If you are designing RF cables, test fixtures, antennas, or high-speed signal paths, matching transmission line impedance is critical. This coaxial impedance calculator helps you estimate characteristic impedance (Z0) from geometry and dielectric constant in seconds.
Coaxial Cable Calculator
Use inner conductor diameter (d), inner diameter of outer conductor (D), and relative permittivity (εr).
What this calculator gives you
The tool computes the characteristic impedance of a coaxial transmission line and several useful derived values:
- Z0 (ohms) — target value for RF system matching.
- D/d ratio — direct geometry indicator used in cable design.
- Capacitance per meter — important for timing and loading.
- Inductance per meter — useful for transient and RF behavior.
- Velocity factor and propagation delay — critical in phased and timing-sensitive systems.
How coaxial characteristic impedance works
Coaxial impedance is set by both geometry and dielectric material. Increasing the spacing between conductors increases impedance, while increasing dielectric constant decreases impedance. That makes design a balancing act between mechanical size, attenuation, power handling, and target system impedance.
Core formula
For an ideal, lossless, non-magnetic coax line:
Z0 = (60 / √εr) ln(D/d)
- D = inside diameter of outer conductor
- d = outside diameter of center conductor
- εr = relative permittivity of dielectric
- ln = natural logarithm
Typical impedance targets
50 ohms
Most RF transmit/receive systems, lab equipment, and antenna feed systems use 50 Ω. It is a practical tradeoff between power handling and attenuation.
75 ohms
Common in video distribution, CATV, and many receive-only systems. 75 Ω provides lower attenuation for a given conductor size compared to 50 Ω.
Quick design guidance
- Keep impedance consistent across connectors, cable, PCB launch, and loads.
- Use realistic dielectric values; foam and mixed dielectrics can vary with manufacturing.
- At high frequency, include conductor loss, dielectric loss tangent, and surface roughness in final verification.
- Always verify with TDR or VNA when performance matters.
Worked example
Suppose you have d = 1.0 mm, D = 4.6 mm, and solid PE dielectric εr = 2.25:
- D/d = 4.6
- ln(4.6) ≈ 1.526
- Z0 = (60 / 1.5) × 1.526 ≈ 61.0 Ω
That is above 50 Ω, so you would decrease D/d (or increase effective dielectric constant) to move down toward 50 Ω.
Common mistakes to avoid
- Mixing radius and diameter in the same formula.
- Using log base-10 formula constants with natural log by accident.
- Ignoring connector transitions that can dominate mismatch.
- Assuming dielectric constant is exactly constant over frequency and temperature.
Final note
This calculator is ideal for first-pass coaxial cable impedance design, educational use, and quick sanity checks. For production hardware, combine these results with EM simulation, manufacturing tolerances, and measurement-based validation.