Radio Horizon Calculator (with Examples)

The Radio Horizon Calculator is used to find the the maximum horizon distance that a radio frequency (RF) signal can travel without interference from obstacles [1].

To find the range, enter the heights of both the Transmit and Receive antennas.


	

			

		

						

				

				

                

			

			
						

		

		






Formula





The Line of sight distance is given by





d =  3.57*(√h1 + √h2)





where 





    

  • d is the vacuum distance 
    • 




  • h1 and h2 are the antenna heights
    • 











The Radio Horizon service range is given by





dr =  4.12*(√h1 + √h2)





This equation includes the effect of atmosphere on the propagation path of RF signals.





Background





The calculator takes into consideration the height of the antenna and the curvature of the earth to determine the radio horizon distance. This distance is the point where the surface of the earth obstructs the signal.





Example Calculations





???? If the transmit and receive antenna are both 10 feet above the ground, the line-of-sight distance is calculated to be 12.5 km. The Radio horizon service range is 14.4 km. 





The radio service range gives the maximum range of a radio transmission. In practice this is limited by transmit power, receive sensitivity and obstructions like tall buildings and trees (for example).





Using the calculated service range to estimate radio range assumes the following: 





    

  1. Frequency of operation is above 30 MHz [1]
    2. 




  2. Transmit power PTx is high enough and Receive sensitivity (SRx) is low enough
    3. 






How do we check 2. above? 





Use the Antenna Range Calculator with PTx = +30 dBm, SRx = -110 dBm. The max range is 24 km which exceeds the Radio Horizon range for antennas that are 10 feet above the ground. The radios should therefore be able to communicate in the absence of any obstructions. 





However, for the same receiver sensitivity, if PTx = +10 dBm the max range drops to 2.4 km. In this case the radios will not be able to communicate over the service range. 





References





[1] Line of Sight on Wikipedia





Related Calculators





    

  • Line of Sight – Calculates the max range for a single antenna at a specified height above the earth
    • 




  • Antenna Range – Uses the free space path loss equations to calculate the range
    •