Calculate ham radio range, link budget, Fresnel zone clearance, and repeater distance from antenna height, frequency, power, and gain.
Ham Radio Range Formula
The following formula estimates the maximum line-of-sight (radio-horizon) range between a transmitter and receiver based on antenna heights, assuming standard atmospheric refraction (effective Earth radius factor k≈4/3).
R = 1.41 \cdot (\sqrt{H_t} + \sqrt{H_r})Variables:
- R is the maximum line-of-sight (radio-horizon) range in miles
- H_t is the height of the transmitter antenna in feet
- H_r is the height of the receiver antenna in feet
To estimate the maximum line-of-sight range, multiply 1.41 by the sum of the square roots of the heights of the transmitter and receiver antennas (in feet). (Metric equivalent: R in kilometers ≈ 4.12 · (√h_t + √h_r), with heights in meters.)
What is Ham Radio Range?
Ham radio range refers to the practical distance over which an amateur radio station can communicate. The achievable range depends strongly on frequency band and propagation mode. For VHF/UHF communication, range is often limited by line-of-sight and terrain, so antenna height is a major factor. For HF bands, signals can propagate well beyond the horizon via ionospheric “skywave” propagation, enabling contacts hundreds or thousands of miles away.
How to Calculate Ham Radio Range?
The following steps outline how to calculate the Ham Radio Range.
- First, determine the height of the transmitter antenna (H_t).
- Next, determine the height of the receiver antenna (H_r).
- Next, calculate the maximum line-of-sight range using the formula R = 1.41 * (√H_t + √H_r). (Heights in feet, result in miles.)
- Finally, calculate the Ham Radio Range.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Height of the transmitter antenna (H_t) = 50 feet
Height of the receiver antenna (H_r) = 30 feet
Estimated line-of-sight range: R = 1.41 · (√50 + √30) ≈ 17.7 miles (≈ 28.5 km)