Antenna Length Calculator
Antenna Length Calculator (Dipole, Quarter-Wave and Loop)
Frequency to free-space wavelength, then the lengths you actually cut: a half-wave dipole and each of its legs, a quarter-wave whip or ground-plane, a 5/8-wave vertical and a full-wave loop — in metres, centimetres, inches and feet, with the end-effect factor exposed.
antenna length
A half-wave dipole for 145 MHz, end-effect factor 0.95
Wavelength first, then the element
half-wave dipole = 0.5 λ k each leg = 0.25 λ k quarter-wave vertical = 0.25 λ k
5/8-wave vertical = 0.625 λ k full-wave loop circumference = λ k
in imperial: free-space half wave = 491.79 ÷ f(MHz) feet, and ×0.95 gives the familiar 468 ÷ f(MHz)
- lambda
- the free-space wavelength: how far the wave travels in one cycle
- c
- 299,792,458 m/s, exact by the SI definition of the metre
- k
- the end-effect or velocity factor, about 0.95 for thin wire in free air. Lower for fat elements, insulated wire, or anything near ground
- 468
- the traditional constant for a half-wave dipole in feet. It is 491.79 x 0.95164 – the end-effect factor baked into a round number
- 5/8
- not a resonant length. It is chosen for its radiation pattern and needs a base loading coil
Worked example
A half-wave dipole for 145 MHz, end-effect factor 0.95
λ = 299,792,458 ÷ 145,000,000 = 2.068 m
A free-space half wave is 1.034 m; multiplied by the 0.95 end-effect factor that becomes 982.1 mm overall
Each leg is half of that: 491 mm, or 19.33 inches
Check it against the old imperial rule: 468 ÷ 145 = 3.228 ft = 0.9838 m, the same answer to a millimetre or two, because 468 is simply 491.79 × 0.9516
A quarter-wave vertical for the same frequency is 491 mm, and a full-wave loop is 1.964 m round
Half-wave dipoles for the bands people build for
| Band | Frequency used | Free-space λ | Dipole, total | Each leg | Each leg, inches | Quarter-wave | Where it applies |
|---|---|---|---|---|---|---|---|
| 40 m amateur | 7.15 MHz | 41.929 m | 19.916 m | 995.8 cm | 392.05 in | 995.8 cm | 7.000–7.300 MHz in ITU Region 2; 7.000–7.200 MHz in Regions 1 and 3 |
| 20 m amateur | 14.18 MHz | 21.149 m | 10.046 m | 502.3 cm | 197.76 in | 502.3 cm | 14.000–14.350 MHz, the same worldwide |
| 10 m amateur | 28.85 MHz | 10.391 m | 4.936 m | 246.8 cm | 97.16 in | 246.8 cm | 28.000–29.700 MHz, the same worldwide |
| 6 m amateur | 52.00 MHz | 5.765 m | 2.738 m | 136.9 cm | 53.91 in | 136.9 cm | 50–54 MHz in the US; 50–52 MHz in much of Region 1 |
| 2 m amateur | 146.00 MHz | 2.053 m | 0.975 m | 48.8 cm | 19.20 in | 48.8 cm | 144–148 MHz in the US; 144–146 MHz in Region 1 |
| 70 cm amateur | 435.00 MHz | 0.689 m | 0.327 m | 16.4 cm | 6.44 in | 16.4 cm | 420–450 MHz in the US; 430–440 MHz in much of Region 1 |
| 433.92 MHz ISM | 433.92 MHz | 0.691 m | 0.328 m | 16.4 cm | 6.46 in | 16.4 cm | An ITU ISM band in Region 1 only, “subject to local acceptance”; it overlaps the 70 cm amateur band |
| 868.3 MHz SRD | 868.30 MHz | 0.345 m | 0.164 m | 8.2 cm | 3.23 in | 8.2 cm | The European short-range-device band, 863–870 MHz. NOT an ITU ISM band, and not available in Region 2 |
| 915 MHz ISM | 915.00 MHz | 0.328 m | 0.156 m | 7.8 cm | 3.06 in | 7.8 cm | 902–928 MHz, ITU Region 2 only, with some exceptions |
| 2.45 GHz ISM | 2,450.00 MHz | 0.122 m | 0.058 m | 2.9 cm | 1.14 in | 2.9 cm | 2.400–2.500 GHz, the one major ISM band available worldwide |
Why the answer is a starting length, not a final one
Everything here begins with one division. The wavelength is the speed of light divided by the frequency, and because the metre is defined by fixing c at exactly 299,792,458 m/s, that division is exact. At 145 MHz the wavelength is 2.068 m; at 2.45 GHz it is 122.4 mm. Half of it, a quarter of it and five-eighths of it are the three lengths almost every simple antenna is built from.
