 °C, 0.00393 at 20 °C and 0.00385 at 25 °C. For aluminum at 20 °C, NBS Handbook 109 table 1 gives 0.00408 for annealed EC-0, 0.00403 for hard-drawn EC-H19 and 0.00347 for alloy 6201-T81.

The numbers 234.5 and 228 in many formulas express the same rule in another form. Each is the inferred zero-resistance temperature, in degrees below 0 °C: K = 1/α20 − 20. For copper, 1/0.00393 − 20 = 234.45, which HB100 table 3 prints as 234.5. For aluminum, K = 228.1.

The form R_T = R20 × (K + T)/(K + 20) gives the same result as the α20 form. Use a 20 °C coefficient with a 20 °C resistance, and never apply a 0 °C coefficient to a 20 °C value.

Sources: NBS Handbook 100 (1966), section 1.2 b, table 3 and table 11; NBS Handbook 109 (1972), table 1; temperature factors and K values calculated.

Should you count the cable length once or twice?

Count it twice for a two-wire circuit: current flows out on one conductor and back on the other, so the loop resistance is the resistance of twice the route length.

Choose “1 conductor” for the resistance of one core, for example to compare with a datasheet or a per-km value. Choose “2 conductors (go-and-return)” for the loop of a DC or single-phase two-wire circuit. If a protective conductor forms part of a loop, calculate it separately with its own size.

In the figure above, k counts the conductors in the loop: k = 1 for the go conductor only, and k = 2 for go and return. Three-phase circuits and percentage limits are outside this calculator; see what this calculator does not cover.

Why is a stranded conductor’s resistance higher than the calculated value?

Because the strands are twisted, each wire is slightly longer than the cable, and real conductors carry manufacturing tolerances. The calculator gives the resistance of a solid round conductor of exactly the entered area.

NBS Handbook 100 quantifies the lay effect. In its tables for concentric-lay stranded copper, resistance and mass are 2 % greater than for a solid rod, for sizes up to 2,000,000 cmil (about 1,013 mm²). Above that size, the increment is 3–5 %, following the ASTM conductor committee. For 2.5 mm² copper at 20 °C, that gives 6.896 × 1.02 = 7.034 Ω/km.

Metric conductors to IEC 60228, Conductors of insulated cables, are specified by a maximum resistance at 20 °C for each size and class. That maximum, on the cable datasheet, is the value to compare, not the calculated one.

For the choice of construction, see solid, stranded and fine-stranded copper. For the area side of the same question, see stranded and solid conductor areas.

Before ordering, ask our engineers to confirm the maximum conductor resistance at 20 °C of the cable you are quoting.

Sources: lay increment, NBS Handbook 100 (1966), explanation of tables 17 and 18 (p. 12) and table 18, note 2; IEC 60228:2023; example calculated.

How much higher is aluminum’s resistance than copper’s?

About 1.64 times: hard-drawn EC aluminum has 61.0 % of the conductivity of annealed copper, so a conductor of the same size has 0.028264 / 0.017241 = 1.639 times the resistance.

The gauge or cross-section stays the same for both metals; only the resistance changes. To reach the same resistance, an aluminum conductor therefore needs a larger cross-section. For the other differences between the two metals, see aluminum vs copper conductors.

Annealed EC-0 aluminum reaches 61.8 % IACS. The calculator uses the hard-drawn value, 61.0 % IACS.

Before ordering an aluminum conductor in place of copper, ask our engineers to confirm the conductor the circuit needs.

Sources: NBS Handbook 109 (1972), introduction and table 1; NBS Handbook 100 (1966), section 1.2; ratio calculated.

Is AC resistance higher than DC resistance?

Yes, for large conductors. At 50 or 60 Hz, skin effect pushes current toward the conductor surface, and proximity effect crowds it under the influence of neighboring conductors. Both raise the effective resistance.

For small conductors the difference is negligible, and this calculator gives DC resistance only. A common way to write the AC value is R_ac = R_T × (1 + y_s + y_p), where y_s and y_p are the skin and proximity terms. Those terms depend on conductor size, construction, spacing and frequency, so the calculator does not estimate them.

Before ordering large conductors for an AC circuit, ask our engineers to confirm the AC resistance at the operating frequency and temperature.

Sources: Siechem, “Conductor resistance” (technical note, PDF).

What does this calculator not cover?

It calculates the DC resistance of copper and aluminum conductors only. It does not give current rating, conductor temperature from current, insulation data or AC impedance.

The temperature you enter depends on the load current and on the installation. For DLO cables, the DLO cable ampacity chart lists the allowed currents.

The optional current input gives only V = I × R across the conductors, in DC. A voltage drop calculation for an AC circuit, with reactance, power factor and percentage limits, is not covered.

The calculator also has these limits:

• Temperature. It accepts −40 to 200 °C. Outside that range, or with a value typed in °F or K, it declines and says why.
• Size. It accepts 0.01–5,000 mm², 40 AWG to 4/0 AWG, and kcmil up to 2000 kcmil. Above 4/0, enter the size in kcmil.
• Length. It accepts up to 100 km (328,084 ft).
• Materials. It covers plain annealed copper and hard-drawn EC aluminum only. For tinned copper, copper alloys and copper-clad conductors, see the last question in the FAQ.
• Conductor shape. The result is for a solid round conductor; see why stranded conductors read higher.

Related tools and guides

These pages cover the topics next to this calculator:

• All cable tools
• AWG to mm² converter, for the cross-section of any gauge from 40 AWG to 2000 kcmil
• Copper conductors: bare, tinned and stranded
• Aluminum conductors
• Types of electrical cables, and how they are classified
• RS-485 data pairs: why gauge sets the DC resistance

Frequently asked questions

Sources: values calculated with the constants of NBS Handbook 100 (1966), section 1.2 and table 3, and NBS Handbook 109 (1972), table 1.

What should you do next?

Enter the conductor temperature rather than the air temperature, and count the length twice for a two-wire circuit. Before you accept a cable, compare the maximum conductor resistance on its datasheet, not the calculated value. On the order, state the size in both mm² and AWG. When you are ready, send the size, the resistance you need, the number of cores and the length to our engineers through the contact page.