coaxial line impedance calculator

What this coaxial line impedance calculator does

This calculator estimates the characteristic impedance of a coaxial transmission line from geometry and material properties. In RF design, impedance matching is critical for low reflection, maximum power transfer, and clean signal integrity. Whether you're designing a custom cable, a PCB launch, or a lab test fixture, this tool gives a fast first-pass value for Z₀.

Formula used

For a coaxial line with inner conductor diameter d, outer conductor inner diameter D, relative permittivity ε_r, and relative permeability μ_r, the calculator uses:

Z₀ = 60 × √(μ_r/ε_r) × ln(D/d)

This is the classic lossless approximation and is accurate for most practical coax design work in early-stage calculations.

Also reported values

• D/d ratio (useful for quick design intuition)
• Velocity factor = 1 / √(ε_rμ_r)
• Propagation velocity in m/s
• Capacitance per meter (pF/m)
• Inductance per meter (nH/m)

How to use it correctly

1. Measure or define the inner conductor diameter d.
2. Measure the inner diameter of the outer conductor D.
3. Enter dielectric constant ε_r for your insulator (PTFE, PE, air, foam, etc.).
4. Leave μ_r = 1 for non-magnetic materials (most coax uses this).
5. Click Calculate.

Important: d and D must be in the same unit. The formula depends on the ratio D/d, so mixed units will produce wrong results.

Example

Suppose a cable has d = 1.0 mm, D = 4.7 mm, and ε_r = 2.25 (a typical polyethylene-like dielectric). With μ_r = 1:

• D/d = 4.7
• Z₀ is approximately 62 Ω

This is in the neighborhood of common RF cable impedance targets and demonstrates how sensitive impedance is to geometry ratio and dielectric.

Common coax impedance targets

50 Ω

• General RF systems
• Transmit/receive equipment
• Test instruments and lab interconnects

75 Ω

• Video and broadcast distribution
• Cable TV and satellite systems
• Low-loss receive-focused links

Design tips for better results

• Use accurate dielectric data at your operating frequency.
• Include manufacturing tolerance in d, D, and dielectric thickness.
• For high frequency and long runs, account for conductor and dielectric losses separately.
• Validate final designs with simulation and TDR/VNA measurement.

Limitations of this calculator

This tool assumes a uniform, ideal coaxial structure and uses closed-form equations. Real cables may include stranded conductors, non-uniform dielectrics, foamed materials, corrugation, plating effects, and frequency-dependent loss behavior. Use this calculator for design estimation, then verify against real parts and measurements.

Quick reference dielectric values (typical)

• Air: ε_r ≈ 1.0006
• PTFE: ε_r ≈ 2.0 to 2.1
• Polyethylene (PE): ε_r ≈ 2.25
• Foam PE: ε_r ≈ 1.4 to 1.7

Use vendor datasheets whenever possible, especially if your design is broadband or tightly tolerance-controlled.