In telecommunication, radio horizon is the locus of points at which direct rays from an antenna are tangential to the surface of the Earth. If the Earth were a perfect sphere and there were no atmospheric anomalies, the radio horizon would be a circle. To compute the radius of the circle drawn on the earth in such a case use the formula:

Radio Horizon = 1.23 * sqrt(Antenna Height)

This is the straight line of sight horizon where Antenna Height is in feet and the Radio Horizon is in miles. The equivalent formula for an antenna height in metres and a radio horizon in kilometres would be

RH = 3.56 * sqrt(antenna height).

Note 1: The radio horizon of the transmitting and receiving antennas can be added together to increase the effective communication range.

Note 2: Antenna Heights above 1 million feet (1966 miles - 3157 kilometres) will cover the entire hemisphere and not increase the radio horizon.

VHF and UHF radio signals will bend slightly toward the earth's surface. This bending effectively increases the radio horizon and therefore slightly increases the formula constant. The ARRL Antenna Book gives a constant of 1.415 for weak signals during normal tropospheric conditions.

In practice, radio wave propagation is affected by atmospheric conditions, and the presence of obstructions, e.g., mountains and the effective radiated power from the transmitter.

References:

• The ARRL Antenna Book, 19th Edition, R. Dean Shaw, pp 22-25
• Federal Standard 1037C, in support of MIL-STD-188