Hong Life CalculatorsUnderstanding the antenna length calculator — concept and principle
This calculator gives the free-space wavelength for a frequency and the practical cut lengths for a half-wave dipole and a quarter-wave element (vertical, ground-plane or whip). It is a quick starting point for building wire and rod antennas for amateur radio, FM, airband, ISM and other bands.
How it is calculated
- Wavelength: λ (m) = c / f = 299.792458 / f (MHz), using the speed of light c = 299,792,458 m/s.
- Half-wave dipole: L = (λ / 2) × VF, shown in centimetres (total length, tip to tip).
- Quarter-wave: L = (λ / 4) × VF, also in centimetres.
VF is the shortening factor. For thin wire in air it is commonly about 0.95; thicker elements need a smaller factor, and an element inside insulation or plastic is shorter still.
The principle
An antenna resonates when its length lets a standing current wave fit with zero current at the open ends. For a dipole this happens at about half a wavelength; for a monopole over a ground plane, the ground acts as a mirror and supplies the missing half, so a quarter wavelength resonates. Real elements resonate a little shorter than the ideal length because of fringing capacitance at the ends (the end effect) and the finite thickness of the conductor. At resonance the impedance is mostly resistive: roughly 73 Ω for a thin dipole in free space and about half that, roughly 36 Ω, for an ideal quarter-wave monopole.
Worked example
- λ = 299.792458 / 146 ≈ 2.0534 m.
- Ideal half-wave: 2.0534 / 2 = 1.0267 m = 102.67 cm.
- Half-wave dipole: 102.67 × 0.95 ≈ 97.54 cm total, so each leg is about 48.8 cm.
- Quarter-wave: 2.0534 / 4 × 0.95 × 100 ≈ 48.77 cm.
| Frequency (MHz) | Half-wave dipole (cm) |
|---|---|
| 36.5 | 390.14087 |
| 73 | 195.070435 |
| 110 | 130.0469567 |
| 146 | 97.5352175 |
| 182 | 78.028174 |
| 219 | 65.02347833 |
| 292 | 48.76760875 |
How to read the result
Treat the result as a cutting guide, not a final length. Cut slightly long, measure SWR across the band, and trim: if the lowest SWR is below your target frequency, the element is too long. The familiar rule "468 / f(MHz) feet" for wire dipoles is the same idea with a factor of about 0.95. For a dipole, the length shown is the whole antenna; the feed point sits at the centre.
Common mistakes
- Cutting each leg of a dipole to the full half-wave length instead of half of it.
- Using the coaxial cable's velocity factor (such as 0.66) for the antenna element; that factor applies only inside the cable.
- Forgetting that nearby metal, ground height and insulation shift resonance.
- Trimming the element when the problem is really the feed line or the ground plane.
Frequently asked questions
Why is the practical antenna shorter than half a wavelength?
End capacitance and conductor thickness lower the resonant frequency, so the element must be trimmed a few percent short.
Can I use a quarter-wave antenna without a ground plane?
It needs a counterpoise such as radials, a car roof or a ground plane of similar size; without it, the feed cable becomes part of the antenna.
What is the 2 m band dipole length?
Near 146 MHz, about 97–98 cm overall, as in the example above.
Sources: Balanis, Antenna Theory: Analysis and Design, Wiley · The ARRL Antenna Book, ARRL