Antenna Length
Finds the free-space wavelength at a frequency and the quarter-wave and half-wave lengths to cut, shortened by a factor k for end effect or for the speed of a wave in a cable. Radio amateurs, RF technicians and antenna installers use it to cut dipoles, verticals and coax stubs.
The length equations
λ = c/f Lλ/4 = k·λ/4 Lλ/2 = k·λ/2
λ is the free-space wavelength, c the speed of light (299,792,458 m/s) and f the frequency. k is a factor no greater than 1 that shortens the free-space length to the length you actually cut.
For a wire antenna, k is the end-effect factor. Current can’t fall to zero exactly at the wire tip, so the wire behaves a little longer than it is and resonates when cut short. The usual rule cuts a half-wave dipole to 468/f ft with f in MHz [1]. That is 0.9516 of the free-space half wave, 491.8/f ft. For a coax stub, k is the cable’s velocity factor: 0.66 for the solid polyethylene dielectric of RG-58/U and RG-213/U [2]. Choosing an Element or line type fills in k. Choose Custom to enter your own.
Limits and common mistakes
- The 468/f rule is a starting point for thin wire well clear of the ground. Thick elements, insulation, nearby objects and height all change the resonant length. Cut a little long and trim while you watch the SWR.
- The Wavelength row is always the free-space value. Only the quarter-wave and half-wave rows include k.
- Don’t use the dipole factor for a coax stub, or the coax factor for a wire. A coax stub cut with k = 0.95 is far too long.
- Foam-dielectric coax has a higher velocity factor, often 0.78 to 0.88. Take it from the cable’s data sheet and enter it as Custom.
Worked example
Cut the wire for a half-wave dipole for the 20 m amateur band, centered on 14.2 MHz.
- Enter Frequency (f) 14.2 MHz.
- Choose Element or line type Thin-wire half-wave dipole or quarter-wave vertical (468/f ft rule): k = 0.9516.
- Press Solve. The Solution shows:
Wavelength (λ): 21.1121 m
Quarter-wave length: 5.02258 m
Half-wave length: 10.0452 m
Cut each leg of the dipole about 5.02 m long, for 10.05 m in all. Check: 468/14.2 = 32.96 ft, and 32.96 ft × 0.3048 = 10.05 m.
