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.
At any rate, this article is certainly worth reading.
I feel lucky I always measure in meters. It’s as easy as that L(m)=300/f and of course you can make the dipole 5% shorter if it should be too long. Never had to make my dipoles longer ;-) 73, Bas
Love your blog very useful! :-) i like your layout to check out my ham website http://www.m6ceb.co.uk 73 matt m6ceb
Excellent! Thank you 73 kj7ern
Thank you for explaining this it’s like most things we are taught about how to use a formula yet I cannot recall even asking where these numbers originated.
Using Tandy Radio shack engineer notebooks, the author provides the formula
For 1/4
L = 234 divided by F (MHz)
Eg 1/4 La wavelength
Whip = 234 divided by 27= 8.67 Ft
Yet at no point does the author explain why
Here’s me 30 years later saying
Thank you very much
You’re welcome!
Did you account for the velocity factor of insulated wire used in the general building of a dipole? For example, THHN wire, which I would guess is what 80+% of HAMs use to build a dipole, had a velocity factor of 95. Take your number of 468/Freq, and then Multiply that by .95. You’re going to end up being VERY close to the correct length.
I went from Tech to Extra in a month with HamStudy.org
Supply & demand? Why would someone buy clothes at the mall when the same clothes are given away free on 235.225,298,337,871 other places in town?
Not being sarcastic or critical, but if the pool questions are all the same, what makes you “study guide” better than all the rest? I get the “I invested my time” thing, unfortunately, you’ve invested your time in something everyone else gives away free, inluding the FCC.
In other words, I could “invest my time” into making paper mache swans in my garage. Just becuase I chose to invest my time doesn’t make them worth anything. Whether I invest 5 minutes or 5 days into folding a piece of paper into a swan, they’re still worth the same price….nothing.
You know, I’d give you a serious answer, if you’d included your name and call sign. But, since you didn’t, I’m just going to blow off this comment.
Maybe my logic is way off but could it be this?:
Convert 300 million meters/s to feet/s = 984.25 million f/s. It’s half wave so divide by 2 = 492.125. Reduce 492.125 by 5% for wire vs free space and it equals 467.518. That rounds to 468.
Please forgive me if I’m way off base – I’m a newbee
This seems to work, and it looks like possible explanation for 468, however the units do not work out. You still get the velocity ft/sec. But maybe NoAX did come up with 468 ft/sec, and it worked. So he said…close enough! I have been searching for the origin of 468, this one sounds good!
KD2WOW
Love your call sign, Marci. I collect QSLs from stations whose call signs spell words.
Hi Dan, After Marci’s comment post, you said you collect callsigns that
spell words. Well, how about “things?”. Mine is: KA6DVR..
Kids born recently might not recognize it. But, older hams like
meself recognize a certain nostalgia in it.
Here’s another trivia, I read in a book about famous people’s callsigns, that KA6DVR was at one time Charlton Heston’s callsign.
Yes, he was a radioman in WW-II.
Have not been able to fully vett this
callsign info out. But, I run with it.
I’ve resisted the urge to include acronyms in my collection. I’m not exactly sure why, though. Maybe at some point, I’ll start a separate collection.