Free Quarter-Wave Vertical Antenna Calculator for US Amateur, CB, and GMRS Radio

The Vertical as Half a Dipole

A center-fed half-wave dipole works because it has two quarter-wave elements, one on each side of the feedpoint. Current flows in one leg and returns through the other. The radiation comes from the acceleration of these charges along the conductor. A quarter-wave vertical eliminates the lower half of the dipole and replaces it with an electrical mirror: the ground system. The earth itself, or a collection of horizontal wires called radials, acts as the missing conductor. RF current flows down the vertical element, through the feedpoint connector, out along the radials, and returns to complete the circuit. Without a good ground return, the current has nowhere to go and instead flows back up the outside of the coaxial feedline shield, causing pattern distortion, RF in the shack, and mysterious VSWR readings.

This is why the ARRL Antenna Book dedicates more pages to vertical antenna ground systems than to the vertical element itself. The element is just wire cut to length. The ground system determines whether the antenna is a contest-grade performer or a dummy load with a stick on top.

Feedpoint Impedance: Why 36 Ohms Is the Target, Not 50 Ohms

A common point of confusion is that the quarter-wave vertical’s natural feedpoint impedance is approximately 36 ohms, not 50 ohms. This compares to a half-wave dipole’s 73 ohms. The 36-ohm figure assumes a perfect, infinite ground plane. In real installations, the actual impedance depends heavily on the ground system quality. With only a few radials on imperfect soil, resistance in the ground path adds to the feedpoint impedance, often pushing it above 50 ohms. With a large number of buried radials approaching a perfect ground, the impedance settles back toward 36 ohms.

This means a quarter-wave vertical with 4 radials might show 55 ohms at the feedpoint, producing a 1.1:1 SWR on 50-ohm coax. The same antenna with 16 radials might show 41 ohms, giving 1.2:1. Both are usable without a matching network. The calculator models this relationship dynamically for any radial count you select.

Alternatively, an elevated ground-plane antenna using 4 radials drooped at 40 degrees below horizontal naturally presents a feedpoint impedance near 50 ohms, enabling a direct coax connection without any matching network. This is why most commercial VHF and UHF ground-plane antennas use four drooped radials at approximately this angle.

Radiation Pattern: The Key Advantage Over Horizontal Dipoles

A horizontal dipole has a figure-eight radiation pattern with maximum radiation broadside to the wire. More importantly, the elevation angle of maximum radiation depends strongly on height above ground. At 33 feet height on 20 meters (about half wavelength), a horizontal dipole has a radiation elevation angle of approximately 30 degrees. A quarter-wave vertical over a good ground system radiates at much lower elevation angles, often 5 to 15 degrees, regardless of how close it is to the ground. This low-angle radiation travels farther via ionospheric propagation for long-distance (DX) contacts. For operators primarily interested in working stations across North America or overseas, this low-angle pattern advantage is significant and helps explain why many competitive DX operators favor a vertical over a dipole.

Quarter-Wave vs 5/8-Wave: When Each Makes Sense

The 5/8-wave vertical is 15 percent taller than a quarter-wave version, which creates both advantages and complications. The advantage is pattern compression. A 5/8-wave element concentrates slightly more energy at lower elevation angles compared to a quarter-wave, giving approximately 1.2 dBi more gain than the quarter-wave over the same ground system. For long-distance HF work, this is a meaningful improvement. For VHF repeater access in a hilly area, this extra low-angle gain can make the difference between a clear signal and a marginal one.

The complication is that a 5/8-wave element is not self-resonant at a convenient feedpoint impedance. The element presents an inductive reactance of approximately +j90 ohms at its feedpoint, in addition to a resistive component similar to the quarter-wave case. To achieve resonance, a series inductor (called a matching coil) must be connected in series with the feedpoint to cancel this reactance. This calculator computes the required inductance automatically when you select 5/8-wave mode.

