How this instrument works
The J-pole antenna gets its capital-J profile from two elements: a half-wave radiator on top and a shorted quarter-wave matching stub underneath, running parallel like the tines of a tuning fork. This calculator finds the stub — the section that presents a clean impedance match to 50 Ω coaxial feedline without any separate matching network, which is the whole appeal of the design for builders working with plain wire or tubing instead of a machined connector.
The formula starts from the free-space wavelength, λ = c ⁄ f, then takes a quarter of it because a shorted quarter-wave section is exactly long enough for current to swing from maximum at the short to zero at the open end — the standing-wave condition a matching stub depends on. Multiplying by the velocity factor accounts for the fact that a real conductor is not empty space: a wave travels a little slower along wire or tubing than it does in vacuum, so the physical cut has to be shorter than the vacuum quarter-wavelength to stay resonant at the target frequency.
Velocity factor is not a universal constant. It depends on the conductor's diameter, its closeness to other metal, and any insulation, and typically runs from about 0.95 to 0.98 for bare copper wire down toward 0.90 for thicker tubing or insulated conductors. The number this calculator returns is a starting cut length, not a guarantee: builders routinely leave the stub a little long and trim it in small steps while watching an SWR meter, because no published velocity factor accounts for every installation's stray capacitance and nearby metalwork.
- Enter the operating frequency in Frequency, MHz — for example 146 for the middle of the 2-meter amateur band.
- Enter Velocity factor (0-1) for your conductor: about 0.95 for bare copper wire, lower for tubing or insulated wire.
- Read Quarter-wave element length, switching its unit to cm or ft if that suits your tape measure better than metres.
- Cut the stub slightly long and trim it in small steps while checking SWR, since real-world velocity factor varies by build.
Worked example — a 2-meter-band J-pole stub at 146 MHz
A builder cutting a J-pole for the 2-meter amateur band sets Frequency, MHz to 146 and Velocity factor (0-1) to 0.95, typical for bare 12-gauge copper wire. The free-space wavelength is λ = c ⁄ f = 299,792,458 ⁄ 146,000,000 = 2.053373 m. A quarter of that is 0.513343 m, and multiplying by the 0.95 velocity factor gives L = 0.4876760875 m — the exact figure this calculator returns.
In builder's units that is 48.77 cm, or about 19.20 inches — close to the 19-inch rule-of-thumb figure hams pass around for a 2-meter J-pole stub, a useful sanity check that the formula and the folklore agree. Forgetting to convert MHz to Hz, or applying the velocity factor twice, are the two most common ways this number comes out wrong by a factor of a million or roughly ten percent respectively.
Questions
What does the quarter-wave stub actually do in a J-pole?
It matches impedance. The shorted stub forms a resonant transformer: current is maximum at the short and falls toward the open end, so tapping the coax at the point along the stub where the impedance equals 50 Ω gives a clean match to standard feedline — no gamma match, hairpin, or separate matching box required.
Why divide the wavelength by four and not by two?
Because a quarter-wave shorted section is the shortest length that puts a current maximum at the short and a current node at the open end — the standing-wave condition a matching stub relies on. A half-wave section instead repeats the impedance seen at its input, which is the job of the J-pole's separate radiating element, not the stub calculated here.
What velocity factor should I use for bare wire versus tubing?
Bare copper wire typically runs 0.95 to 0.98; aluminum or copper tubing, being thicker and often closer to nearby structures, tends toward 0.90 to 0.95. Insulated wire or conductors mounted very close to metal can drop below 0.90. When unsure, start with 0.95 and trim the built stub while watching an SWR meter.
Do I need to trim the stub after cutting it to the calculated length?
Yes — treat the result as a starting cut, not a final one. Published velocity factors are averages; your specific wire gauge, insulation, and nearby metal all shift the true resonant length slightly. Cut a centimeter or two long, then trim in small steps while watching an SWR meter until the reading bottoms out at your target frequency.
How is this quarter-wave stub different from the half-wave radiator above it?
They do different jobs and use different lengths. The radiator is the roughly half-wavelength wire that actually radiates the signal; the stub calculated here is the shorter, shorted quarter-wave section beneath it that transforms the radiator's high feedpoint impedance down to near 50 Ω. A complete J-pole build needs both pieces, cut and tuned separately.
Why must frequency be entered in MHz rather than Hz or GHz?
Because the underlying formula multiplies the entered value by one million to convert it to hertz before dividing into the speed of light. Entering 146 for 146 MHz gives the correct 146,000,000 Hz; entering 146000000 directly, expecting Hz, would return a stub length about a million times too short.