Wire & Cable Formulas
Wire and cable formulas relate conductor gauge to resistance, current capacity, and voltage drop over distance. These calculators help you pick wire that carries current safely without excessive loss. They are vital for power wiring and long cable runs.
Wire & Cable Formula Calculators
- Wire Resistance R = ρ × L / A Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm, Cross-Section Area 0.1 mm² → Resistance = 0.01 mΩ
- AWG to Cross-Section Area A = 0.012668 × 92^((36−AWG)/19.5) Wire Gauge (AWG) 0.025 → A = 53.17
- Cable Voltage Drop Vdrop = 2 × I × R/m × L Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm → Voltage Drop = 0.4 nV
- Maximum Cable Length L = Vdrop / (2 × I × R/m) Max Voltage Drop 0.33 V, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → Max One-Way Length = 825 km
- Skin Effect AC Resistance Rac = Rdc × (1 + (d/(2δ))²) DC Resistance 0.1 mΩ, Wire Diameter 0.1 mm, Skin Depth 0.22 mm → Rac = 0.1052 mΩ
- Coaxial Cable Impedance Z0 = (138/√εr) × log10(D/d) Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Inner Conductor OD 0.22 mm → Outer Conductor ID = 0.2206 mm
- Connector Contact Resistance Rc = ρ / (π × a) Resistivity (Ω·m) 0.025 Ω·m, Contact Spot Radius 1 µm → Contact Resistance = 7.958 kΩ
- Cable Shielding Effectiveness SE = 20 × log10(1 + 2πfµσt²) Frequency 100 kHz, Permeability (H/m) 0.025 H/m, Conductivity (S/m) 0.055 S/m, Shield Thickness 0.1 mm → SE = 7.5 × 10⁻⁵ dB
- AWG Wire Ampacity Estimate I_max ≈ 10^((40 − AWG)/15) Wire Gauge (AWG) 0.025 → I_max ≈ 10^((40 − AWG)/15) = 462.4
- Coaxial Cable Loss α ≈ R / (2 × Z0) dB/m Resistance per Meter 0.055, Characteristic Impedance 1 Ω → Loss per Meter = 0.0275
- Coax Electrical vs Physical Length l_elec = l_phys × VF Physical Length 2.2 mm, Velocity Factor 2.5 % → Electrical Length = 0.055 mm
Worked result for every Wire & Cable formula
| Formula | Expression | Worked result |
|---|---|---|
| Wire Resistance | R = ρ × L / A | Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm, Cross-Section Area 0.1 mm² → Resistance = 0.01 mΩ |
| AWG to Cross-Section Area | A = 0.012668 × 92^((36−AWG)/19.5) | Wire Gauge (AWG) 0.025 → A = 53.17 |
| Cable Voltage Drop | Vdrop = 2 × I × R/m × L | Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm → Voltage Drop = 0.4 nV |
| Maximum Cable Length | L = Vdrop / (2 × I × R/m) | Max Voltage Drop 0.33 V, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → Max One-Way Length = 825 km |
| Skin Effect AC Resistance | Rac = Rdc × (1 + (d/(2δ))²) | DC Resistance 0.1 mΩ, Wire Diameter 0.1 mm, Skin Depth 0.22 mm → Rac = 0.1052 mΩ |
| Coaxial Cable Impedance | Z0 = (138/√εr) × log10(D/d) | Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Inner Conductor OD 0.22 mm → Outer Conductor ID = 0.2206 mm |
| Connector Contact Resistance | Rc = ρ / (π × a) | Resistivity (Ω·m) 0.025 Ω·m, Contact Spot Radius 1 µm → Contact Resistance = 7.958 kΩ |
| Cable Shielding Effectiveness | SE = 20 × log10(1 + 2πfµσt²) | Frequency 100 kHz, Permeability (H/m) 0.025 H/m, Conductivity (S/m) 0.055 S/m, Shield Thickness 0.1 mm → SE = 7.5 × 10⁻⁵ dB |
| AWG Wire Ampacity Estimate | I_max ≈ 10^((40 − AWG)/15) | Wire Gauge (AWG) 0.025 → I_max ≈ 10^((40 − AWG)/15) = 462.4 |
| Coaxial Cable Loss | α ≈ R / (2 × Z0) dB/m | Resistance per Meter 0.055, Characteristic Impedance 1 Ω → Loss per Meter = 0.0275 |
| Coax Electrical vs Physical Length | l_elec = l_phys × VF | Physical Length 2.2 mm, Velocity Factor 2.5 % → Electrical Length = 0.055 mm |
Variables used across Wire & Cable formulas
- R — Wire resistance (Ω)
- ρ — Resistivity of the conductor material (Ω·m)
- L — Wire length (m)
- A — Cross-sectional area (m²)
- AWG — American Wire Gauge number (integer, smaller = thicker)
- Vdrop — Total round-trip voltage drop (V)
- I — Load current (A)
- Vdrop_max — Maximum acceptable voltage drop (V)
- R_per_m — Wire resistance per meter (Ω/m)
- Rac — AC resistance at the operating frequency (Ω)
- Rdc — DC resistance of the conductor (Ω)
- d — Wire diameter (m)
- δ — Skin depth at the operating frequency (m)
- Z0 — Characteristic impedance (Ω)
- εr — Relative dielectric constant of the insulating material
- D — Inner diameter of the outer conductor (shield) (mm)
- Rc — Constriction resistance at one contact spot (Ω)
- a — Effective radius of the contact spot (m)
- SE — Shielding effectiveness (dB)
- f — Frequency (Hz)
- µ — Permeability of shield material (H/m)
- σ — Conductivity of shield material (S/m)
- t — Shield thickness (m)
- α — Attenuation coefficient (dB/m, approximate)
- Z₀ — Cable characteristic impedance (Ω)
- l_electrical — Equivalent free-space length (m)
- l_physical — Actual cable length (m)
- VF — Velocity factor (0 to 1, dimensionless)
Questions people ask about Wire & Cable
- Maximum length calculator — Maximum Cable Length
- Resistance skin effect — Skin Effect AC Resistance
- Skin effect resistance equation — Skin Effect AC Resistance
- Calcul attenuation cable coaxial — Coaxial Cable Impedance
Related Formula Categories
Browse the full formulas index for all 32 categories.