Ham Radio Antenna Length Calculator
Introduction to resonant wire antenna dimensions on the amateur bands
A wire antenna is a resonant structure. Feed it at a frequency where the current and voltage distributions fit naturally along the conductor and the feed-point impedance collapses to a pure resistance; feed it a few percent away from that frequency and the impedance acquires reactance, the standing wave ratio climbs, and a modern transmitter starts folding back its output power to protect itself. Everything an operator wants from a home-built antenna therefore begins with one number: how long to cut the wire.
That number is not simply half of the free-space wavelength, and the difference is where most home-brew antenna projects go wrong. This calculator keeps the two quantities strictly separate. It reports the true free-space wavelength, which depends only on frequency and the speed of light, and it separately reports the shortened physical length of a resonant element, which depends on end effect, conductor diameter and installation height. It then converts those lengths into a practical cut sheet: total wire, per-leg length for centre-fed antennas, side length for a square loop, a trim allowance to cut long, and the physical length of a quarter-wave coaxial matching section if you need one.
The antenna types offered here cover the wire antennas that fill most amateur stations. A centre-fed half-wave dipole is the reference against which almost everything else is measured. An inverted V is the same dipole with a single high support and drooping legs. A quarter-wave vertical, also called a ground plane or monopole, is a dipole with one half replaced by radials or by earth. A full-wave horizontal loop is a closed wire whose perimeter is one wavelength, and it behaves differently from every open-ended antenna in the list. An end-fed half-wave is a half-wave radiator driven at a high-impedance point through a transformer.
Formula: free-space wavelength versus the 468/f, 234/f and 1005/f constants
Start with the definition of wavelength for a wave travelling at the speed of light. The SI defines the speed of light in vacuum as exactly 299 792 458 metres per second, so wavelength follows directly from frequency:
Expressed in the units hams actually use, with frequency in megahertz, that becomes a pair of convenient constants. Neither of them has anything to do with wire:
ARRL teaching material states the free-space case exactly this way: the wavelength is c/f, or 300/f in metres, and half of it is 492/f in feet. That 492 is simply 983.571 divided by two, rounded:
A real dipole is shorter than that. Its ends are open circuits with physical capacitance to the insulators, the supporting rope, the mast and the ground, and the conductor has a finite diameter. The wire therefore behaves as though it were electrically longer than a tape measure says, so the physical length must be cut back to bring resonance up to the wanted frequency. This is end effect, and it is emphatically not a transmission-line velocity factor. The classic amateur correction is about five percent, and the resulting constant is the most memorised number in amateur radio:
Cut a dipole in half at the feed point and replace the missing half with radials and you have a quarter-wave vertical. The same five percent correction applies, so the practical constant is exactly half of 468. ARRL material gives 234/f feet for a ground plane, and refines it to 231/f when the element is #14 wire and 221/f when it is 5/8-inch tubing, which is the length-to-diameter effect in numbers: fatter conductors are electrically longer and therefore have to be cut physically shorter.
A full-wave loop breaks the pattern, and this is the single correction most often missed. A closed loop has no free ends, so there is no end effect to shorten it. Its resonant perimeter is slightly longer than one free-space wavelength, and the long-standing amateur rule of thumb, published with the Loop Skywire design in QST and repeated in the ARRL loop-antenna literature, is:
Everything the calculator does can therefore be written as one expression, where K is the published constant for the chosen antenna family and F is a dimensionless conductor factor that accounts for wire gauge and jacketing:
Velocity factor does have a place in antenna work, but it belongs to the feed line, not to the radiator. Inside coaxial cable the wave travels through a dielectric at a fraction of light speed: roughly 0.66 for solid polyethylene, around 0.78 to 0.85 for foamed dielectrics, and close to 0.95 for open-wire line. When you need a quarter-wave matching section, a Q-section or a phasing line, the electrical length is what matters and the physical length shrinks accordingly:
How to use the band presets, conductor factor and trim allowance
Pick a band first. The band menu is built from the amateur allocations in 47 CFR 97.301, the FCC rule that lists every band available to a US amateur station by ITU region, and selecting one drops the mid-band frequency into the frequency field. If you already know the segment you will operate in, overwrite the frequency directly; the band menu switches to a custom entry and the results panel tells you which allocation your frequency falls inside, or warns you if it falls outside every US amateur band.
Choose the antenna type next. Dipole, inverted V and end-fed half-wave all use the 468 family constant; the quarter-wave vertical uses 234; the full-wave loop uses 1005. The results panel names the constant it used, so the arithmetic is never hidden from you.
