Transmission Line Velocity Factor Calculator
Calculate velocity factor (VF), in-cable wave speed, physical-to-electrical-length conversion, and wavelength inside a transmission line from cable dielectric constant or common cable type.
How to Use
- Pick a common cable type or select "Custom εr" to enter a specific relative dielectric constant.
- Enter the physical length of cable (m or ft with suffix).
- Enter the operating frequency (Hz, kHz, MHz, GHz).
- Results: velocity factor (fraction of c), in-cable wavelength, and electrical length in wavelengths — the number that matters for stub tuning and impedance matching.
Show Work
Formulas
History of Velocity Factor
The relationship v = c / √εr comes directly from Maxwell\'s 1865 electromagnetic theory — an electromagnetic wave propagates slower through any medium with dielectric constant greater than 1. Heaviside\'s telegrapher\'s equations (1880s) showed how this plays out specifically for transmission lines, giving engineers formulas relating cable geometry and dielectric properties to wave speed, characteristic impedance, and attenuation.
Velocity factor as a specified cable parameter entered engineering practice in the early 20th century with the growth of wireless telegraphy and broadcasting. Once stations operated above 1 MHz, the difference between free-space and in-cable wavelength mattered for matching networks, antenna feed lines, and phased arrays. By the 1930s, the RMA (later EIA) had standardized VF reporting on cable datasheets, and it\'s been a baseline spec ever since.
Modern developments include: foam polyethylene dielectrics (1960s, raising VF from 0.66 to 0.82–0.88 while reducing loss), Teflon (PTFE) dielectrics for high-temperature applications (VF ≈ 0.70), and air-spaced hardline with periodic spacers for near-vacuum VF approaching 0.98. Waveguide bypasses the VF issue entirely — there\'s no dielectric to slow waves, just a conductor geometry that supports specific propagation modes.
About This Calculator
Pick a common cable type or enter a custom dielectric constant. Enter the physical cable length (m or ft) and operating frequency. The tool returns velocity factor, effective dielectric constant (back-calculated), in-cable wavelength at that frequency, and electrical length in wavelengths — the last value being what matters for stub tuning, impedance matching, and phase alignment work.
Note: this calculates transmission-line VF. For antenna end-effect velocity factor (typically 0.95), use the Antenna Length calculator — that\'s a different physical phenomenon related to fringing fields at the antenna tips, not bulk dielectric propagation. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
What is velocity factor?
The speed of a signal on a transmission line as a fraction of the speed of light in vacuum. VF = 1 / √ε<sub>r</sub> where ε<sub>r</sub> is the relative dielectric constant of the insulating material between the conductors. Solid-PE coax (RG-58, RG-8) has ε<sub>r</sub> ≈ 2.3 giving VF ≈ 0.66; foam-PE (LMR-400) has ε<sub>r</sub> ≈ 1.4 giving VF ≈ 0.85.
Why does it matter?
Any "electrical length" calculation — matching stubs, phase-delay lines, baluns, antenna feed lines cut to specific fractions of a wavelength — must use the in-cable wavelength, not the free-space wavelength. A quarter-wave stub at 150 MHz is 33 cm in vacuum but only 22 cm in RG-58. Ignoring VF gives results that don\'t resonate where you expect.
How do I measure VF?
TDR (time-domain reflectometer) measures round-trip delay on a known-length cable; divide cable length by (c × measured delay / 2) to get VF. Alternatively, cut a cable to a guess at λ/2 at some frequency, short one end, and use a network analyzer or dip meter to find the actual resonance — VF = (actual resonant frequency × 2 × physical length) / c.
Solid vs foam vs air dielectric?
Solid polyethylene: VF 0.66, cheap, flexible, reasonable loss. Foam polyethylene: VF 0.80–0.85, lower loss (less dielectric material to absorb), slightly more expensive. Air-dielectric (hardline, semi-rigid with spacers): VF 0.95–0.98, lowest loss of any flexible cable, most expensive and stiffest. Waveguide has no dielectric — VF depends on geometry, not on solid material.
Does VF depend on frequency?
Very weakly for most cables. The bulk dielectric constant of polyethylene is essentially constant from DC through microwaves, so VF stays flat. Exception: in very dispersive materials (ferrite-loaded coax, some specialty cables) dielectric constant varies with frequency and VF changes noticeably across wide bands.
Common Use Cases
Matching Stub Design
A quarter-wave stub at 146 MHz in RG-58 is 0.34 m (λ<sub>cable</sub>/4), not 0.51 m (λ<sub>free</sub>/4). Using the wrong number puts your resonance in the wrong place by 30%.
Phase-Matched Array Feed
A 4-dipole antenna array needs equal electrical-length feed lines. "Equal physical length" only works if all four use the same cable type — different VFs in mixed cables ruin the phasing.
Balun Construction
A 4:1 half-wave coaxial balun uses a loop of cable half a wavelength long <em>inside the cable</em>. Cut from a free-space calculation and your balun impedance-transforms at the wrong frequency.
Time-Domain Reflectometry (TDR)
Interpreting TDR displays requires knowing VF to convert round-trip time into physical distance to a fault.
Cable-Run Phase Compensation
In radar and phased-array systems, precise phase match across many cable runs requires accounting for VF of each run. Lines are laser-trimmed in length to compensate.
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