Formulas for Antennas and Feedlines
Here are some formulas that are useful in antenna design and should be kept handy for all antenna experimenters. These formulas can be found in the ARRL handbook and other similar books, but since not everyone in the world has access to these publications, the formulas are being presented here for all to see and use. The quad formulas came from the book “All about Cubical Quads”by Bill Orr, and the Yagi formulas came from the Radio Handbook, by Bill Orr.
General formulas
Length of a 1/2 wave antenna in free space
Length in ft = 492/F (Frequency in MHz)
Length of a wire 1/2 wave antenna
Length in ft = 468/F (Frequency in MHz) up to 30 MHz
For 50 MHz to 144 MHz, length in feet = 460/F(Frequency in MHz)
For 144 MHZ, 5600/F(Frequency in MHz)
Vertical quarter wave antenna
Length (in feet) = 234/F (Frequency in MHz)
Full wave Loop (in feet)
Length =1005/F (Frequency in MHz)
Length of a Harmonically Operated Doublet
Length = (K-.05)x492/F (Frequency in MHz), where K = number of half waves in antenna and Length = feet
Cubical Quads
Side dimension length in feet for single band with stub tuned reflector
Length = 248/F (Frequency in MHz), Spacing in feet = S-118/F (Frequency in MHz)
Side dimensions for single band quad using closed loop reflector
Length 1 = 250/F (Frequency in MHz) for driven element
Length 2 = 258/F (Frequency in MHz) for reflector element
Element Spacing = S=118/F ( Frequency in MHz)
Full Sized X-Beam
Arm Length in feet = 195/F (Frequency in MHz)
Driven element Tail Length in feet = 106.5/F (Frequency in MHz) for each Tail
Total Director element Length in feet = 575/F (Frequency in MHz)
Driven element Tail Length in feet = 106.5/F (Frequency in MHz) for each Tail
Director Tail Length = 92.5/F (Frequency in MHz) for each Tail)
Small Sized X-Beam
Arm Length in feet = 177/F (Frequency in MHz)
Driven element Tail Length in feet = 603/F (Frequency in MHz) for each Tail
Total Director element Length in feet = 575/F (Frequency in MHz)
Director Tail Length in feet = 110.5/F (Frequency in MHz) for each Tail
2 Element Yagi
Driven element Length in feet = 476/F (Frequency in MHz)
Director Length in feet = 450/F (Frequency in MHz)
Element Spacing in feet = 120/F (Frequency in MHz)
3 Element or more, Yagis
Driven element Length in feet = 473/F (Frequency in MHz)
Reflector Length in feet = 501/F (Frequency in MHz)
Director Length in feet = 445/F (Frequency in MHz)
For 4 elements, use the same 450/F for the first and second and third Directors.
This is for element spacings of .2 wavelength for both 4 and five elements.
Element length formulas are the same for a 5 element yagi.
For a 3 element wide spaced yagi, using .25 wavelengths spacing for Reflector and Director, the only change is that the formula for first element length is now the same as for the directors for a four or 5 element yagi.
Originally posted on the AntennaX Online Magazine by Richard Morrow, K5CNF
Last Updated : 9th March 2024