Transmission line length calculator

Why a “quarter wave” of cable is shorter

In a dielectric a wave travels more slowly than in air, so the wavelength is shorter too. The ratio of the speeds is the velocity factor vf: 0.66 for solid polyethylene, 0.82–0.85 for foamed. A quarter-wave section has to be cut to the wavelength in the cable, not the one in free space.

The lengths are measured from the cut end of the cable, allowing for the velocity factor

Frequency (MHz)
Cable	Enter by handRG-58 (vf 0.66)RG-213/U (vf 0.66)RG-174 (vf 0.66)RG-316 PTFE (vf 0.695)RG-142 PTFE (vf 0.695)RG-8X foam (vf 0.82)RG-6 foam (vf 0.83)H-1000 (vf 0.83)LMR-400 (vf 0.85)Heliax 7/8" (vf 0.88)Open-wire line (vf 0.95)
Insulation material	Enter by handAir / vacuum (1.0)Foam PE, LMR (1.38)Foam polyethylene (1.53)PTFE (2.07)Solid polyethylene (2.25)Polypropylene (2.3)Polystyrene (2.55)PVC (3.3)FR-4 laminate (4.4)
ε of the insulation
Result
Free-space wavelength (λ)
Wavelength in the line (λg)
Quarter wave (λg/4)
Half wave (λg/2)
Three quarter waves (3λg/4)
Coefficients

📐 The formulas

Wavelength in free space and in the line:

λ  = 299792.458 / f        [mm]
λg = λ / √ε
vf = 1 / √ε

Useful sections:

λg/4    quarter-wave transformer, stub
λg/2    impedance repeater
3λg/4   inversion where the layout is awkward

Symbols:

• f — frequency [MHz]
• ε — permittivity of the insulation
• vf — velocity factor

Where this calculator stops:

• The quoted vf varies by ±2–3 % from batch to batch
• The result is an electrical length; connectors add a delay of their own
• For foamed dielectric the vf depends on how much it is foamed — use the maker's figure

🎯 In practice

• Matching impedances. A λ/4 transformer made from cable of the right Z₀ — see the quarter-wave transformer.
• A half-wave repeater. A λ/2 section carries the antenna impedance to the input unchanged, which is handy for measurements.
• Phasing lines in antenna arrays and power dividers.

Practical advice:

1. Cut 3–5 % long and trim to the analyser — you cannot add cable back.
2. The easiest check is with the far end open: a quarter-wave section shows a minimum impedance at the working frequency.
3. Measure from cut to cut of the centre conductor, not along the jacket.

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UR3PKI. «Transmission line length calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/cable_length (licence CC BY-NC-SA 4.0).

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