Quarter-Wave Vertical Antenna Calculator
Calculate quarter-wave vertical antenna length and ground radial dimensions for any amateur radio frequency.
Includes loading coil for shortened verticals.
Quarter-Wave Vertical A quarter-wave (λ/4) vertical monopole is one of the most common amateur radio antennas. It is a single vertical element fed at the base, with a ground plane (radials or earth ground) acting as the other half of the antenna system. The antenna resonates at the design frequency with a feedpoint impedance of about 36.5 Ω over a perfect ground plane. In practice the figure you measure is higher than that, because soil loss under the radials adds resistance in series with it. The section on ground loss below explains why that makes a flat SWR reading a poor test of how well the antenna is working.
Element Length Formula L = 71.3 / f (meters), which is the free-space 75/f shortened by the roughly 0.95 velocity factor of real wire. Or: L = (234 / f) feet, the same standard cutting formula (f in MHz). Full half-wave dipole: 142.6/f (m). The vertical is half of that. In free space: λ/4 = 74.95/f exactly. Real wire ends up 3 to 5% shorter, so cut long and trim to lowest SWR (Standing Wave Ratio).
Ground Radials Ground radials are horizontal wires at the base of the antenna, simulating an infinite ground plane. Minimum: 4 radials at 90° spacing. Optimal: 16 to 64 radials. Radial length: ideally λ/4 each (same as the vertical). Shorter is acceptable. Elevated radials (above ground): 2 to 4 radials at exact λ/4 work as well as many buried radials. Buried radials: go at 2 to 5 cm depth, and 16 or more radials for best ground loss reduction.
Ground Loss, And Why A Perfect SWR Can Be Bad News A resonant full-size λ/4 vertical over a perfect ground plane feeds at about 36.5 Ω. Everything above that number is loss resistance in the soil under your radials, and it burns transmit power as heat without radiating any of it. This calculator uses the following ground loss figures, which sit in the middle of the range published from the Brown, Lewis and Epstein measurements onward:
| Radials | Ground loss | Feedpoint Z | SWR to 50 Ω | Efficiency |
|---|---|---|---|---|
| 4 | ~35 Ω | ~71.5 Ω | 1.43:1 | ~51% |
| 8 | ~20 Ω | ~56.5 Ω | 1.13:1 | ~65% |
| 16 | ~10 Ω | ~46.5 Ω | 1.08:1 | ~78% |
| 32 | ~5 Ω | ~41.5 Ω | 1.20:1 | ~88% |
| 64 | ~2.5 Ω | ~39.0 Ω | 1.28:1 | ~94% |
Read the SWR column, then read the efficiency column. Four radials and sixty-four radials give you almost the same SWR, 1.43 against 1.28, and a difference in radiated power of nearly 3 dB. The meter on the front of the radio cannot see the thing that actually matters here.
That is the trap with ground-mounted verticals. The antenna comes out of the box, you throw down four radials, the SWR reads flat, and it looks finished. It is not finished. Half the transmit power is warming the dirt under your feet, and no amount of tuning at the shack end will get it back. The only fix is more copper in the ground, and the SWR meter will barely acknowledge that you did it.
Mobile/Loaded Verticals For HF bands (160m, 80m, 40m), a full λ/4 may be impractically tall. A loading coil placed at the base (base-loading) or center (center-loading) electrically lengthens a shorter antenna. The base-loading inductance here comes from the standard thin-wire monopole model. The element behaves like an open-circuited transmission line of characteristic impedance Zo = 60 x (ln(2h/a) - 1), where h is the physical height and a the conductor radius, so its base reactance is X = -Zo x cot(2πh/λ). The coil has to cancel whatever is left after subtracting the reactance the full-size element would have shown, and L (µH) = X / (6.2832 x f in MHz).
That is why conductor diameter is an input. A fat aluminum tube has a lower Zo than thin wire and needs noticeably less inductance for the same height. Coil Q is assumed to be 200, which is realistic for a well-made air-wound coil and optimistic for a small commercial mobile whip.
Radiation Resistance Of A Shortened Element Radiation resistance falls fast as the element gets shorter, and it is what decides how much of the power reaching the base actually leaves the antenna. The figure used here is Rr = 36.5 x (h / full-size λ/4)^2.235, an exponent fitted to the published radiation-resistance curve so it lands on 36.5 Ω at full size and on about 1 Ω at 0.05λ. Treat it as a first-order estimate: it runs 10 to 15% high through the middle of the range.
Common Band Lengths (λ/4) 160m (1.85 MHz): ~38.5 m | 80m (3.65 MHz): ~19.5 m | 40m (7.1 MHz): ~10 m 20m (14.1 MHz): ~5.1 m | 10m (28.4 MHz): ~2.5 m | 6m (50.2 MHz): ~1.4 m 2m (144.2 MHz): ~49 cm | 70cm (432 MHz): ~16.5 cm
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