For most US amateurs building their first vertical, the quarter-wave is the right choice: simpler, cheaper, easier to tune, and only marginally less effective than the 5/8-wave version. Save the 5/8-wave for VHF and UHF installations where the mechanical length is manageable and the pattern compression advantage is most pronounced, or for HF competition stations where every decibel counts.

FCC Part 97 Antenna Requirements for Amateur Stations

Unlike some countries that impose physical antenna restrictions, the FCC’s Part 97 rules for amateur radio do not specify antenna types, heights, or construction details beyond the fundamental requirement to operate the station in accordance with good engineering practice and to use the minimum power necessary to maintain communications. The practical constraints come from local zoning, HOA covenants, and structure loading requirements. FCC rules do specify maximum transmitter output power by band, license class, and frequency, which this calculator displays when it identifies your target frequency as an amateur band. The FCC’s antenna regulations guide is useful background for operators navigating local restrictions.

Radial Count vs Feedpoint Impedance (Ground-Mounted)

Source: NEC-4 modeling data from ARRL Antenna Book, Radial Systems chapter. The first 8 radials produce the largest improvement; adding more shows diminishing returns after 32.

Element Length: Starting from Exact Physics

The free-space wavelength is calculated using 299,792,458 m/s (NIST-defined exact speed of light), giving lambda = 299.792458 / f(MHz) meters. A quarter of this is the theoretical element length. The velocity factor K for your selected conductor is then applied: element_length = (lambda / 4) times K. For #14 AWG copper wire with K = 0.951, this simplifies to 234 / f(MHz) feet, the familiar ARRL formula. For 1/2-inch aluminum tubing with K = 0.982, the formula yields 241 / f(MHz), producing a slightly longer cut for the same frequency.

Radial Length Calculation

Radials are quarter-wave conductors, same formula as the element. For elevated resonant radials, exact quarter-wave tuning is important because they form the electrical return path and affect feedpoint impedance significantly. For buried or on-ground radials, the exact length matters less because the soil provides an additional current path, and the ARRL recommends running radials as long as physically practical regardless of exact electrical length. This calculator shows quarter-wave radial length as the design target.

Total Radial Wire Budget

The total radial wire figure (radial count times individual length) is a direct input for materials planning. A 40-meter vertical with 16 radials at 32.5 feet each requires 520 feet of wire, approximately two standard 500-foot spools of #14 copper wire from a hardware store. Running this calculation before ordering materials prevents the common experience of returning to the hardware store mid-project.

Feedpoint Impedance Model

The ground-mounted feedpoint impedance is modeled using a lookup table derived from NEC-4 (Numerical Electromagnetics Code version 4) antenna modeling software results, as published in the ARRL Antenna Book radial systems chapter. The table maps radial count to feedpoint resistance: 2 radials gives approximately 75 ohms, 4 radials gives 55 ohms, 8 radials gives 46 ohms, and the impedance asymptotically approaches 36 ohms as radial count increases toward 120.

The elevated ground-plane impedance model uses an empirical relationship between the number of radials and their droop angle below horizontal. With 4 horizontal radials (0 degrees droop), impedance is approximately 36 ohms. At 40 degrees droop, impedance rises to approximately 50 ohms, a direct 50-ohm coax match. With only 2 elevated radials, the symmetry change produces approximately 50 ohms regardless of droop angle, which is why many commercial VHF antennas use 2 or 4 drooped radials for a clean 50-ohm feed.

5/8-Wave Matching Coil

The 5/8-wave element presents approximately +j90 ohms of inductive reactance at its feedpoint. The required series inductance to cancel this reactance is L = 90 / (2 times pi times f_MHz) microhenries. At 14.225 MHz this equals approximately 1.01 microhenries. A practical coil for HF use can be wound using 16 to 20 turns of #14 wire on a 1-inch diameter form, adjusting turn spacing until the reactance cancels and SWR minimizes. Commercial 5/8-wave VHF antennas typically include this matching coil factory-wound and integrated into the base connector assembly.