Velocity Factor
In free space — a perfect vacuum — radio waves travel at the speed of light: 300,000,000 meters per second (3 × 10⁸ m/s). Inside a coaxial cable or any other transmission line, waves travel slower than this because of the dielectric material between the conductors. The fraction of the speed of light at which the wave travels in a particular cable is called the velocity factor of that cable, usually written as VF or v/c.
Velocity factor matters every time you need to cut a piece of cable to a specific electrical length — for a phasing line, a matching section, a stub, or a quarter-wave transformer. If you ignore it and cut for the free-space wavelength, your cable will be too long and the circuit will not behave as expected.
At 14 MHz, one wavelength in free space is 21.4 meters. Inside RG-213 coax (VF = 0.66), one wavelength is only 14.1 meters — 66% as long. Any cable cut to free-space length will be electrically longer than intended.
View LargerWhat Velocity Factor Is
The velocity factor of a transmission line is the ratio of the wave propagation speed in that line to the speed of light in a vacuum:
- VF = velocity factor (dimensionless, between 0 and 1)
- v = wave propagation speed in the cable (m/s)
- c = speed of light in vacuum = 3 × 10⁸ m/s
Velocity factor is also sometimes expressed as a percentage. A cable with VF = 0.66 is said to have a 66% velocity factor, meaning waves travel at 66% of the speed of light inside it.
The wave propagation speed in a cable is:
v = c × VF = c / √εr
For standard RG-213 with solid polyethylene dielectric (εr = 2.26):
v = 3 × 10⁸ / √2.26 = 3 × 10⁸ / 1.503 = 1.996 × 10⁸ m/s
VF = 1.996 × 10⁸ / 3 × 10⁸ = 0.665 (about 66%)
Why RF Travels Slower in Cable
The speed of an electromagnetic wave in any medium is determined by two properties of that medium: its electric permittivity (ε) and its magnetic permeability (μ). In a vacuum, these take their minimum values (ε₀ and μ₀), and the resulting wave speed is c = 1/√(ε₀μ₀) = 3 × 10⁸ m/s.
When you fill the space between the conductors with a dielectric material (polyethylene, PTFE, foam, or air), the dielectric has a relative permittivity εr greater than 1. This means the electric fields can be established with greater intensity for a given voltage, which increases the effective capacitance per unit length of the line. As you learned in the distributed circuit model from lesson M13B, increasing capacitance per unit length while keeping inductance per unit length the same slows the wave: v = 1/√(LC), and if C increases, v decreases.
Physically, the reason a dielectric slows the wave is that its molecules polarize under the influence of the electric field — positive and negative charge centers shift in opposite directions. This polarization stores energy in the molecular structure and slightly delays the propagation of the field. A denser dielectric (higher εr) polarizes more strongly and causes more slowing.
Most practical dielectrics used in coaxial cable have εr between 1.0 (air) and 2.3 (solid polyethylene). Materials with higher εr would reduce the cable's VF further, which is generally undesirable for RF coaxial cable because it would make cut-to-length cables physically shorter and increase dielectric loss.
For most practical transmission lines, the magnetic permeability is essentially the same as in vacuum (μr ≈ 1) because the dielectric materials used are non-magnetic. In ferrite-loaded cables (which exist but are unusual), the permeability would also differ from vacuum, but this is the exception rather than the rule.
Velocity Factor and Dielectric Constant
The relationship between velocity factor and relative dielectric constant is straightforward:
or equivalently:
εr = 1 / VF²- εr = relative dielectric constant of the insulating material
- VF = velocity factor (between 0 and 1)
This formula lets you calculate VF from the published dielectric constant, or determine the effective dielectric constant from a measured VF:
VF = 1/√2.08 = 1/1.442 = 0.694 (about 69%)
εr = 1/0.82² = 1/0.672 = 1.49 — consistent with foam polyethylene dielectric.
Note that this formula is exact for a cable filled uniformly with a single dielectric, but is only approximate for cables where the dielectric is partly air (such as foam-filled or air-spaced cables). For those, an effective dielectric constant must be determined empirically or from detailed modeling of the field distribution. This is why the published VF for foam-dielectric cables can vary slightly between manufacturers even for nominally similar products.
