Dipole Length Formula: How to Cut a Half-Wave Dipole for Any Band
Almost every ham cuts a dipole at some point, and almost every ham asks the same first question: how long should the wire be? The short answer is the dipole length formula that appears in every handbook: total length in feet equals 468 divided by the frequency in megahertz, or about 142.5 divided by the frequency when you want meters. The longer answer explains why those numbers are not simply half a wavelength, what changes them in your backyard, and how to use the figure as a starting point rather than a final answer. This guide walks through the arithmetic, gives a cut table for the HF bands, and shows a repeatable method to trim the wire until the antenna is resonant where you actually operate.
Where 468 Comes From
A radio wave travels through free space at roughly 299,800 kilometers per second, so its wavelength in meters is about 299.8 divided by the frequency in megahertz. A half-wave dipole is, in theory, half of that, which is about 149.9 divided by the frequency. At 14.2 MHz the free-space half wavelength is therefore close to 10.56 meters. If you cut a wire to exactly that length and hang it up, you will find that it resonates noticeably higher in frequency than you planned. The wire is electrically a little longer than its physical length, or, put the other way round, the physical wire needs to be a little shorter than half a wavelength.
The ratio between the practical length and the free-space length is often called the shortening factor or the K factor. For a dipole made from ordinary wire it is typically around 0.95, and that is exactly where the familiar numbers come from. Multiply the free-space half wavelength of 491.8 divided by the frequency, in feet, by 0.95 and you get roughly 468 divided by the frequency. In meters the same arithmetic gives about 142.5 divided by the frequency. The Wikipedia article on the dipole antenna describes the half-wave dipole as the basic building block of many antennas and explains that real dipoles are slightly shorter than the theoretical half wavelength, which is the effect that the factor 0.95 captures.
Why a Real Dipole Is Shorter Than Half a Wavelength
Several effects combine to shorten the resonant length. Understanding them is more useful than memorizing the factor, because each one tells you what to expect when your installation differs from the textbook case.
- End effect. Current does not stop abruptly at the tip of the wire. The electric field spreads around the ends, which makes the antenna behave as if it were slightly longer than it is. The thicker the conductor is compared with its length, the stronger the effect.
- Conductor diameter. A thin wire for 80 meters is a very slender radiator, so its factor is close to 0.98. Aluminum tubing on 10 meters is stout relative to the wavelength, and its factor can drop to about 0.93.
- Insulation. Plastic-covered wire is slower than bare wire, because the dielectric around the conductor slows the wave along it. The wire must be cut a few percent shorter than a bare conductor of the same size. Our article on velocity factor and wire length covers this in detail.
- Height and surroundings. Ground, trees, gutters, masts and house wiring all load the antenna and move its resonance, usually downward in frequency. Height matters too, as discussed in our guide to antenna height and takeoff angle.
- Support ropes and end insulators. The wire loops through the insulators at the ends use up a few centimeters, and any rope near the tips adds a little capacitance. These small details can shift the result by tens of kilohertz on the lower bands.
Because the effects add up in ways that you cannot calculate precisely in a garden, treat the formula as the answer to the question where to start cutting, not where to stop.
The Formula Step by Step
The method has only three steps. First choose the frequency where you want the antenna to be resonant. Do not pick the middle of the band by reflex: pick the part where you will spend your time. On 80 meters in IARU Region 1 the band is much wider in percentage terms than the others, so a CW operator and an SSB operator should choose different frequencies. Second, divide 142.5 by that frequency in megahertz to get the total length in meters, or divide 468 by the frequency to get feet. Third, divide the result by two to get the length of each leg, measured from the feed point to the tip.
For example, to resonate a dipole on 7.1 MHz, divide 142.5 by 7.1. The answer is 20.07 meters in total, or 10.04 meters for each leg. In feet, 468 divided by 7.1 gives 65.9 feet. Add a little extra for the wire that is wrapped around the insulators, and, as explained below, keep a spare margin so that you can trim.
The same formula serves for any band, as the table shows. The frequencies in the table are examples chosen in the part of each band where many operators are active; replace them with your own.
| Band | Design frequency | Total length | Each leg | Total in feet |
|---|---|---|---|---|
| 80 m (CW end) | 3.55 MHz | 40.1 m | 20.1 m | 131.8 ft |
| 80 m (SSB end) | 3.70 MHz | 38.5 m | 19.3 m | 126.5 ft |
| 40 m | 7.10 MHz | 20.1 m | 10.0 m | 65.9 ft |
| 30 m | 10.125 MHz | 14.1 m | 7.0 m | 46.2 ft |
| 20 m | 14.20 MHz | 10.0 m | 5.0 m | 33.0 ft |
| 17 m | 18.10 MHz | 7.9 m | 3.9 m | 25.9 ft |
| 15 m | 21.20 MHz | 6.7 m | 3.4 m | 22.1 ft |
| 12 m | 24.94 MHz | 5.7 m | 2.9 m | 18.8 ft |
| 10 m | 28.50 MHz | 5.0 m | 2.5 m | 16.4 ft |
These lengths are for a straight horizontal dipole made of ordinary wire, at a reasonable height, away from large objects. Band edges differ between countries, so check the national band plan and the IARU band plan for your region before you pick the frequency.
Cut Long, Then Trim
The professional habit is to cut the wire about 5 percent longer than the formula result, then shorten it. A wire that is too short cannot be lengthened without splicing, while a wire that is a bit long can be trimmed at the tip. With the numbers above for 20 meters, you would start with 10.5 meters in total, or 5.25 meters per leg. Fold the surplus back along itself and tie it with a wire tie or tape rather than cutting at once, so that you can release it if you went too far.
