Velocity Factor: Why Coax and Antenna Wire Are Cut Shorter

Every amateur who has cut a coax balun, a phasing line or a dipole has met the same puzzle: the length from the textbook formula never quite fits the real material. The explanation is velocity factor. A radio wave travels more slowly in a cable than in empty space, so a cable that is a quarter wavelength long electrically is physically shorter than a quarter of a wavelength in air. If you ignore the difference, your stub is the wrong length, your phasing line is out of phase and your coax balun does not do what you built it to do.

This guide explains velocity factor in plain terms, gives typical values for the materials amateurs actually use, shows the formulas for common jobs and describes how to measure a cable you cannot identify. It also covers the related shortening of antenna wire, which has a different cause but a similar effect.

What Velocity Factor Is

The velocity factor of a transmission line is the ratio of the speed of a signal in that line to the speed of light in a vacuum. A velocity factor of 0.66 means the signal travels at 66 percent of the speed of light. The effect comes mainly from the insulating material between the conductors. In a cable with a solid plastic dielectric, the electric field passes through the plastic and the wave slows down. The higher the dielectric constant of the insulation, the lower the velocity factor, and for the usual case the factor is the reciprocal of the square root of the dielectric constant.

Two practical consequences follow:

• Electrical length and physical length differ. A line that is one wavelength long electrically is shorter physically by the velocity factor. A cable with a velocity factor of 0.66 that is a quarter wavelength electrically is 0.66 times as long as a quarter wavelength in free space.
• The factor belongs to the cable, not to the frequency. Over the amateur bands it is close to constant for a given cable, so you can look it up once and reuse it. It does differ between types, and between manufacturers, so the data sheet matters.

Typical Values

Handbook values for common radio cables vary, and published figures are typically given as percentages. Use the table as a guide and prefer the manufacturer’s data sheet for the actual cable. The ranges below are consistent with the figures published in reference tables.

Two warnings. First, the factor for a cable changes slightly with age and with moisture in the dielectric, which is a reason to measure a cable you plan to cut to a critical length. Second, many cables sold as generic have a different dielectric from the type they imitate. A cable labelled with a certain RG number is not guaranteed to have the factor of the original military specification. Our comparison of coaxial cable for ham radio explains how these cables differ in construction and loss.

The Formulas You Actually Need

The free-space lengths come from the speed of light. A half wavelength in free space is approximately 492 divided by the frequency in megahertz, giving feet, and a quarter wavelength is approximately 246 divided by the frequency. To cut a coax line to an electrical length, multiply the free-space length by the velocity factor.

• Quarter-wave coax: length in feet = 246 x VF / frequency in MHz.
• Half-wave coax: length in feet = 492 x VF / frequency in MHz.
• Metric equivalents: multiply the free-space length of 75 metres per MHz for a quarter wave or 150 metres per MHz for a half wave by VF, divided by the frequency in MHz. In short, a quarter wave in metres is 75 x VF / f, and a half wave is 150 x VF / f.

A worked example. You want a half-wave piece of solid polyethylene coax for 14.2 MHz. The free-space half wave is 492 / 14.2, which is about 34.6 feet. Multiply by 0.66 and you get about 22.9 feet. Cutting 34.6 feet would have been far off, and a coax balun cut to the wrong length does not give the phase shift it is meant to.

Always cut a little long, test, and trim. Exact lengths are sensitive to the cable, the connectors and the way the cable is coiled, and trimming against a measurement is more reliable than trusting a formula alone.

Where Velocity Factor Matters in the Shack

Several common projects depend on getting the electrical length right:

• Coax stubs and filters. An open-circuit quarter-wave stub connected across a line looks like a short circuit at its design frequency, so it can act as a notch to suppress a harmonic or a strong nearby signal. Its length must be correct for the frequency you want to reject.
• Phasing lines for antenna arrays. Two vertical antennas fed through a quarter-wave section of cable are driven 90 degrees apart in phase to produce a directional pattern. The phase shift depends on the electrical length, not the physical one.
• Half-wave coax baluns. A balun that provides a four-to-one impedance transformation and a balanced output uses a half-wave loop of coax. See our explanation of baluns and ununs for how the family of baluns differs.
• Quarter-wave matching sections. A quarter-wave section of cable of a specific impedance can match two different impedances, and again the cut length uses the velocity factor.
• Cable length in modelling and analysers. Test equipment asks for the velocity factor when it estimates fault distance. If the figure is wrong, the reported distance to a break is wrong by the same proportion.

In none of these jobs does the velocity factor affect the cable’s loss or the SWR directly. It sets the electrical length, and electrical length sets the phase and the transformation of impedance along the line.

Antenna Wire Also Runs Short

Antenna wire is a different matter. The wave does not slow down in a bare wire in the same way, but a real dipole still resonates at a lower frequency than the simple half-wave formula suggests. The main reason is the end effect, which makes the antenna behave as if it were slightly longer electrically than its physical length. The thickness of the conductor and the insulation on the wire add to the effect. Insulation increases the capacitance to the surroundings and lowers the resonant frequency, so insulated wire needs to be cut a little shorter than bare wire.