Velocity Factor of Common Cables
| Cable Type | Dielectric | Velocity Factor | Notes |
|---|---|---|---|
| RG-58A/U | Solid polyethylene | 0.659 (66%) | Common thin coax |
| RG-58C/U | Solid polyethylene | 0.659 (66%) | As above |
| RG-8/U (solid PE) | Solid polyethylene | 0.659 (66%) | Standard RG-8 |
| RG-8X | Foam polyethylene | 0.82 (82%) | Mini-8 flexible cable |
| RG-213/U | Solid polyethylene | 0.659 (66%) | Standard HF coax |
| LMR-400 | Foam polyethylene | 0.85 (85%) | Low-loss cable |
| LMR-240 | Foam polyethylene | 0.84 (84%) | Flexible low-loss |
| RG-6/U (CATV) | Foam polyethylene | 0.82 (82%) | 75-ohm CATV cable |
| RG-11/U (CATV) | Foam polyethylene | 0.82 (82%) | 75-ohm larger CATV |
| RG-142 | Solid PTFE | 0.694 (69%) | High-temp military |
| Semi-rigid coax (UT-141) | Solid PTFE | 0.695 (70%) | Microwave assemblies |
| 450-Ω ladder line | Air (with spacers) | 0.91–0.95 | Open balanced feeder |
| 600-Ω open wire | Air | 0.97–0.99 | Nearly free-space speed |
Notice that open-wire feeders have velocity factors close to 1.0 — because the wave travels mostly in air, not in a solid dielectric. This is one of the advantages of open-wire feeders for applications where the electrical length of the feedline must be predictable. The wavelength in open wire is almost the same as in free space, making cut-to-length calculations straightforward.
How VF Affects Wavelength in Cable
The wavelength of an RF signal in a transmission line is shortened by the velocity factor:
- λcable = wavelength in the cable (meters)
- λfree space = c / f = wavelength in free space (meters)
- c = 3 × 10⁸ m/s (speed of light)
- f = frequency (Hz)
- VF = velocity factor of the cable
In practical units with f in MHz and length in feet:
λcable (feet) = (984 / fMHz) × VFOr in meters:
λcable (meters) = (300 / fMHz) × VFλfree space = 300 / 14.2 = 21.13 meters = 69.3 feet
λRG-213 = 21.13 × 0.66 = 13.95 meters (45.7 feet)
A quarter-wave section would be 13.95 / 4 = 3.49 meters (11.4 feet)
This matters enormously for applications like phasing harnesses for vertical arrays, where two elements must be fed with signals exactly 90 degrees apart. If you use a quarter-wave phasing line cut for the free-space wavelength, it will actually be about 52% longer electrically than intended (using VF = 0.66) and the array will not work properly.
Cutting Cable to Length: Worked Examples
The most common practical application of velocity factor is cutting a transmission line to a specific electrical length. The general formula is:
For a quarter-wave section (90°):
Physical length = (1/4) × (c / f) × VFFor a half-wave section (180°):
Physical length = (1/2) × (c / f) × VFλfree space at 146 MHz = 300/146 = 2.055 meters = 6.74 feet
Quarter-wave in LMR-400 = 2.055 × 0.85 / 4 = 0.437 meters = 1.43 feet = 17.2 inches
If you had used the free-space quarter-wave (0.514 meters), the section would have been 18% too long, ruining the impedance transformation.
λfree space at 3.6 MHz = 300/3.6 = 83.3 meters = 273 feet
Half-wave in RG-213 = 83.3 × 0.66 / 2 = 27.5 meters = 90.2 feet
Note: in a matched 50-ohm system, adding any multiple of a half-wave section of 50-ohm cable does not change the impedance at the source, but the phase relationship does matter for phasing applications.
λfree space at 7.15 MHz = 300/7.15 = 41.96 meters = 137.7 feet
Quarter-wave in 450-ohm ladder line = 41.96 × 0.92 / 4 = 9.65 meters = 31.7 feet
Because ladder line has a VF close to 1.0, the free-space approximation (41.96 / 4 = 10.49 meters = 34.4 feet) introduces an error of only 8% — acceptable for rough calculations but not for precision work.
