# 468: Ham Radio’s Magic Number

Here in the U.S.—where we still measure length in feet—468 is a magic number.  Why? Well, the formula for calculating the length, in feet, of a half-wave dipole antenna is:

L (ft) = 468 / f (MHz)

If you do the math, a half-wavelength is actually 492/f, so where did the number 468 come from? The explanation most often given these days is that a radio wave travels about 5% slower in wire than it does in free space, so the distance that a radio wave would travel in a wire is about 5% less than it would travel in free space.

Now, I don’t know about you, but while I’ve used this formula for building dipoles, I’ve never had one tune up perfectly using that number. There are a number of reasons for this, the main one being the height above ground of the dipole. What I’ve found is that the elements of the dipole are usually longer than they need to be.

I sometimes joke that whoever came up with that number did so so that hams wouldn’t cut their dipoles too short. After all, it’s much easier to make a length of wire shorter than it is to make it longer.

Ward, N0AX, wasn’t satisfied with any of the common answers to where the number 468 came from. In the latest issue of QST, he consulted the materials in the ARRL library and found the answer. The October 1926 issue of QST included an article titled, “The Length of the Hertz Antenna.” (“Hertz antenna” was the name most commonly used for a dipole in the early days of radio.)

The author of that article constructed nine different dipoles and measured their resonant frequencies. He then calculated a value, K, by which you’d multiply the wavelength to get the wire length in feet. If you multiply that number by 300, you’d get values ranging from 423 to 471.

The number 468 first appeared in the 1929 ARRL Handbook.

For this article, N0AX did a number of simulations of a 20m dipole at various heights, ranging from 1/8 wavelength to 2 wavelengths. He came up with numbers ranging from 466.4 to 483.4. This is somewhat at odds with my experience, although I must admit that I’ve never been able to get my dipoles up that high. That’s my guess for why my dipoles are almost always shorter than 468/f.