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Antenna

Half-Wave Dipole Antenna Calculator

Calculate dipole antenna length for any frequency — enter MHz, get half-wave and quarter-wave dimensions in mm. Includes gain (2.15 dBi), radiation resistance (73 Ω), and 50 Ω VSWR. Supports velocity factor for insulated wire.

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Formula

Lλ/2=vf⋅c2f,Zin≈73.1 Ω,G=2.15 dBiL_{\lambda/2} = \frac{v_f \cdot c}{2f}, \quad Z_{in} \approx 73.1\,\Omega, \quad G = 2.15\,\text{dBi}

Reference: Balanis, "Antenna Theory: Analysis and Design", 4th ed., Chapter 4

L_{λ/2}— Half-wave dipole total length (m)
v_f— Velocity factor of the wire
c— Speed of light (299 792 458 m/s) (m/s)
f— Operating frequency (Hz)
Z_{in}— Input impedance (radiation resistance) (Ω)
G— Antenna gain (dBi)

How It Works

Dipole antenna calculator computes resonant length, feed impedance, and bandwidth for any frequency — antenna engineers, amateur radio operators, and wireless system designers use this to design practical antennas and establish the gain reference (dBd). A center-fed conductor exactly lambda/2 long resonates with 73.1 ohms radiation resistance and 2.15 dBi gain (0 dBd by definition), per Balanis's 'Antenna Theory: Analysis and Design' (4th ed.) and IEEE Standard 145-2013.

The physical length L = 0.95 * lambda/2 = 142.5/f_MHz meters accounts for end effects that make resonant length 5% shorter than free-space half wavelength. Radiation pattern is omnidirectional in the H-plane (perpendicular to antenna axis) with figure-eight pattern in the E-plane (along antenna axis), providing maximum radiation broadside to the element. Bandwidth (VSWR < 2:1) is approximately 5-10% of center frequency for typical wire dipoles.

Feed impedance at resonance is 73.1 + j0 ohms in free space per Kraus's 'Antennas' (3rd ed.). Height above ground affects impedance: at lambda/4 height, impedance drops to 50-60 ohms (better match to 50-ohm coax); at lambda/2 height, impedance rises to 85-100 ohms. Folded dipoles (300 ohms) are used with ladder line or 4:1 baluns. The dipole's simplicity, predictable characteristics, and well-documented behavior make it the starting point for all antenna education.

Worked Example

Problem: Design a half-wave dipole for the 2-meter amateur band (144-148 MHz) with direct 50-ohm coax feed.

Design per Balanis methodology:

  1. Center frequency: f_c = 146 MHz
  2. Free-space half wavelength: lambda/2 = 150/146 = 1.027 m
  3. Practical length with end effect: L = 142.5/146 = 0.976 m (97.6 cm total)
  4. Each element: 97.6/2 = 48.8 cm
Impedance analysis:
  1. Free-space impedance: 73.1 ohms (theoretical)
  2. Mount at lambda/4 height (51 cm) for 50-60 ohm match to coax
  3. VSWR to 50 ohms: (73.1/50) = 1.46:1 (acceptable without matching)
  4. Mismatch loss: 0.18 dB (96% power transfer)
Bandwidth verification:
  1. Q factor (typical wire dipole): approximately 15
  2. Bandwidth = f_c/Q = 146/15 = 9.7 MHz
  3. 2:1 VSWR bandwidth: approximately 140-150 MHz — covers entire 2m band
Construction recommendations:
  1. Use 12 AWG copper wire or 6 mm aluminum tubing for mechanical stability
  2. Include 1:1 current balun at feedpoint to prevent feedline radiation
  3. Secure center insulator with UV-resistant housing for outdoor installation
  4. Tune by trimming 1 cm at a time while monitoring VSWR with antenna analyzer
Expected performance:
  • Gain: 2.15 dBi (0 dBd) — reference for all comparisons
  • F/B ratio: 0 dB (bidirectional)
  • Polarization: linear (horizontal if mounted horizontally)

Practical Tips

  • ✓For quick deployment, cut elements 3% long and trim to resonance — it's easier to shorten than lengthen; use antenna analyzer or VNA to find minimum VSWR point
  • ✓Mount horizontally for horizontal polarization (typical for VHF/UHF weak-signal work) or as inverted-V (apex up, 90-120 degree included angle) for broader coverage and easier single-support installation
  • ✓For multiband operation, use fan dipole (multiple dipole pairs from same feedpoint) or trap dipole — resonant traps isolate sections for different bands

