For resonant antennas, the most important parameter is length relative to wavelength. The free-space wavelength is λ = c / f, where c = 299,792,458 m/s. From there, every antenna type is a fraction of λ chosen to make the antenna resonate (low SWR) at the desired frequency.
Half-wave dipole
A wire half a wavelength long, fed at the center. The classic balanced antenna. Theoretical free-space length is λ/2, but the wire's velocity factor (~0.95 for thin wire in air) and end-effect capacitance reduce this slightly. Most ham radio handbooks use the shorthand length (ft) = 468 / f_MHz or length (m) = 142.65 / f_MHz — both bake in a ~0.95 reduction. Each half is half the total.
Quarter-wave monopole
Half a dipole stood vertically against a ground plane (the ground plane "mirrors" the missing half, effectively making a dipole). Length is λ/4. Used for AM broadcast verticals, CB whips, WiFi router monopoles. Needs a good ground plane — a metal car body for VHF, radials for HF, or copper-tape sheet for UHF.
5/8-wave vertical
A taller monopole that gives ~3 dB more gain than a 1/4-wave because it concentrates radiation at a lower elevation angle (better for long-distance VHF/UHF mobile). Length is 5λ/8. Requires a matching network (loading coil) at the base since 5/8 is not resonant by itself.
Yagi-Uda array (Yagi)
A driven element (resonant dipole) plus parasitic elements: reflector behind it (~5% longer), director(s) in front (~5% shorter each). Element-length ratios used by this tool: reflector 0.5 λ, driven 0.473 λ, director 0.45 λ — typical 3-element starting point from antenna handbooks. Adding more directors increases forward gain. Spacing between elements is also critical (0.1–0.25 λ); use NEC modeling for final tuning.
Why is the practical dipole shorter than λ/2?
Two effects shorten it: (1) the velocity of EM waves on a conductor is slightly less than c (typically 95% for thin copper wire in air), and (2) "end-effect" capacitance at the wire tips adds an apparent extra length. Combined, an idealized λ/2 wire actually resonates at ~95% of that length. Insulated wire is slower still (~85–92%); for HF balanced lines you often want VF = 0.95, for thick aluminum tubing VF = 0.92.
What's the "468 / f" formula?
An old-school ham radio rule of thumb: half-wave dipole length in feet = 468 / frequency in MHz. The 468 implicitly bakes in the velocity factor and end-effect for typical 12-gauge wire. In metric: length in meters = 142.65 / f_MHz. This calculator's "VF · λ/2" form makes the underlying physics explicit — you can vary VF for different conductors.
Do Yagi element lengths depend on element thickness?
Yes, somewhat. Thicker elements (larger diameter relative to length) resonate slightly shorter due to capacitive end-effect being more pronounced. The 0.473 / 0.5 / 0.45 ratios used here assume "moderate" element diameter typical of 6-12 mm aluminum tubing. For wire Yagis or very fat tubular elements, you'd want NEC2 / 4nec2 modeling for precise lengths. These calculator values are a 90%-correct starting point — final tuning is empirical.
Why doesn't a quarter-wave monopole need a balun?
Because it's not balanced — one terminal is the antenna, the other is the ground plane. Coaxial cable's outer conductor connects to the ground plane and inner conductor to the antenna element; this is naturally "unbalanced," matching the antenna's unbalanced nature. A balanced antenna like a dipole DOES need a balun (or current-choke) to avoid currents flowing on the outside of the coax shield, which would radiate from the feedline.
How does antenna height affect resonance?
For HF dipoles, height above ground (in wavelengths) affects the impedance significantly. At λ/2 above ground (e.g., 10 m for a 20m dipole), impedance is close to the free-space 73 Ω. Lower than ~λ/4 above ground, impedance drops, often to 30–50 Ω, and the radiation pattern becomes mostly straight up (NVIS — Near Vertical Incidence Skywave, useful for regional comms). At very low heights the SWR also worsens. Height doesn't change the resonant length much (just a few percent), but it dramatically changes the impedance match and radiation pattern.
Is this calculator accurate for WiFi / 2.4 GHz antennas?
For free-space λ/4 vertical (often used in routers), yes — ~3.1 cm × VF ≈ 2.9 cm. For PCB trace antennas, microstrip, dielectric-loaded chip antennas, etc., you need different math accounting for the substrate's dielectric constant (effective VF drops to 0.5 or below). This tool gives the "in-air" reference; for PCB design use the relevant microwave-design formulas or HFSS / CST simulation.