Radar Horizon Calculator: 4/3 Earth Radius Model

The Radar Horizon Calculator estimates line-of-sight range using the standard k = 4/3 Earth radius adjustment: d ≈ 4.12 ( √h_radar + √h_target ). Enter antenna and target heights in meters or feet and choose output in kilometers, miles, or nautical miles. Pair it with the Distance to Horizon Calculator for optical LOS comparisons.

How to Use

Set heights: Enter radar antenna height and optional target height.
Select units: Heights in meters or feet; output in km, mi, or nm.
Compute: Click Calculate to apply the 4/3 Earth radius model.
Review steps: See the worked formula and converted distance.
Reset: Clear inputs to run another scenario quickly.

Core Formula

d_{km} = 4.12 \times (\sqrt{h_{radar}} + \sqrt{h_{target}})

Distance in kilometers using antenna heights in meters with the 4/3 Earth radius approximation.

Single-site horizon (target near ground): d ≈ 4.12 × √h_radar
Add target height for ship-to-ship or aircraft-to-aircraft links
Use nautical miles by selecting nm in the output

Practical Tips

Higher antenna height extends radar line-of-sight dramatically due to square-root scaling
Nautical miles are standard for maritime and aviation planning
Use meters for engineering specs; feet for tower datasheets
4/3 Earth radius model approximates standard atmospheric refraction
For optical LOS, compare with the Distance to Horizon Calculator

Why use the 4/3 Earth radius model?

It approximates standard atmospheric refraction, extending the effective horizon compared to pure geometric Earth radius.

Which units are supported?

Heights: meters or feet. Output: kilometers, miles, or nautical miles.

Does this include clutter or ducting?

No. It provides clear-air line-of-sight range only; terrain, ducting, or clutter are not included.

Radar Horizon Calculator