Coaxial Cable Impedance Calculator
Characteristic impedance, capacitance and inductance per metre, velocity factor and delay of a coaxial line, with its cross-section drawn to scale.
Results
The dashed line marks the value you entered.
What this tool does
A coaxial cable's characteristic impedance depends only on the ratio of its two diameters and on the insulation between them — not on its length and not on the copper. The familiar 50 Ω and 75 Ω are a compromise: with air insulation, loss is lowest near 77 Ω and power handling is highest near 30 Ω, and 50 Ω sits in between. Because the impedance follows the logarithm of D/d, a small error in either diameter hardly moves it, which is part of why coax is so forgiving to make.
Formula
Z₀ = (Z_vac ÷ (2π √εᵣ)) × ln(D ÷ d) ≈ (59.96 ÷ √εᵣ) × ln(D ÷ d) · C′ = 2π ε₀ εᵣ ÷ ln(D ÷ d) · L′ = (μ₀ ÷ 2π) ln(D ÷ d)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
di | Inner conductor diameter d | mm |
dd | Dielectric diameter D (inside the shield) | mm |
er | Relative permittivity εr | — |
Z | Characteristic impedance | Ω |
C | Capacitance per metre | pF/m |
L | Inductance per metre | nH/m |
VF | Velocity factor | % |
DL | Delay per metre | ns/m |
RT | Diameter ratio D/d | — |
Worked example
- Inner conductor diameter d0.9 mm
- Dielectric diameter D (inside the shield)2.95 mm
- Relative permittivity εr2.25
- Characteristic impedance47.45 Ω
- Capacitance per metre105.4 pF/m
- Inductance per metre237.4 nH/m
- Velocity factor66.7 %
- Delay per metre5.003 ns/m
- Diameter ratio D/d3.278
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.