Why are dipoles shorter than a half wavelength?

This morning, a reader emailed me:

I love your study guide. Reading the ARRL technician guide has proven to be difficult for me but your study guide has helped tremendously! I would like your help to clarify something. When trying to figure out the length of a dipole antenna, you say to divide the wavelength in meters by two, change from meters to inches, and then multiply by .95. I’m curious where the .95 number comes from.

I replied:

Good question! Here’s how the book, The Fundamentals of Single Sideband, published by Collins Radio in the late 1950s, explains this:

Resonance occurs when [a dipole antenna’s] length is a half wave length or multiples thereof. A practical rectilinear conductor will resonate when it is slightly less than a half-wave in length due to the end effect. End effect is due to a decrease in inductance and an increase in capacitance near the end of the conductor, which effectively lengthens the antenna. End effect increases with frequency and varies with different installations. In the high-frequency region, experience shows that the length of a half-wave radiator is in the order of 5% less than the length of a half-wave in free space. The greater the diameter of the conductor, the greater the difference between its electrical and physical length.

In actual practice, the presence of supporting insulators, feed systems, and surrounding objects, such as the earth and other antenna elements have an aggregate effect upon the electrical length which may even exceed the variation in length caused by practical variations in conductor diameter. This makes the unknown length difficult if not impossible to predict under practical conditions. Therefore, the usual procedure is to cut or adjust the radiator to a length equal to or slightly less than the correct free-space physical length, check the characteristics of the antenna experimentally, and then alter the physical length as necessary.

This explanation is found in Chapter 9. There’s also an explanation of radiation resistance and other basic antenna topics. Those will be the subjects of future blog posts.

Here in the U.S, you’ll often see the formula l = 468/f(MHz) for the length of a resonant, half-wavelength dipole. Here’s how they get this:

λ(m) = 300/f(MHz)

where λ is the wavelength. Since there are 3.28 ft/m,

λ(ft) = 984/f(MHz)

and

λ(ft)/2 =  492/f(MHz).

Multiply that by 0.95, and you get

l = 0.95 x 492/f(MHz) = 468/f(MHz).

Of course, no matter how you calculate it, that’s only the starting point. Many different things can affect the length of a resonant dipole antenna, and some of these are installation-specific. To achieve the lowest SWR, you’ll need to adjust the length, once you have installed the antenna.