Here is a formula and calculator for creating a loaded (shortened) quarter wave vertical or balanced dipole. The original javascript was created by Prof Jack Ponton from The University of Edinburgh. As seen on his page, the original formula seems to come from an article by J. Hall, “Off-center loaded dipole antennas”, QST Sept 1974, 28-34. Please see the original javascript for additional references. The formula is below:

Original formula from QST Sept, 1974.

Original formula from QST Sept, 1974.

I used this formula and it seemed to work pretty accurately for centre loaded quarter wave antennas on the 160m band. The original formula was in inches and feet, so with Jack’s permission, I have modified the script to work with metric units, and this is presented below.

Frequency MHz
Length of vertical or dipole element Metres
Coil position (Distance from feedpoint) Metres
Wire diameter (Millimetres) mm
Loading coil calculated inductance ┬ÁH

The calculation refers to either a loaded 1/4 wave (typically a vertical, in which case flip the picture below through 90o) or a loaded dipole, in which case the dimensions refer refer to one arm and two coils will be required. I used centre loaded. Base loaded will require a lower inductance and more towards the top will require more inductance. The antenna can therefore be matched by creating a fixed inductor at say the centre and moving it up or down until you have a good match on your desired frequency. You will need a good ground system with an end fed quarter wave, but use two in a dipole for a nice shortened loaded dipole antenna.

Antenna

Antenna