Convert Ohms/1000 ft to Ohms/km Instantly – Fast Resistance per Length Calculator

Quick, precise conversions from ohms per 1000 feet to ohms per kilometer for engineering calculations.

This technical guide provides formulas, examples, tables, and normative references for accurate resistance per length.

Fundamental relationships and unit conversion for resistance per length

Resistance of a uniform conductor scales linearly with length and inversely with cross-sectional area. Unit conversion between non-metric and metric lengths is essential for international engineering practice.

Basic physical law

Ohm’s law for a uniform conductor combined with material resistivity gives the primary relationship:

• R: resistance (ohms, Ω)
• ρ: electrical resistivity of the conductor material (ohm·metre, Ω·m)
• L: conductor length (metres, m)
• A: cross-sectional area (square metres, m²)

For cross-sections commonly specified in square millimetres (mm²), convert A to m² by A[m²] = A[mm²] × 1e-6.

Conversion between resistance per 1000 ft and resistance per km

Define R_1000ft as resistance measured per 1000 feet, and R_km as resistance per 1 kilometre. The unit-length conversion factor derives from the length ratio:

R_km = R_1000ft × (1000 m / 304.8 m)

Numerical factor:

1000 m / 304.8 m ≈ 3.280839895

Therefore:

R_km ≈ R_1000ft × 3.28084

Conversely:

R_1000ft ≈ R_km / 3.28084

Material constants and typical values

At 20 °C typical resistivity values:

• Copper (ρ_Cu @20 °C) ≈ 1.724 × 10^-8 Ω·m
• Aluminium (ρ_Al @20 °C) ≈ 2.826 × 10^-8 Ω·m

Using these constants, resistance per kilometre for a conductor with cross-section A in mm² is convenient to express as:

R_km,Cu ≈ 17.241 / A[mm²] (Ω/km at 20 °C)

R_km,Al ≈ 28.260 / A[mm²] (Ω/km at 20 °C)

Derivation (compact):

R = ρ · L / A = ρ · 1000 m / (A·1e-6 m²) = (ρ·1e9)/A[mm²]

For copper ρ·1e9 ≈ 17.241, for aluminium ρ·1e9 ≈ 28.260.

Common conductor resistance tables (copper, at 20 °C)

Notes: Resistance (Ω/1000 ft) column equals Ω/km divided by 3.28084 (unit-length conversion). Values rounded to two decimal places for readability. Temperature coefficient not applied here; values are at 20 °C baseline.

AWG to metric cross-section and resistance (copper)

Applying the formulas: calculation method and variable clarification

When converting from a resistance specified per 1000 ft to per km, apply the linear length scaling: the resistance per unit length scales directly with the length ratio.

Algorithm (step-by-step):

1. Identify given value R_given and its unit (Ω per 1000 ft, or Ω per km).
2. If converting 1000 ft → km, multiply by 1000 m / 304.8 m ≈ 3.28084.
3. If converting km → 1000 ft, divide by 3.28084.
4. For temperature-corrected resistance, apply the temperature coefficient: R(T) = R(20 °C) × [1 + α × (T - 20 °C)], where α is typically 0.00393 °C^-1 for copper.

Temperature correction formula:

R(T) = R_ref × (1 + α × (T - T_ref))

• R(T): resistance at temperature T (Ω)
• R_ref: reference resistance at temperature T_ref (Ω), typically 20 °C
• α: temperature coefficient (per °C). For copper α ≈ 0.00393 /°C at 20 °C.

Worked example 1 — Direct conversion plus voltage drop calculation

Problem statement

A power distribution cable has a manufacturer-specified resistance of 0.321 Ω per 1000 ft (copper, 20 °C). Determine:

• Resistance in Ω/km.
• Voltage drop on a one-way run of 2.5 km carrying 120 A DC.
• Power loss in the conductor for that run.

Solution step-by-step

Step 1 — Convert resistance per length:

R_km = 0.321 Ω/1000 ft × 3.28084 = 1.053 (approximately) Ω/km

R_total = R_km × L = 1.053 Ω/km × 2.5 km = 2.6325 Ω

Step 3 — Voltage drop (DC):

Step 4 — Conductor power loss:

P_loss = I² × R_total = (120 A)² × 2.6325 Ω = 14400 × 2.6325 = 37,890 W ≈ 37.9 kW

Comments:

• This example demonstrates that a seemingly small Ω/1000 ft value can produce large drops and losses over multi-kilometre runs at high current.
• For alternating current (AC) circuits, include reactance and skin/stranding effects; for long runs use cable manufacturer data and standards.

Worked example 2 — Selecting conductor size from required resistance per km

Problem statement

Design requirement: maximum allowable conductor resistance not to exceed 0.2 Ω/km (copper) for a feeder. Determine the minimum cross-sectional area in mm² and equivalent resistance per 1000 ft.

Solution step-by-step

Use R_km ≈ 17.241 / A[mm²]. Solve for A:

A[mm²] = 17.241 / R_km

Substitute R_km = 0.2 Ω/km:

A = 17.241 / 0.2 = 86.205 mm²

Choose the next commercially available conductor size greater than 86.205 mm². Typical close standard sizes: 95 mm².