The conductor factor is a multiplier on that constant. Leave it at 1.000 for thin bare wire between about #18 and #12 AWG hung in the clear, which is the condition the published constants assume. Select the #14 AWG option to reproduce the ARRL 231/f ground-plane figure, the insulated option when the wire carries a PVC or polyethylene jacket, and the tubing option for 5/8-inch or larger elements, which reproduces the ARRL 221/f figure. If you have measured your own wire on a previous build, enter that ratio as a custom factor.
Set the units to feet and inches, to metres, or to both. Set the trim allowance to the percentage of extra wire you want on each end before tuning; three percent is a sensible default. Finally, if you plan to build a quarter-wave matching section, choose the velocity factor of the cable you will use, and the results will include its physical length. Press Calculate antenna length, and the scale drawing under the form redraws to match the antenna you chose, with the principal dimension annotated.
Worked example: cutting a 20-metre dipole for 14.175 MHz
Suppose you want a flat-top dipole centred on the 20-metre band. The FCC allocation runs from 14.000 to 14.350 MHz, so the mid-band frequency is 14.175 MHz. You will use #16 bare hard-drawn copper, hung between two trees, so the conductor factor stays at 1.000.
The free-space wavelength is 983.571 divided by 14.175, which is 69.39 feet, or 21.15 metres. Half of that free-space wavelength is 34.69 feet. That figure is a physics reference point, not a cutting instruction, and cutting to it would put resonance roughly 5 percent low, near 13.5 MHz.
The resonant physical length is 468 divided by 14.175, which is 33.02 feet. Converting the fractional foot, 0.016 feet is 0.19 inches, so the flat top is 33 feet 0.2 inches from end to end. Each leg is half of that, 16.51 feet, or 16 feet 6.1 inches, measured from the centre insulator to the end insulator. With a 3 percent trim allowance you would actually cut two legs of 17.00 feet each, giving 34.01 feet of wire in the air before tuning.
ARRL teaching material points out that installation height moves the effective constant across a band from about 460/f to about 490/f, and that 468/f is rarely exactly right. At 14.175 MHz that range is 32.45 to 34.57 feet, a spread of more than two feet. The calculator prints that window so you know how much trimming to expect rather than assuming your antenna analyser is broken when the first sweep is not centred.
If you plan to feed the dipole through a quarter-wave section of RG-213, whose solid polyethylene dielectric has a velocity factor of 0.66, the physical length of that section is 245.89 multiplied by 0.66 and divided by 14.175, which is 11.45 feet. Note how differently the velocity factor behaves here: it shortens the cable by a third, whereas end effect shortens the radiator by only five percent.
US amateur band reference and calculated lengths
The frequencies below are the mid-band points of the allocations published in 47 CFR 97.301 for ITU Region 2, which covers the United States. Individual operating privileges inside each band depend on licence class, and the 60-metre band is channelised rather than continuous.
| Band | Allocation (MHz) | Mid-band f (MHz) | Half-wave dipole 468/f | Quarter-wave vertical 234/f | Full-wave loop 1005/f |
|---|---|---|---|---|---|
| 160 m | 1.800-2.000 | 1.900 | 246.32 ft (75.08 m) | 123.16 ft (37.54 m) | 528.95 ft (161.22 m) |
| 80/75 m | 3.500-4.000 | 3.750 | 124.80 ft (38.04 m) | 62.40 ft (19.02 m) | 268.00 ft (81.69 m) |
| 60 m | 5.332-5.405 (5 channels) | 5.3585 | 87.34 ft (26.62 m) | 43.67 ft (13.31 m) | 187.55 ft (57.17 m) |
| 40 m | 7.000-7.300 | 7.150 | 65.45 ft (19.95 m) | 32.73 ft (9.98 m) | 140.56 ft (42.84 m) |
| 30 m | 10.100-10.150 | 10.125 | 46.22 ft (14.09 m) | 23.11 ft (7.04 m) | 99.26 ft (30.25 m) |
| 20 m | 14.000-14.350 | 14.175 | 33.02 ft (10.06 m) | 16.51 ft (5.03 m) | 70.90 ft (21.61 m) |
| 17 m | 18.068-18.168 | 18.118 | 25.83 ft (7.87 m) | 12.92 ft (3.94 m) | 55.47 ft (16.91 m) |
| 15 m | 21.000-21.450 | 21.225 | 22.05 ft (6.72 m) | 11.02 ft (3.36 m) | 47.35 ft (14.43 m) |
| 12 m | 24.890-24.990 | 24.940 | 18.77 ft (5.72 m) | 9.38 ft (2.86 m) | 40.30 ft (12.28 m) |
| 10 m | 28.000-29.700 | 28.850 | 16.22 ft (4.94 m) | 8.11 ft (2.47 m) | 34.84 ft (10.62 m) |
| 6 m | 50.000-54.000 | 52.000 | 9.00 ft (2.74 m) | 4.50 ft (1.37 m) | 19.33 ft (5.89 m) |
| 2 m | 144.000-148.000 | 146.000 | 3.21 ft (0.98 m) | 1.60 ft (0.49 m) | 6.88 ft (2.10 m) |
| 1.25 m | 222.000-225.000 | 223.500 | 2.09 ft (0.64 m) | 1.05 ft (0.32 m) | 4.50 ft (1.37 m) |
| 70 cm | 420.000-450.000 | 435.000 | 1.08 ft (0.33 m) | 0.54 ft (0.16 m) | 2.31 ft (0.70 m) |
Antenna families, feed-point impedance and pattern
Length is only half of the design. The feed-point impedance decides whether 50-ohm coaxial cable is a reasonable match or whether you need a transformer, and the pattern decides whether the antenna is useful for the contacts you want.
