Formula
Wavelength is c times the velocity factor, divided by frequency. c is 299,792,458 m/s. The half-wave wire is half of that, times the end-effect factor. The quarter-wave is half of the half-wave. The default end effect, 0.95, shortens the wire for the capacitance of the ends. The 468 rule is 468 divided by megahertz, in feet. It is 492 × 0.95 rounded, and 492 is itself a rounding of the free-space half-wave in feet per megahertz.
λ = c × VF / f
L½ = (λ / 2) × end effect
feet ≈ 468 / fMHz
Ham buttons are band centers for a first cut, not the edges of a license. The wavelength calculator is the same speed without the end effect. Match the finished wire on the SWR calculator from a measurement, not from this length.
Worked examples
14.1 MHz, velocity factor 1, end effect 0.95. Wavelength 21.262 m. Half-wave 10.099 m, 33.13 ft. The 468 rule gives 33.19 ft.
146 MHz, same factors. Quarter-wave 0.488 m. Half-wave 0.975 m.
End effect set to 1. The half-wave is the free-space figure, and it will read longer than a wire you actually put up.
Reference
Band-center buttons: 160 m 1.9, 80 m 3.75, 40 m 7.15, 20 m 14.175, 15 m 21.225, 10 m 28.4, 6 m 52, 2 m 146 MHz.
Questions
How long is a half-wave at 14.1 MHz?
With velocity factor 1 and an end effect of 0.95, 10.099 m, which is 33.13 ft. The free-space half-wave before the end effect is 10.631 m.
What is the 468 rule?
468 divided by the frequency in MHz is a rounded feet rule for a half-wave wire. It is 492 × 0.95, and 492 itself is a rounding of c in feet per megahertz, divided by 2. This page shows the physics length and mentions 468 as that rounded rule.
Are the ham buttons the band edges?
No. They are planning centers: 1.9, 3.75, 7.15, 14.175, 21.225, 28.4, 52, and 146 MHz. They are not a band plan and not an antenna design.
Sources
- c = 299,792,458 m/s. Half-wave length (c / 2f) × velocity factor × end effect.
- The 468/fMHz rule is the rounded form of that half-wave in feet with an end effect near 0.95.