Measuring VF When It Is Not Published
Sometimes you have a reel of cable with no markings, or the manufacturer's published VF does not match what you observe. In these cases you can measure the velocity factor directly using one of two methods.
Method 1: Antenna analyzer dip method
The simplest method uses an antenna analyzer or vector network analyzer (VNA). Cut a piece of cable of known physical length L. Short one end (connect center conductor to outer conductor with a short wire). Connect the other end to your analyzer. Sweep the frequency while observing the SWR or impedance. A short-circuited quarter-wave transmission line looks like an open circuit (maximum SWR), and a half-wave line looks like a short circuit (minimum SWR, nearly zero impedance). Find the first frequency f₁ at which the shorted cable looks like an open circuit — this is the quarter-wave resonance.
- L = physical length of cable (meters)
- f₁ = first quarter-wave resonant frequency (Hz)
- c = 3 × 10⁸ m/s
With L in feet and f₁ in MHz:
VF = L (feet) × f₁ (MHz) / 246VF = 10 × 16.1 / 246 = 161 / 246 = 0.655
This matches solid polyethylene dielectric (VF = 0.659), confirming the cable is likely standard RG-58 or RG-213 type.
Method 2: TDR (Time Domain Reflectometer) method
A TDR sends a fast pulse down the cable and measures the time for the reflection from the far end to return. If the cable is L meters long and the reflected pulse returns after a time delay Δt seconds, then the one-way travel time is Δt/2, and the velocity is:
v = 2L / Δt
VF = v / c = 2L / (Δt × c)
Most modern TDR instruments measure velocity factor directly, asking you to enter the cable length and reporting the VF, or conversely asking for the VF and reporting cable length (for fault location). TDR is covered in detail in Module 17 (Test Equipment: Advanced).
Frequently Asked Questions
Does velocity factor change with frequency?
For most practical cables in the amateur radio frequency range, the velocity factor is essentially constant. The dielectric constant of polyethylene and PTFE varies very slightly with frequency over the HF to UHF range — typically less than 1% — so this effect is negligible for almost all applications. At extremely high frequencies (beyond 10 GHz) or in cables with polar dielectric materials, dispersion effects become significant. For 160 meters through 23 centimeters, you can treat VF as a fixed constant for a given cable type.
Why does my antenna seem to work fine even though I did not account for velocity factor?
The antenna works because the feedline does not need to be any particular electrical length for a matched system. If your antenna already presents 50 ohms to a 50-ohm feedline, the SWR is 1:1 and the feedline length is irrelevant — power flows freely regardless. Velocity factor becomes critical only when you need the feedline to be a specific electrical length for a specific purpose: a quarter-wave matching section, a half-wave phasing line, a stub filter, or a delay line. For general station feedlines where you simply want to get power from the radio to the antenna, you do not need to worry about velocity factor as long as the impedances are matched.
Why does foam dielectric give a higher velocity factor than solid polyethylene?
Foam dielectric is essentially a mixture of solid polyethylene and air bubbles. Air has εr = 1.0, and solid polyethylene has εr = 2.26. By foaming the plastic to, say, 40–50% air content, the effective dielectric constant drops to about 1.4–1.5, raising the velocity factor from 66% to 82–86%. This also reduces dielectric losses (since air has near-zero loss compared to solid plastic), which is why foam-dielectric cables like LMR-400 have lower attenuation than their solid-dielectric equivalents. The tradeoff is that foam dielectric cables must be handled more carefully — the foam structure can be damaged by sharp bends or excessive compression, which would change the effective dielectric constant and alter both the impedance and velocity factor.
If I am cutting a balun feed line for a dipole, does velocity factor matter?
Only if the feedline is specifically cut to a particular electrical length for the balun or choke design. For a current balun made from a ferrite core with wound coax — the standard for most dipole installations — the length of coax wound on the ferrite is determined by the number of turns for adequate choking impedance, not by a specific electrical length, and velocity factor is irrelevant for the winding. For a coaxial choke balun where the coax is coiled into an inductor, the key parameter is the inductance of the coil, not its electrical length. For a specific design like a W2DU bead balun, the coax length through the beads is very short and velocity factor has negligible effect. The situations where VF matters for balun/feedline design are specific: sleeve baluns, certain broadband balun designs, and some phased feed networks.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.