0.4877
m
48.77
cm
1.6
ft
19.2
in
0.4877
m
36.5
Ω
0.4877
m
48.77
cm
1.6
ft
19.2
in
0.4877
m
36.5
Ω
The Quarter Wave Antenna Calculator determines the physical length of a quarter-wave monopole antenna — one of the most widely deployed antenna types in the world. From the rubber duck antennas on hand-held radios to cellular base station antennas, marine VHF whip antennas, and broadcast AM towers, the quarter-wave vertical monopole is ubiquitous in wireless communications due to its simplicity, effectiveness, and ease of matching to standard 50 Ω transmission lines with the addition of a ground plane.
The quarter-wave monopole operates on the same principle as one half of a dipole antenna. When mounted above a conducting ground plane, the ground plane acts as a mirror, and the image of the antenna below the plane creates the electrical equivalent of a complete half-wave dipole. The result is a low-profile radiating element that is half the physical size of a dipole but exhibits similar electrical characteristics — with the key difference that all radiated power is directed into the upper hemisphere, resulting in approximately 5.19 dBi theoretical gain (compared to 2.15 dBi for a dipole).
The antenna length is calculated using the formula L = 75/f(MHz) meters (equivalent to about 246/f(MHz) feet in imperial units), which incorporates the practical velocity factor correction of approximately 0.95–0.97. More precisely, L = (λ/4) × VF = (c / (4 × f)) × VF, where c = 299.792 m/MHz. This calculator allows the velocity factor to be adjusted for different conductor materials and installation conditions.
The ground plane is essential for the quarter-wave monopole. It can be the earth itself (for AM broadcast towers and buried radial systems), a vehicle body (mobile VHF/UHF antennas), an aircraft fuselage, or a set of radial wires extending outward from the antenna base. For portable and base station antennas, a ground plane of three or four radial wires at approximately 45° below horizontal is common. The number of radials affects the feed impedance: with perfect ground, the theoretical impedance is approximately 36.5 Ω; with practical radial systems, it varies from about 30–50 Ω depending on the number and length of radials.
For a perfect match to 50 Ω coaxial cable, the radials of a ground-plane antenna are typically drooped downward at about 45°, which increases the feed impedance to approximately 50 Ω — eliminating the need for a matching network. This technique is widely used in VHF and UHF base station antennas.
Quarter-wave antennas are preferred over half-wave dipoles in many applications because they require only a single conductor (plus a ground reference), have a lower radiation angle (better for long-distance mobile communications), and can be constructed mechanically as a rigid whip antenna. This calculator provides all necessary dimensions including the radial wire length (also λ/4) for building a complete ground-plane antenna system.
The element length is computed as L = (c / (4 × f_MHz)) × VF meters, where c = 299.792458 m/MHz. For a standard wire antenna, VF = 0.95 is recommended. The radials for a ground-plane antenna are the same length as the main element (λ/4 each). Feed impedance is shown as an approximation based on the number of radials selected — perfect ground gives ~36.5 Ω, which increases slightly with fewer, drooped radials.
Build the antenna with the element and radials slightly longer than calculated (add 5% extra). Trim for minimum SWR at the desired frequency. For a 50 Ω match without a matching network, droop the radials to approximately 45° below horizontal — this modification raises the feed impedance to near 50 Ω. Confirm with an antenna analyzer or SWR meter before transmitting at full power.
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A quarter-wave vertical for 146 MHz is about 48.7 cm (19.2 inches) long, with four radials of the same length for the ground plane.
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A quarter-wave CB antenna at 27.185 MHz is approximately 2.62 m (8.6 ft) long — typical of the 9-foot CB whip antennas used on vehicles.
The quarter-wave monopole is only half of a complete dipole. The ground plane provides the missing half as a mirror image through electromagnetic reflection. Without a proper ground plane, the antenna's radiation pattern and feed impedance are undefined and the antenna will perform poorly. The ground plane can be the earth, a vehicle body, a set of radial wires, or any other large conducting surface.
The minimum practical number is 3 radials (arranged 120° apart). Four radials (90° apart) are more common and provide good performance. For best efficiency, especially at lower frequencies, more radials are better — AM broadcast towers often use 120 or more buried radials. For portable and base station VHF/UHF antennas, 3–4 radials drooped at 45° provide both adequate ground reference and natural 50 Ω impedance match.
Three common methods: (1) Droop the radials to 45° below horizontal — this raises feed impedance from ~36.5 Ω to ~50 Ω; (2) Use a 1.5:1 impedance transformer (matching network); (3) Install the antenna over a large ground plane (vehicle roof, metal plate) and accept the slight SWR of 1.46:1. Most modern HF and VHF transceivers tolerate SWR up to 1.5:1 without issue.
A quarter-wave monopole over a perfect ground plane has approximately 5.19 dBi gain versus 2.15 dBi for a free-space dipole — a difference of about 3 dB. This gain comes from the fact that the ground plane reflects all downward radiation back upward, concentrating all power into the upper hemisphere. Over real earth with a limited radial system, the practical gain advantage is typically 1–2 dB over a dipole at the same height.
Technically yes, but performance will be poor and unpredictable. The outer conductor of the coaxial feed line will carry return current and become part of the 'antenna,' leading to pattern distortion, RFI, and operator RF exposure issues. A simple choke at the feed point (ferrite bead balun) can help, but proper radials are always the better solution.
A 5/8-wave antenna (L = 5λ/8 = 2.5 × quarter-wave) provides approximately 3 dBi more gain toward the horizon compared to a quarter-wave, because its radiation pattern is flatter (more horizontal). This makes 5/8-wave antennas popular for mobile VHF/UHF communications. However, the 5/8-wave antenna is not self-resonant and requires a matching coil at the base to resonate at the feed point.
Thicker conductors have a slightly higher capacitance per unit length, which reduces the velocity factor slightly and shortens the required physical length. As a rule of thumb, for conductor diameters up to about 1% of the wavelength, the effect is small (less than 1%). For very thick elements like those used in UHF base station antennas, this factor is important and antenna manufacturers provide specific length data for their element dimensions.
1) Cut the vertical element to the calculated length (add 5% extra for trimming). 2) Cut four radials to the same length. 3) Solder or clamp the radials to the outer conductor of a PL-259 or N-type connector chassis. 4) Solder the vertical element to the center pin. 5) Mount and adjust element and radials to 45° droop. 6) Check SWR with an analyzer and trim the vertical element for minimum SWR at target frequency.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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