Coaxial cable impedance calculator
Characteristic impedance of coax from the conductor and shield diameters and the dielectric.
Fill in the fields and the result will appear here automatically.
Compare the characteristic impedance, capacitance per metre and delay of an ideal coax from conductor dimensions. d is the centre conductor outer diameter; D is the shield inner diameter, not the cable jacket diameter. The model assumes concentric conductors, a uniform nonmagnetic dielectric and lossless TEM propagation. It does not calculate loss, dispersion or higher modes.
How it works
Formula and logic
Z₀ ≈138·log₁₀(D/d)/√εr Ω; C′=2π·ε₀·εr/ln(D/d), VF=1/√εr and delay=√εr/c. The coefficient 138 and ε₀=8.8541878128·10⁻¹² F/m are rounded; c=299792458 m/s. Both diameters are entered in mm, so their ratio has no unit. The declared model requires D>d>0 and εr≥1.
Example
For d=0.9 mm, D=2.95 mm and εr=2.25, the model gives 47.433 Ω, 105.44 pF/m and 5.003 ns/m. Doubling both diameters leaves their ratio and these results unchanged. D=d is invalid geometry with a zero logarithm, not a usable zero-impedance cable.
Fields and units
- Centre conductor outer diameter — mm
- Shield inner diameter — mm
- Relative permittivity εr — 1
How to use
- — Use the conductor outer diameter and shield inner diameter in the same unit; omit the jacket thickness.
- — Enter relative permittivity at the relevant material and frequency, not absolute permittivity in F/m.
- — Velocity factor describes propagation speed; εr=2.25 gives 2/3.
- — Compare with a cable datasheet: geometry does not identify a product or certify its power and frequency ratings.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Steer: coaxial TEM and general RLGC model
- Limitation
- Ideal uniform TEM-line model; not a cable specification, loss calculation or power/mode rating.
FAQ
Does the impedance depend on cable length?
For a uniform line, choosing a longer piece does not change its characteristic Z₀. A terminated section has a different input impedance that depends on length and frequency. Generally Z₀=√((R′+jωL′)/(G′+jωC′)), so losses and dispersion can introduce frequency dependence.
Why 50 and 75 ohms specifically?
The commonly cited 30 Ω power optimum and 77 Ω loss optimum belong to particular air-filled coax models. They are not universal for other dielectrics. At εr=2.25, D/d=8.8 produces about 86.9 Ω, not 75 Ω.
What is the velocity factor?
The ratio of the wave speed in the cable to the speed of light. In polyethylene it is about two thirds, so a quarter-wave stub is physically shorter than a quarter wavelength in air by exactly that factor.
What happens on a mismatch?
An impedance mismatch causes reflection. In a simple termination Γ=(ZL−Z₀)/(ZL+Z₀); resulting heating, errors and permissible reflected power depend on the source and load and are not calculated here.