Radar Horizon Calculator
Calculate radar horizon, target visibility, and maximum detection distance
Radar Horizon and Detection Range Calculator
Atmospheric refraction extends radar range by ~33% due to radio wave bending
Height of radar antenna above ground level
Height of target (aircraft, missile, etc.) above ground
Radar Detection Results
Formulas Used
dr = √(2 × RE × hr)
Radar Horizon (simplified)
dt = √(2 × RE × ht)
Target Visibility
D = dr + dt
Maximum Distance
Reff = 4/3 × RE
Effective Earth Radius
Physical Constants
Earth's Radius: 6371.009 km
Effective Radius: 6371.009 km
Refraction Factor: 1.000
Sound Speed (ref): 343 m/s
Quick Presets
Example Calculations
AWACS vs Ground-Based Radar
Scenario: Detecting low-flying bomber at 122m altitude
AWACS at 9,150m:
Radar horizon: 394.3 km, Target visibility: 45.5 km
Maximum detection: 439.8 km (~22 minutes warning)
Ground radar at 10m:
Radar horizon: 13.0 km, Target visibility: 45.5 km
Maximum detection: 58.6 km (~3 minutes warning)
Atmospheric Refraction Effect
Without refraction: Standard geometric calculation
With refraction: ~33% increase in detection range
Physical cause: Radio waves bend downward due to atmospheric density gradients
Result: Radar "sees" as if Earth were 33% larger
Typical Radar Heights
Radar Applications
Military Defense
Early warning systems, air traffic control, missile guidance
Aviation
Air traffic control, weather monitoring, collision avoidance
Maritime
Ship navigation, coastal surveillance, search and rescue
Weather
Precipitation detection, storm tracking, wind measurement
Automotive
Adaptive cruise control, collision detection, parking assistance
Understanding Radar Horizon
What is Radar Horizon?
The radar horizon is the maximum distance at which a radar system can detect ground-level targets. Due to Earth's curvature, radar waves travel in straight lines and cannot "see" beyond the horizon created by the planet's spherical shape.
Key Factors
- •Radar Height: Higher antennas see farther
- •Target Height: Elevated targets are visible at greater distances
- •Earth's Curvature: Limits line-of-sight detection
- •Atmospheric Refraction: Extends detection range
Mathematical Foundation
dr = √(2 × RE × hr)
Simplified radar horizon formula
Atmospheric Refraction
Reff = (4/3) × RE
The 4/3 Earth radius model accounts for atmospheric refraction. Radio waves bend downward due to decreasing air density with altitude, effectively extending the radar's reach by approximately 33%.
Radar Range Limitations
Shadow Zone
Area behind Earth's curvature where targets cannot be detected regardless of radar power
Clutter Zone
Near-surface area with interference from ground reflections, weather, and other sources
Detection Zone
Optimal area between clutter zone and horizon where clear target detection is possible
Historical Context
World War II
Radar technology proved crucial in the Battle of Britain. British Chain Home radar stations provided early warning of German aircraft approaching across the English Channel.
Cold War Era
Development of over-the-horizon radar to detect ballistic missiles and aircraft beyond conventional radar horizon using ionospheric reflection.