The end effect. A dipole cut to exactly half a free-space wavelength does not resonate at the frequency you wanted — it resonates lower. Two things cause it: the current travels slightly slower along a conductor than a wave does in free space, and the electric field fringes out past the physical ends, so the antenna is electrically longer than it looks. The correction is a factor of roughly 0.95 for thin wire well clear of everything, and it gets smaller as the element gets fatter, as insulation is added, and as the antenna comes down towards the ground. Published figures for the factor run from about 0.94 to 0.98 depending on the length-to-diameter ratio. That range is why this page puts the factor in your hands rather than burying it.
Where 468 comes from. The old amateur rule is “length in feet = 468 ÷ frequency in megahertz”. A free-space half wave in feet is 491.79 ÷ f(MHz); multiply that by 0.95 and you get 467.2, which somebody rounded to 468. Working backwards, 468 corresponds to an end-effect factor of 0.9516. It is a perfectly good rule for thin wire on the HF bands and a poor one for a fat aluminium element at VHF, which is exactly what you would expect of a constant with one assumption baked into it.
Cut long, trim short. Every antenna book gives the same advice and it is right: make the first version a few per cent longer than the calculation, then shorten it a little at a time and watch the resonance move up. You cannot put wire back. Expect to trim — the surroundings matter more than most builders expect, and a dipole at a quarter wavelength above ground behaves differently from the same dipole at a half. Measure the result with an antenna analyser and convert what it tells you with the VSWR and return loss converter. The quarter-wave vertical is a special case worth spelling out: it is half a dipole, with the ground plane acting as the other half, so it needs radials or a real metal plane, and its feedpoint impedance is about half the dipole’s.
A word on the ISM bands. Which one you may use depends on where you are. 433.05–434.79 MHz is an ITU ISM band in Region 1 only and subject to local acceptance; 902–928 MHz is Region 2 only; 2.400–2.500 GHz is the one that is worldwide. The European 863–870 MHz band that 868 MHz modules use is a short-range-device allocation, not an ITU ISM band, and does not exist in Region 2 — which is exactly why the same product is sold as an 868 MHz version in Europe and a 915 MHz version in North America. The physics on this page does not care; the regulator does.
For the feedline that carries the power to it, the VSWR and return loss converter and the L-network matching calculator; for the transmitter power in dBm, the dBm to watts calculator; and for a trace on a circuit board rather than a wire in the air, the microstrip impedance calculator.
Frequently asked questions
How long should a dipole be?
About 0.95 of a half wavelength in total, split into two equal legs. For 145 MHz that is 982.1 mm overall and 491 mm per leg. Cut it a few per cent long and trim it down while watching the SWR.
What is the 468 formula for a dipole?
Length in feet = 468 ÷ frequency in MHz. It is the free-space half wave, 491.8 ÷ f(MHz) feet, multiplied by an end-effect factor of about 0.952. It works well for thin wire on HF and less well for thick elements at VHF and above.
How long is a quarter-wave antenna for 433 MHz?
16.4 cm with a 0.95 factor, or 6.46 inches — and it needs a ground plane. For a small module that usually means a copper pour under the connector, which is why the same whip performs differently on different boards.
Why is my antenna resonant below the frequency I calculated?
Because it is electrically longer than it is physically — that is the end effect. If you cut to the free-space half wave with no correction, resonance lands about 5% low. Shorten it. The same thing happens when you add insulation or bring the antenna close to ground or to metal.
What velocity factor should I use for a dipole?
0.95 for bare thin wire in the clear. Use less for a fat tubular element (its larger diameter increases the end effect), less again for insulated wire, and less still for an antenna mounted close to a roof or to other conductors. Treat the number as a first guess and let the trimming find the real one.
Is 868 MHz an ISM band?
Not in the ITU sense. The European 863–870 MHz band is a short-range-device allocation under European rules; the ITU ISM bands nearby are 433.05–434.79 MHz in Region 1 and 902–928 MHz in Region 2. That regional split is why the same radio module ships as an 868 MHz part in Europe and a 915 MHz part in North America.
Related calculators
References
- Electronics Notes. Dipole antenna length: calculation and formula. “length (feet) = 492 A / f”, with the familiar “468 / frequency” obtained by “multiplying it by the typical A or end effect factor of 0.95”; and the standing advice to “make any prototype antenna slightly longer than the calculations might indicate and then shorten the antenna”.
- American Radio Relay League. The ARRL Antenna Book, and the ARRL Frequency Allocations chart for the US amateur bands used in the table below. The half-wave dipole’s traditional 468/f(MHz) feet is 492/f (a free-space half wave) times an end-effect factor of about 0.95.
- Wikipedia contributors. ISM radio band, reproducing the ITU Radio Regulations table: 433.05–434.79 MHz “only in Region 1, subject to local acceptance”; 902–928 MHz “Region 2 only (with some exceptions)”; 2.4–2.5 GHz “Worldwide”. The European 863–870 MHz band is a short-range-device allocation, not an ITU ISM band.
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure), 9th ed., 2019 — the speed of light fixed at exactly 299,792,458 m/s, which is where every wavelength on these pages comes from.