| Antenna | Length rule | Feed-point impedance | Gain reference | Practical notes |
|---|---|---|---|---|
| Half-wave dipole | 468/f feet, total | About 72 ohms in the clear | 2.15 dBi in free space | Broadside radiation, nulls off the ends; a 1:1 current balun keeps RF off the coax shield |
| Inverted V | 468/f feet, total | Lower than a flat top, often near 50 ohms | Bent dipole, pattern rounds out | One support only; drooping legs usually resonate lower, so trim more than for a flat top |
| Quarter-wave vertical | 234/f feet, element only | About 35 ohms over a good ground plane | Equivalent to a half-wave dipole | Needs radials; sloping the radials raises the impedance, and about 45 degrees of droop lands roughly halfway to 72 ohms |
| Full-wave loop | 1005/f feet, total perimeter | Typically 100 to 130 ohms | Slightly above a dipole when horizontal | No end effect; a square is the easiest shape to support and comes closest to the ideal circle |
| End-fed half-wave | 468/f feet, single wire | Thousands of ohms at the end | Same as a half-wave dipole | Needs a 49:1 or 64:1 transformer and a counterpoise; there is no second leg to measure |
Interpreting the calculated length and the first SWR sweep
Treat the calculated length as the centre of a target, not as a machining tolerance. Build with the trim allowance in place, hoist the antenna to its final height with the feed line connected exactly as it will be used, and sweep the standing wave ratio across the band with an analyser or a vector network analyser rather than with a transmitter.
Read the frequency of minimum SWR. To first order, resonant frequency and physical length are inversely proportional, so a small fractional change in length produces the same fractional change in frequency in the opposite direction:
If the dip is 200 kHz low on a 14.175 MHz dipole, that is 1.4 percent, so about 1.4 percent of 33.02 feet, roughly 5.5 inches, needs to come off the total, which means about 2.8 inches from each leg. Take small bites, sweep again, and stop when the dip sits where you want it. On the higher HF bands the same fractional change is only a couple of inches, so measure carefully.
Height matters as much as length. A horizontal dipole at half a wavelength above ground develops a lower take-off angle useful for long-haul work, while the same antenna at a quarter wavelength or less radiates mostly upward, which suits regional near-vertical-incidence contacts. The results panel prints both of those heights for your frequency so you can judge what your supports allow.
Limitations and assumptions behind rule-of-thumb antenna constants
These constants are engineering approximations with a real spread, and the calculator is honest about that rather than implying four-digit precision. The main assumptions are worth stating plainly.
The constants assume thin wire in the clear. ARRL material is explicit that the effective dipole constant runs from roughly 460/f to 490/f depending on height, and that 468/f is rarely exactly right. The same source gives 234/f, 231/f and 221/f for a ground plane depending on whether the element is generic, #14 wire or 5/8-inch tubing. Expect a percent or two of error before you trim.
Nearby objects retune the antenna. Metal roofs, gutters, aluminium siding, chain-link fencing, other antennas and wet foliage all couple to the element and shift resonance. So does the feed line itself if common-mode current is allowed to flow on the coax shield, which is why a current balun on a balanced antenna is not optional.
