Coaxial cable impedance calculator
Enter the diameter of the centre conductor, the diameter of the dielectric (inside of the shield) and the dielectric constant. The calculator gives the characteristic impedance, or the dielectric diameter for a target impedance, and the capacitance, inductance, velocity factor and delay per metre.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose impedance to calculate Z0, or dielectric diameter to size a line for a target impedance.
- Enter the centre conductor diameter d (and the dielectric diameter D for Z0).
- Enter εr of the insulation: 2.25 for solid PE, 2.1 for PTFE, 1 for air.
- Read Z0 or D, the ratio D/d, the velocity factor and the per-metre values.
For a lossless coaxial line:
- Impedance: Z0 = (60 / √εr) × ln(D / d).
- Ratio for a target: D / d = exp(Z0 × √εr / 60).
- Capacitance: C′ = 2π ε0 εr / ln(D / d), ε0 = 8.854 × 10⁻¹² F/m.
- Inductance: L′ = (µ0 / 2π) × ln(D / d) = 2 × 10⁻⁷ × ln(D / d) H/m.
- Velocity factor: VF = 1 / √εr; delay = √εr / c per metre.
Worked example
A 1 mm conductor in a 3.5 mm solid polyethylene dielectric: ln 3.5 = 1.2528, √2.25 = 1.5, so Z0 = 60 ÷ 1.5 × 1.2528 = 50.11 Ω. The velocity factor is 0.6667, the capacitance 99.92 pF/m, the inductance 250.55 nH/m and the delay 5.003 ns/m.
For 75 Ω with the same 1 mm conductor and PE: D/d = exp(75 × 1.5 ÷ 60) = exp(1.875) = 6.5208, so D = 6.521 mm.
Tips
- Measure the dielectric, not the jacket. D is the inside diameter of the braid or tube.
- Stranded conductors behave like a slightly smaller solid wire; the datasheet impedance is the reliable figure.
- Velocity factor matters for stubs and phasing lines: a quarter wave of cable is VF times a quarter wave in air.
Frequently asked questions
What is the formula for coaxial cable impedance?
Z0 = (60 / √εr) × ln(D / d) ohms, where D is the inside diameter of the shield, d the outside diameter of the centre conductor and εr the relative permittivity of the insulation. The more exact constant is 59.96; 60 is the usual rounding.
What εr should I use?
Solid polyethylene is about 2.25, PTFE about 2.1 and air 1. Foamed dielectrics are lower and vary by cable, so take εr or the velocity factor from the datasheet: εr = 1 / VF².
Why are cables 50 or 75 ohms?
For an air-dielectric line the loss is lowest near 77 Ω and power handling is highest near 30 Ω. 75 Ω, close to the low-loss point, became the standard for video and TV; 50 Ω is a compromise between the two and is the standard for radio equipment. The diameter ratio, not the size, sets the impedance.
Do the units of the diameters matter?
Only their ratio enters the formula, so any unit works as long as both diameters use the same one. The calculator labels them in mm.