Radio Horizon Distance Calculator
Estimate the maximum line-of-sight distance between two antennas over a smooth earth. Because radio waves bend slightly downward in the lower atmosphere, they reach past the true visual horizon — this tool uses the standard 4/3-earth model and shows the optical horizon alongside for comparison.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the height of the first antenna h1 in metres above the ground or sea.
- Enter the height of the second antenna h2 in metres; leave it blank (0) to find the horizon distance from a single antenna.
- Read the radio horizon distance in km, with the optical horizon shown for reference.
How it works
Under the 4/3-earth approximation the radio horizon is d(km) = 4.12·(√h1 + √h2) with heights in metres. The 4.12 constant already includes the effective earth-radius increase from atmospheric refraction. The purely geometric optical horizon uses the smaller constant 3.57, so the radio horizon is about 15% (4.12/3.57) further than the line of sight you could see.
Worked example
Worked example. For h1 = 30 m and h2 = 10 m: √30 + √10 = 5.4772 + 3.1623 = 8.6395, so the radio horizon is 4.12 × 8.6395 = 35.595 km and the optical horizon is 3.57 × 8.6395 = 30.843 km.
Common mistakes
- Treating the result as a guaranteed range — it is a smooth-earth maximum; hills, buildings and trees between the antennas will cut it short.
- Entering antenna heights in feet: the 4.12 and 3.57 constants require metres (use 2.0 and 1.23 respectively for statute miles from feet).
- Ignoring Fresnel-zone clearance and fade margin — reaching the horizon geometrically does not guarantee a usable link.
Frequently asked questions
Why is the radio horizon further than the optical one?
Radio waves refract (bend) downward as they travel through the density gradient of the lower atmosphere, effectively following the curve of the earth a little. The 4/3-earth model captures this, giving about 15% more range than the straight-line optical horizon.
What does entering only one antenna height give?
Leaving h2 at 0 returns the distance from a single antenna to the horizon, 4.12·√h1. Add a second antenna height to get the maximum separation at which the two can see each other over the curve.
Related tools
- Two-Ray Ground Reflection Loss Calculator
- Fresnel Zone Clearance Calculator
- Link Margin Calculator
- Repeater Coverage Radius Estimator
- Channel Count / Bandwidth Occupancy Calculator
- Shannon Channel Capacity Calculator
Explore more in Telecommunications & Radio.
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.