DIPOLE ANTENNA CALCULATIONS

A dipole antenna is typically designed to be a half-wavelength long at its resonant frequency. Two quarter wave lengths, one on each side of feed point or center insulator to make a half wavelength.
The wavelength (λ lambda) is calculated with the speed of light (c) divided by
the frequency (f): λ = c / f.

The speed of light is approximately 300,000,000 meters per second or 300 Million meters per second.
The speed of light is approximately 984,000,000 feet per second or 984 Million feet per second.
Therefore, a half-wavelength in feet is calculated (c ÷ f) ÷ 2 or 984,000,000 ÷ f ÷ 2 = 492,000,000/f.
A half-wavelength in meters is (c ÷ f) ÷ 2 or 300,000,000 ÷ f ÷ 2 = 150,000,000/f.
The formula for feet 468,000,000 ÷ frequency or 468 ÷ (frequency in MHz) provides a practical length for a half-wave dipole in feet.

This velocity factor of wire is approximately 95% or 0.95 the speed of light. So you can take the speed of light times 95% or 0.95 to calculate the speed of RF in the wire. For coax, it is best to do a measurement with specialized equipment to find velocity factor accurately.
The number 468 is used to calculate the speed of RF in wire to determine the length of wire for a dipole and is derived from the half-wavelength calculation, incorporating a velocity factor of wire to account for the fact that radio waves travel slightly slower in a wire than in a vacuum or open air (492 x 0.95=467.5 or 468 rounded up).

The formula for length in meters is 142,500,000 ÷ frequency or 142.5 or 143 rounded up (frequency in MHz), provides a practical length for a half-wave dipole in feet.
The number 143 is derived from the half-wavelength calculation, incorporating a velocity factor to account for the fact that radio waves travel slightly slower in a wire than in a vacuum (150 x 0.95=142.5 or 143 rounded up).

For example, for 7.2 MHz, the calculation would be 468 ÷ 7.2 = 65 feet. Each half of the dipole or leg would be half of 65feet (65 ft ÷ 2) = 32.5 feet long.
This same example for 7.2 MHz in meters is 143 ÷ 7.2 = 19.86 meters. Each half of the dipole or leg would be half of 19.86 meters = 9.93 meters.

Side note, 7.2 MHz is in the 20 meter band and 19.86 meters is really close to 20 meters.