The familiar rule for a half-wave dipole in feet is 468 divided by the frequency in megahertz, and in metres it is about 142.5 divided by the frequency. The figure of 468 is smaller than 492 because it includes about five percent of shortening for the end effect, as the general description of a dipole antenna explains. For a full-wave loop the corresponding rule is about 1005 divided by the frequency in feet.

The practical lesson is to start from the formula but expect to trim:

1. Cut the wire a few percent longer than the formula gives.
2. Raise the antenna to its working height, because ground proximity and nearby objects change the resonance.
3. Measure the resonant frequency with an antenna analyser.
4. Shorten the wire at the ends in small steps until the resonance is where you want it.

It is easier to remove wire than to add it, and each trimming step moves resonance by an amount you can calculate. Our guide to the NanoVNA antenna analyser shows how to take the measurement, and the article on a first HF antenna gives a simple dipole to practise on.

How to Measure a Velocity Factor

If you have an unlabelled cable, or you want to confirm a data sheet, a measurement is straightforward with a vector network analyser or an antenna analyser. There are two common methods.

1. Frequency method. Leave the far end of the cable open. Sweep the analyser and find the lowest frequency at which the input shows a short circuit, which is where the cable is an electrical quarter wavelength long. The velocity factor is then the quarter-wave frequency multiplied by four times the physical length, divided by the speed of light. In practical units, the cable’s electrical length in feet at that frequency is 246 / f, so the factor is the physical length divided by (246 / f).
2. Time-domain method. Some analysers have a distance-to-fault feature. Enter a trial velocity factor, read the displayed length of the cable and scale the factor until the displayed length matches the true length with a tape measure.

Measure the cable straightened out or in a gentle coil, and with the connectors fitted, because the connectors add a small amount of apparent length. For a long cable, the result is more accurate. For a short piece, you may need to measure at a higher harmonic frequency, where the sweep shows more than one resonance.

Ladder Line and Open Wire in Practice

Open-wire line has a velocity factor close to that of free space, so the electrical length of a run of ladder line is almost the same as its physical length. That is one reason it is popular for multiband antennas: the line length behaves in a predictable way, and the loss stays low even when the standing wave ratio is high. See our article on a doublet antenna with ladder line for how that is used. Remember that the factor of window-type and solid twin-lead is lower than that of true open wire, because the plastic web that holds the conductors apart slows the wave. If you are cutting a ladder line section to a precise electrical length, measure it as you would a coax, and keep it away from metal objects and wet surfaces, which change the figure.

Common Mistakes

• Using 0.66 for every coax. It is correct for solid polyethylene and wrong for foam and air-dielectric cables.
• Applying the velocity factor to antenna wire as if it were coax. Wire shortening has a different cause and a different size. Use the dipole rule of thumb and then trim.
• Ignoring connectors. A connector adds a small length. For a precise cut, include its effect or trim with the connector fitted.
• Expecting velocity factor to change loss. It does not. A cable can have a high factor and a high loss, or the reverse.
• Cutting once. Measure after the first cut and trim in small steps. The calculation is a starting point.

The Bottom Line

Velocity factor is the ratio of a signal’s speed in a line to the speed of light. It is about 0.66 for solid polyethylene coax, higher for foam and air-dielectric cables and highest for open-wire ladder line. Multiply the free-space length by the factor whenever you cut coax to an electrical length, and treat antenna wire separately, using the 468 rule and trimming against a measurement. When length matters, cut long, measure and trim.

Frequently Asked Questions

What is the velocity factor of RG-58 and RG-213?

Both are usually made with a solid polyethylene dielectric, and the common figure is about 0.66. Always check the data sheet for the actual cable, because the factor depends on the insulation used.

Does velocity factor affect SWR or loss?

Not directly. It sets the electrical length of the line, which determines phase and impedance transformation along the line. Loss depends on the conductors and the dielectric, and SWR depends on the match at the load.

How long is a quarter-wave piece of coax for 7 MHz?

For a cable with a velocity factor of 0.66, the length is 246 x 0.66 / 7, which is about 23.2 feet or about 7.1 metres. Cut it a little long and trim against a measurement.

Why is a dipole shorter than the half-wave formula?

The end effect makes the antenna look slightly longer electrically than it is, so the physical wire must be a few percent shorter. Insulated wire adds a little more shortening, so you should expect to trim a new dipole.

Can I use any coax for a coax balun or stub?

Yes, but you must use the correct velocity factor for that cable, and for power use the cable must handle the voltage and current. Different types give different physical lengths for the same electrical length.

How do I find the velocity factor of an unknown cable?

Measure it with an analyser. Find the frequency at which an open-ended cable first shows a short, which is the quarter-wave frequency, and compare the physical length with the free-space quarter-wave length. Some analysers also give the factor directly from a distance-to-fault reading.