Common Mistakes

  • ✗Using free-space lambda/2 without end-effect correction — resonant length is 95% of theoretical due to capacitive loading at wire ends; a 2.4 GHz dipole cut at 62.5 mm will resonate at 2.28 GHz, not 2.4 GHz
  • ✗Omitting balun causing feedline radiation — coax outer conductor carries common-mode current that radiates, distorting pattern and causing RF in the shack; always use a 1:1 current choke balun
  • ✗Ignoring ground proximity effects — a dipole at 0.1 lambda height has 50% lower radiation resistance and distorted pattern; mount at least lambda/4 above ground for predictable performance
  • ✗Expecting perfect 50-ohm match — resonant dipole is 73 ohms; VSWR 1.46:1 is normal and acceptable; forcing exact 50 ohms with matching network adds loss and complexity

Frequently Asked Questions

Inversely proportional: L = 142.5/f_MHz meters for half-wave dipole with end-effect correction. At 7 MHz (40m band): L = 20.4 m. At 144 MHz (2m): L = 0.99 m. At 2.4 GHz (WiFi): L = 59 mm. Higher frequencies mean shorter, more compact antennas. The 142.5 constant (approximately c/2 * 0.95) accounts for the 5% shortening from end capacitance. For different wire diameters, constant varies 140-146: thicker conductors have more end effect.
The 73.1-ohm value derives from solving Maxwell's equations for a thin, perfectly conducting, center-fed half-wave antenna in free space per Balanis analysis. It represents the real part of feed impedance at resonance where the reactive component is zero. This is NOT a design choice but a fundamental electromagnetic property. Variations occur: folded dipole = 292 ohms (4x), off-center feed increases impedance, proximity to ground changes value. The 73 ohms is close enough to 50 and 75 ohm standards that direct coax connection is practical.
A simple dipole is inherently narrowband (5-10% bandwidth). Multi-frequency options: (1) Fan dipole: multiple dipole pairs cut for different bands, fed from single point — elements must be separated to avoid interaction. (2) Trap dipole: resonant traps (LC circuits) isolate sections; outer section resonates lower band when trap opens at higher frequencies. (3) Multiband dipole with tuner: use antenna tuner to match, accepting efficiency loss from non-resonant operation. (4) Off-center-fed dipole (Windom): 1/3-2/3 feed point provides resonance at fundamental and third harmonic. Best efficiency: dedicated single-band dipoles.
2.15 dBi is the maximum gain of a half-wave dipole relative to an isotropic radiator (hypothetical point source radiating equally in all directions). Since isotropic antennas cannot physically exist, the dipole serves as the practical reference — gain relative to a dipole is expressed in dBd, where 0 dBd = 2.15 dBi. An antenna with 8.15 dBi gain has 6 dBd gain (6 dB better than dipole). The 2.15 dB difference comes from the dipole's figure-eight pattern concentrating energy broadside to the wire versus isotropic's uniform sphere.
Using the standard formula L = 142.5/f_MHz: L = 142.5/144 = 0.990 m total (99.0 cm), or 49.5 cm per element. For 12 AWG wire: use 143/144 = 99.3 cm. For 1/2-inch aluminum tubing: use 141/144 = 97.9 cm. Start 2-3% long (102 cm) and trim while measuring VSWR. Mount at least 50 cm above ground (lambda/4) for proper impedance. With 1:1 balun to 50-ohm coax, expect VSWR 1.3-1.5:1 at resonance without additional matching.
73 ohms is the electromagnetic reality of a resonant half-wave dipole per Maxwell's equations — it's physics, not design. The 50-ohm coax standard evolved from transmission line tradeoffs (compromise between minimum loss at 77 ohms and maximum power at 30 ohms). Solutions: (1) Accept 1.46:1 VSWR with direct connection (0.18 dB mismatch loss — negligible). (2) Cut dipole slightly short of resonance for 50-55 ohm impedance with small capacitive reactance. (3) Use lambda/4 matching section of 60-ohm coax (RG-62). (4) Use a 4:1 balun with folded dipole (292 ohms / 4 = 73 ohms). For most applications, direct connection with 1:1 balun is sufficient.
Simple construction for 144-148 MHz: (1) Cut two 49.5 cm pieces of stiff copper wire or aluminum rod. (2) Mount on center insulator with SO-239, BNC, or direct solder to coax. (3) Add 1:1 current balun: wind 6-8 turns of feedline coax (RG-58 or RG-174) on a 5-6 cm diameter form, or use 10 ferrite beads on coax. (4) Mount horizontally or as inverted-V at 120-degree angle. (5) Tune by trimming 5 mm at a time to minimize VSWR at 146 MHz. For SDR receive-only: balun is optional but improves pattern; add LNA at antenna for best weak-signal performance. Total cost: under $10 in materials.

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