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Coaxial line impedance calculator

What sets the impedance of coax

Only two things: the ratio of the shield and conductor diameters, and the permittivity of the dielectric. Length has no bearing on characteristic impedance — it decides the loss and the phase shift.

D 8 mmd 2.3 mmε 2.25shielddielectric
D — inner diameter of the shield, d — diameter of the centre conductor, ε — permittivity of the dielectric
Inner shield diameter D (mm)
Centre conductor diameter d (mm)
Insulation material
ε of the insulation
Result
Characteristic impedance Z₀
Critical frequency
Propagation delay
Inductance per metre
Capacitance per metre
Velocity factor vf

📐 The formulas​

Characteristic impedance:

Z₀ = (59.9585 / √ε) × ln(D / d)

Cutoff frequency (the onset of higher-order modes), D and d in millimetres:

Fcr = 190.8538 / (√ε × (D + d))

Per-metre parameters:

v  = c / √ε           propagation velocity
Td = 10⁹ × √ε / c     delay, ns/m
Lp = 10⁹ × Z₀ / v     inductance, nH/m
Cp = 10¹² / (Z₀ × v)  capacitance, pF/m

Symbols:​

  • D — inner diameter of the shield [mm]
  • d — diameter of the centre conductor [mm]
  • ε — permittivity of the dielectric
  • c — the speed of light, 299,792,458 m/s
Where this calculator stops:
  • The formula holds for the TEM mode, that is below the cutoff frequency
  • The centre conductor must be exactly on the axis of the shield
  • Losses in the metal and the dielectric are not included — for those see the coax loss calculator
  • The ε of foamed dielectric depends on how much it is foamed and may differ from the book value

🎯 In practice​

  • Home-made lines. Rigid feeders from copper pipe are worked out exactly this way: pick the conductor diameter for the 50 or 75 Ω you want.
  • Identifying unknown cable. Cut it, measure the diameters, and you know whether it is 50 or 75 Ω.
  • Capacitance per metre. Needed when a length of cable is used as a capacitor in a matching network.
Practical advice:
  1. The classic 50 Ω in polyethylene comes from a D/d ratio of about 3.5; 75 Ω from about 6.5.
  2. An air line has minimum loss at 77 Ω and maximum power handling at 30 Ω. 50 Ω is the historical compromise between them.
  3. Measure the shield diameter on the inside of the braid, not over the jacket.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Coaxial line impedance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/lines/coax_impedance (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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