The loop constant is the least precise of the three. Loop resonance depends on conductor diameter and on the shape of the loop, and 1005/f is a rule of thumb tied to roughly square horizontal loops of ordinary wire. Triangles, deltas and very fat conductors will land elsewhere.
Impedance figures are nominal. The 72-ohm dipole and 35-ohm ground-plane values are free-space and ideal-ground references. Real ground conductivity, height, radial count and radial layout move them substantially, and an end-fed half-wave in particular has an end impedance that varies over a wide range with the counterpoise arrangement.
This tool does not model gain, pattern, efficiency or matching networks. It computes lengths. For pattern and impedance prediction use a NEC-based modelling package, and always verify a build with a measurement rather than a calculation.
Regulatory and safety limits apply. Operating privileges within each band depend on your licence class under 47 CFR Part 97, and the 60-metre band is restricted to five channels. Never install an antenna where it could reach a power line, and follow the National Electrical Code requirements for amateur station grounding and lightning protection.
Frequently asked questions about antenna length calculations
Why is a half-wave dipole shorter than half a free-space wavelength?
A half wavelength in free space is 492/f feet, but a real wire is not in free space. Charge stored between the wire ends, the end insulators and nearby objects makes the antenna behave as though it were electrically longer than it measures, so the physical wire has to be cut about 5 percent short to resonate. That correction turns 492/f into the familiar 468/f.
Is the 468/f dipole constant a velocity factor?
No. Velocity factor describes how slowly a wave travels inside a transmission line such as coaxial cable, where a solid polyethylene dielectric gives roughly 0.66. A bare antenna wire radiates into air, so its wave speed is essentially the speed of light. The 5 percent shortening in 468/f comes from end effect and the length-to-diameter ratio of the conductor, not from a slow dielectric.
Why does the calculator use 1005/f for a full-wave loop instead of 984/f?
A closed loop has no free ends, so it has no end effect to shorten it. A resonant one-wavelength loop is actually a little larger than one free-space wavelength, and the long-standing amateur rule of thumb published with the Loop Skywire design is a total perimeter of 1005/f feet, about 2 percent longer than the free-space 984/f.
How much wire should I add before trimming to resonance?
Add the trim allowance shown in the results, which defaults to 3 percent. Length and resonant frequency are inversely proportional to first order, so removing 1 percent of the wire raises the resonant frequency by roughly 1 percent. Cutting long lets you trim down to the target frequency; cutting short forces you to splice.
Does installation height change the length I should cut?
Yes. ARRL teaching material notes that height above ground moves the effective dipole constant across roughly 460/f to 490/f, and that the textbook 468/f is rarely exactly right. Expect the resonant frequency of a wire antenna to shift when you raise or lower it, especially below about a quarter wavelength of height.
Where does the coaxial matching section length come from?
A quarter-wave matching stub is measured in electrical degrees along the cable, so it does depend on velocity factor. The calculator multiplies the free-space quarter wavelength of 245.89/f feet by the velocity factor you select, which gives 11.45 feet at 14.175 MHz for solid-polyethylene coax with a velocity factor of 0.66.
Sources. Antenna length constants, the free-space relations and the end-effect explanation follow ARRL (the national association for amateur radio), Antennas 101 - The Basics by Ward Silver N0AX, published by ARRL, which gives the free-space wavelength as c/f or 300/f in metres, the free-space half wavelength as 492/f in feet, the installed dipole range as 460/f to 490/f, and the ground-plane element as 234/f feet with 231/f for #14 wire and 221/f for 5/8-inch tubing (arrl.org). The 468/f dipole formula is stated as Length (feet) = 468/frequency (MHz) in ARRL's Single Band Dipoles technical page (arrl.org) and as "Wire length (feet) = 468/f, f in MHz" in the ARRL Basic Antennas product notes (arrl.org). The 1005/f full-wave loop perimeter is the rule of thumb introduced with the Loop Skywire antenna by D. Fischer W0MHS in QST, November 1985, and carried in the ARRL loop-antenna literature. Band edges and the five 60-metre channels are taken from the FCC rules at 47 CFR 97.301 and 97.303(h), Amateur Radio Service (govinfo.gov). The speed of light in vacuum, 299 792 458 m/s exactly, is the SI defining constant published by NIST and the BIPM.
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Arcade Mini-Game: Ham Radio Antenna Length Calculator Calibration Run
Use this quick arcade run to practice separating useful scenario inputs from common planning mistakes before you rely on the calculator output.
Start the game, then use your pointer or arrow keys to catch useful inputs and avoid bad assumptions.