Coaxial Cable Impedance Calculator — Z₀, Velocity Factor & Capacitance
Find the characteristic impedance (Z₀), velocity factor, and per-metre capacitance of a coaxial cable: enter the inner and outer conductor diameters and the dielectric material to instantly see whether your cable is matched to 50 Ω or 75 Ω systems.
mm
mm
Dielectric material
Coaxial line impedance — 50 Ω for RF, 75 Ω for video/TV
- 1
Diameter ratio D ÷ d
7 ÷ 1.5 = 4.6667 - 2
Natural log ln(D/d)
ln(4.6667) = 1.540445Geometry factor — wider spacing between conductors raises impedance. - 3
√εr
√2.25 = 1.5 - 4
Characteristic impedance Z₀
60 ÷ 1.5 × 1.540445 = 61.6 Ω
How does this calculator work?
Z₀ = (60/√εr) × ln(D/d) Ω. For solid polyethylene (εr = 2.25), a D/d ratio of about 3.48 gives 50 Ω; about 6.0 gives 75 Ω. Velocity factor = 1/√εr (≈ 0.66 for solid PE). Enter diameters and dielectric to check impedance match instantly.
Formula
How this is calculated
A coaxial cable is a transmission line formed by a centre conductor of diameter d inside a tubular outer conductor of inner diameter D, separated by a dielectric insulator. The characteristic impedance Z₀ — the impedance the line presents to a travelling wave regardless of length — is determined by the geometry and the electrical properties of the dielectric.
The formula Z₀ = (60/√εr) × ln(D/d) is derived from Maxwell's equations for a lossless coaxial line, where εr is the relative permittivity (dielectric constant) of the insulating material and ln(D/d) is the natural logarithm of the diameter ratio. Standard systems use 50 Ω for RF/microwave work (optimum power handling/loss compromise) and 75 Ω for video and cable TV (minimises attenuation for a given outer conductor size). The velocity factor VF = 1/√εr tells you how fast a signal travels relative to the speed of light — solid polyethylene gives about 66%, PTFE about 69%, foam PE about 82%.
This calculator assumes an ideal lossless coaxial geometry with a uniform, homogeneous dielectric. Real cables have conductor losses (skin effect, increasing with frequency) and dielectric losses that are not modelled here. For precision RF design, use the full loss model from IEC 62153 or consult the cable datasheet.
Frequently asked questions
50 Ω is a compromise between maximum power transfer (~30 Ω) and minimum attenuation (~77 Ω) in an air-dielectric coaxial line, optimising for both in high-power RF applications. 75 Ω minimises attenuation for a given outer diameter, making it ideal for long cable TV and satellite runs where signal loss is the primary concern.
Enter D as the inner diameter of the outer conductor (the inside of the braid or foil shield) and d as the outer diameter of the centre conductor. Both in millimetres. For standard RG-58, D ≈ 2.95 mm, d ≈ 0.91 mm (solid PE core); for RG-6, D ≈ 4.57 mm, d ≈ 1.0 mm.
Velocity factor is the fraction of the speed of light at which signals travel in the cable. It matters for antenna tuning (a quarter-wave stub cut to physical length = λ/4 × VF) and time-delay calculations. Solid PE cables are about 0.66–0.67 c; foam PE cables are about 0.78–0.88 c.
TG we-Calculate Editorial Team. (2026). Coaxial Cable Impedance Calculator — Z₀, Velocity Factor & Capacitance [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cable-impedance-calculator
TG we-Calculate Editorial Team. "Coaxial Cable Impedance Calculator — Z₀, Velocity Factor & Capacitance." TG we-Calculate. 2026. https://we-calculate.com/calculator/cable-impedance-calculator.
TG we-Calculate Editorial Team, "Coaxial Cable Impedance Calculator — Z₀, Velocity Factor & Capacitance," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cable-impedance-calculator
@misc{wecalculate_cable_impedance_calculator, title = {Coaxial Cable Impedance Calculator — Z₀, Velocity Factor & Capacitance}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cable-impedance-calculator}}, year = {2026}, note = {TG we-Calculate} }
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