Quarter-Wave Vertical Antenna Calculator

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 ~36 Ω. A matching network or ground radials close to resonant length bring impedance closer to 50 Ω.

Element Length Formula L = 71.3 / f (meters) — the free-space 75/f shortened by the ~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). Vertical is half of that. In free space: λ/4 = 74.95/f exactly. Real wire ends up 3–5% shorter; 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: 16–64 radials. Radial length: ideally λ/4 each (same as the vertical). Shorter is acceptable. Elevated radials (above ground): 2–4 radials at exact λ/4 work as well as many buried radials. Buried radials: go at 2–5 cm depth; 16+ radials for best ground loss reduction.

Mobile/Loaded Verticals For HF bands (160m, 80m, 40m), a full λ/4 may be impractically tall. Loading coil: placed at the base (base-loading) or center (center-loading) to electrically lengthen a shorter antenna. The required inductance depends on the shortening amount and antenna diameter.

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