Here is a formula and calculator for creating a loaded (shortened) quarter wave vertical or balanced dipole. The original javascript was created by Jack Ponton and can be seen here. 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.
I used this formula and it seemed to work pretty accurately for centre loaded quarter wave antennas on topband. The original formula was in inches and feet, so with Jack's permission, I have modified the script to work with metric units, and is presented below.
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.