Compute resistance for 95 mm²:

R_km = 17.241 / 95 = 0.1815 Ω/km

Convert to Ω/1000 ft:

R_1000ft = 0.1815 / 3.28084 ≈ 0.0553 Ω/1000 ft

Summary:

• Minimum theoretical area: 86.2 mm².
• Selected standard size: 95 mm² (R ≈ 0.1815 Ω/km, ≈ 0.055 Ω/1000 ft).

Practical considerations and corrections

Temperature effects

All tabulated resistances assume 20 °C. For elevated ambient or conductor operating temperature, apply the temperature coefficient. Example for copper:

R(75 °C) = R(20 °C) × [1 + 0.00393 × (75 - 20)] = R(20 °C) × [1 + 0.00393 × 55] ≈ R(20 °C) × 1.216

AC effects and conductor construction

• Skin effect increases effective resistance with frequency for solid conductors; stranded/rope-lay or multi-strand designs reduce AC resistance increase.
• Proximity effect and harmonic content in power systems further modify impedance; use manufacturer datasheets or compute using electromagnetic models for precision.
• IEC and IEEE standards describe measurement methods and correction procedures.

Measurement best practice

1. Use four-point (Kelvin) resistance measurement for low resistances to avoid lead resistance errors.
2. Record ambient and conductor temperature; correct to reference temperature (usually 20 °C) using the temperature coefficient.
3. For field measurements over long lengths, use calibrated test instruments and consider guard connections for very low resistances.

Calculator logic — building an instant conversion tool

To implement an instant converter between Ω/1000 ft and Ω/km, the minimal logic is:

1. Input: numeric value and input unit (Ω/1000 ft or Ω/km).
2. Apply conversion factor: multiply by 3.28084 to go from Ω/1000 ft to Ω/km, or divide by 3.28084 to go back.
3. Optional: accept cross-sectional area and material to compute resistance from scratch via R = (ρ·1e9)/A[mm²].
4. Optional: temperature input to perform correction with R(T) = R(20 °C) × [1 + α × (T - 20 °C)].

Validation tests for the tool should include:

• Round-trip conversion (A → B → A) to verify numerical stability.
• Comparison to tabulated manufacturer values for standard conductors.
• Edge-case handling for zero or negative inputs with clear error messages.

Standards, normative references, and authoritative resources

Key standards and authoritative references for conductor resistance, definitions, and measurement methods:

• ISO — International Organization for Standardization (general referencing site)
• IEC 60228 — Conductors of insulated cables (cross-sectional area definitions) (International Electrotechnical Commission)
• IEEE Standards — e.g., IEEE Std 141 (Green Book) for grounding and conductor considerations
• NIST — National Institute of Standards and Technology (definitive constants and unit conversions, including foot-to-metre exact definition)
• CENELEC / EN standards — European norms for cables and electrical conductors
• Material datasheets from major cable manufacturers (e.g., Prysmian, Nexans) for practical AC resistance and stranding corrections

Important citations (examples):

• IEC 60228: Conductors of insulated cables — definitions and standard cross-sections.
• NIST Special Publication: units and constants — exact conversion 1 ft = 0.3048 m.
• IEEE Green Book (IEEE Std 142) — grounding, conductor selection and effects on impedance.

Checklist for engineers converting and validating resistance per length

• Confirm reference temperature for quoted resistances.
• Identify whether the quoted value is per 1000 ft, per 100 m, per km, per conductor run, or per phase.
• Use exact foot-to-metre conversion: 1 ft = 0.3048 m (international foot).
• Apply temperature correction when operating temperature differs from reference.
• For AC circuits, examine frequency-dependent effects and consult manufacturer AC resistance tables.
• When in doubt, measure using four-wire methods and correct to reference conditions.

Final technical notes and recommended practices

When specifying cable resistance for procurement or calculations, prefer metric units (Ω/km or mΩ/m) for clarity in international projects. Provide the temperature at which resistance is quoted, conductor material, stranding type, and standard reference (IEC or ASTM) to ensure unambiguous interpretation.

For automated calculators or spreadsheets document the exact conversion factors used and include a visible check indicating whether temperature correction has been applied.

Quick reference formulas summary

Direct unit conversions:

R_km = R_1000ft × 3.28084

R_1000ft = R_km / 3.28084

From cross-section and resistivity (20 °C):

R_km,Cu ≈ 17.241 / A[mm²]

R_km,Al ≈ 28.260 / A[mm²]

Temperature correction:

References and external authority links

• IEC 60228 — Conductors of insulated cables: https://www.iec.ch (search IEC 60228)
• NIST Reference on Units and Constants — foot to metre exact relation: https://www.nist.gov
• IEEE Standards — https://standards.ieee.org (search specific standards such as IEEE Std 141)
• Manufacturer technical pages (examples): Prysmian cables technical library, Nexans cable datasheets.

If you need, I can produce a compact conversion widget (spreadsheet logic or pseudo-implementation) or generate downloadable tables formatted for insertion into CAD or calculation templates. Specify preferred output format and I will prepare.