Hang the antenna at the height and in the shape in which it will live, because moving it afterward changes the resonance. Connect an antenna analyzer or a NanoVNA with the cable that you will use, and sweep across the band. Our guide to the NanoVNA, calibration and sweeps explains how to calibrate and read the plot. Note the frequency at which the SWR is lowest. If it is below your target, the antenna is too long, which is what you expect from the extra 5 percent.
The Trimming Calculation
You do not have to trim by trial and error. The resonant frequency is inversely proportional to the length, so a simple proportion gives the new length. If your antenna resonates at 13.6 MHz and you want 14.2 MHz, multiply the present total length by 13.6 and divide by 14.2. For a total of 10.5 meters, the result is about 10.06 meters, so you should remove about 0.44 meters in total, or 22 centimeters from each tip.
Always trim a little less than the calculation suggests, and measure again. The relation is only approximate, because the end effect does not scale perfectly with length, and one cut is very hard to undo. Equal lengths on both legs keep the antenna balanced, so trim the same amount from each side. When the minimum SWR sits at your chosen frequency, fix the end loops permanently and write the final lengths on a tag at the feed point. That tag will save you a lot of trouble the next time you take the antenna down for the winter or for a storm.
Feed Point Impedance and What to Expect From the SWR
The dipole length formula tells you about resonance, which is the frequency at which the reactance is zero, not about the impedance at that point. A half-wave dipole in free space has a feed point resistance near 73 ohms. Close to the ground the figure changes with height, and it can fall well below or rise above that value as the height varies between a fraction of a wavelength and a full wavelength. A sloping or inverted-V dipole, with the ends drooping, usually has a lower impedance, often close to 50 ohms, which is one reason why it works so well with common coaxial cable. Our guide to the inverted V antenna explains what happens to the length and the impedance when the ends droop.
The practical consequence is that you should not expect an SWR of exactly 1.0 at resonance. A reading of 1.2 to 1.5 is normal and perfectly acceptable. If the minimum is much higher than that, the cause is more likely to be common-mode current on the feed line, a damaged connector or a poor ground than the length of the wire. A current balun or a choke at the feed point helps keep the coaxial shield from becoming part of the radiator and makes the sweep more repeatable.
Bent, Drooping and Crowded Dipoles
Not everybody has a clear 20-meter span. If space is tight, you can let the ends droop, bend them around a corner or run them back along a fence, at the cost of some efficiency and pattern. Each bend changes the resonant length: a drooping or folded wire usually needs to be cut a little longer than a straight one, because the ends are closer to each other and to the ground. A dipole whose ends hang down steeply will resonate higher than a straight one of the same wire length, so the correct move is to measure rather than assume.
The same caution applies when you build a multiband antenna. A fan dipole uses several wires cut for different bands at one feed point, and the wires interact. Cut each one for its own band and then trim in order, starting with the highest band, because the other wires change the result. Our article on the fan dipole shows the sequence and the usual spacing.
Common Mistakes
- Trusting the number blindly. The formula is a starting point. The actual resonance is whatever the analyzer shows when the antenna is in place.
- Measuring on the ground. A dipole lying on the grass or leaning against a wall resonates at a different frequency from one in the air. Measure at the working height.
- Using the wrong frequency. A dipole designed for 7.1 MHz is far from resonant at 7.0 MHz in percentage terms on 40 meters, which matters little, but for 80 meters a 100 kHz error is visible in the SWR curve. Decide first whether you operate CW, SSB or digital.
- Forgetting the insulation. Covered wire is shorter than bare wire for the same frequency. If your formula result worked for a bare conductor and you are using insulated wire, expect to trim a few percent more.
- Cutting both legs differently. Unequal legs are not wrong in themselves, but they make an antenna that is harder to understand. Keep them symmetric until you have a reason not to.
The Bottom Line
The dipole length formula, 468 divided by the frequency in feet or about 142.5 divided by the frequency in meters, is the practical form of half a wavelength after the shortening caused by end effect and conductor size. Use it to calculate a first length for your chosen frequency, cut the wire about 5 percent long, hang it where it will live, sweep it with an analyzer and trim with a simple proportion until the minimum SWR sits where you operate. Expect a result between 1.2 and 1.5, not a perfect 1.0, and treat a much higher figure as a sign that the feed line or the surroundings need attention. For more background on how the formula fits the wider subject, the ARRL Antenna Book reference page is a good place to continue.
Frequently Asked Questions
What is the formula for the length of a half-wave dipole?
The total length in feet is about 468 divided by the frequency in MHz. In meters it is about 142.5 divided by the frequency in MHz. Divide by two to get the length of each leg.
Why is a dipole shorter than half a wavelength?
The end effect makes the antenna behave as if it were slightly longer than the wire, so the physical wire must be shorter. The usual shortening factor is about 0.95, and it varies with the conductor diameter.
Should I cut the wire exactly to the calculated length?
No. Cut it about 5 percent long, hang it where it will be used, measure the resonance with an analyzer and trim the tips until the lowest SWR is at your chosen frequency.
How do I know how much to trim?
Multiply the present length by the measured resonant frequency and divide by the target frequency. Remove slightly less than the difference, then measure again.
Why is my dipole resonant at a lower frequency than calculated?
Insulated wire, nearby objects, a low height and extra rope or loops at the ends all lower the resonance. Trim the wire as the measurement shows.
What SWR should I expect from a dipole?
Usually between 1.2 and 1.5 at resonance with 50-ohm coaxial cable. A much higher value points to common-mode current, a poor connector or a difficult location rather than the length of the wire.