Radar Horizon Calculator
Calculate the maximum detection range for radar systems
Height of the target object above sea level
How to Use This Calculator
Enter Antenna Height
Input the height of the radar antenna above sea level in meters. For example, 10 m for a ship's radar, 100 m for an aircraft radar, or 500 m for a ground-based radar on a hill.
Enter Target Height
Input the height of the target object above sea level in meters. For sea-level targets, use 0. For ships or aircraft, use their typical operating height.
Calculate
Click the "Calculate Radar Horizon" button to get the maximum detection range in meters, kilometers, and nautical miles.
Formula
d = √(2Rh₁) + √(2Rh₂)
Where:
- d = Radar horizon distance (in meters)
- R = Earth's radius ≈ 6,371,000 meters
- h₁ = Antenna height above sea level (in meters)
- h₂ = Target height above sea level (in meters)
Note: This formula accounts for Earth's curvature. For targets at sea level (h₂ = 0), the formula simplifies to d = √(2Rh₁).
Example Calculation:
For a radar at 10 m height detecting a sea-level target:
h₁ = 10 m, h₂ = 0 m
d = √(2 × 6,371,000 × 10) + √(2 × 6,371,000 × 0)
d = √(127,420,000) + 0
d = 11,290 m ≈ 11.3 km
Another Example:
For a radar at 100 m detecting a target at 10 m:
h₁ = 100 m, h₂ = 10 m
d = √(2 × 6,371,000 × 100) + √(2 × 6,371,000 × 10)
d = 35,691 + 11,290 = 46,981 m ≈ 47 km
About Radar Horizon Calculator
The radar horizon is the maximum distance at which a radar system can detect objects, limited by Earth's curvature. Unlike the optical horizon, the radar horizon accounts for both the antenna height and the target height, as radar waves can detect objects even when they're slightly below the line-of-sight horizon due to atmospheric refraction. This calculator helps determine the maximum detection range for radar systems, which is crucial for navigation, air traffic control, and maritime radar applications.
When to Use This Calculator
- Radar System Design: Determine maximum detection range for radar installations
- Navigation: Understand radar detection limits for ships and aircraft
- Air Traffic Control: Calculate radar coverage areas for ATC systems
- Maritime Applications: Plan radar installations on ships and coastal stations
- Educational Purposes: Learn about radar propagation and Earth's curvature effects
Why Use Our Calculator?
- ✅ Instant Results: Get accurate radar horizon calculations immediately
- ✅ Easy to Use: Simple interface requiring only antenna and target heights
- ✅ Multiple Units: Results in meters, kilometers, and nautical miles
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
Common Applications
Maritime Radar: Ship radar systems are limited by the radar horizon. A typical ship's radar at 10-20 m height can detect other ships at sea level up to about 11-15 km away. Understanding this limit is crucial for navigation and collision avoidance.
Air Traffic Control: ATC radar systems need to detect aircraft at various altitudes. Higher radar antennas provide longer detection ranges. This calculator helps design radar coverage for airport and en-route air traffic control.
Military Radar: Defense radar systems must account for horizon limitations when detecting aircraft, ships, or missiles. Understanding radar horizon helps optimize radar placement and coverage.
Tips for Best Results
- Use heights in meters above sea level for consistency
- Higher antennas provide significantly longer detection ranges
- Target height also extends range—higher targets can be detected at greater distances
- Atmospheric refraction can extend the actual radar range by about 15% under standard conditions
- Remember that radar power and target size also affect detection, but horizon is the fundamental limit
- For over-the-horizon radar systems, different propagation mechanisms apply
Frequently Asked Questions
What's the difference between radar horizon and optical horizon?
The radar horizon is typically slightly longer than the optical horizon due to atmospheric refraction, which bends radar waves slightly. However, both are fundamentally limited by Earth's curvature. The radar horizon formula accounts for both antenna and target heights.
Why does radar horizon depend on both antenna and target height?
The radar horizon is the sum of two distances: how far the antenna can "see" and how far the target can "be seen." A higher antenna can see farther, and a higher target can be seen from farther away. The total distance is the sum of these two contributions.
Can radar detect objects beyond the horizon?
Standard line-of-sight radar cannot detect objects beyond the geometric horizon. However, over-the-horizon (OTH) radar systems use different propagation mechanisms like ionospheric reflection or ground wave propagation to detect objects beyond the line-of-sight horizon.
How does atmospheric refraction affect radar range?
Under standard atmospheric conditions, refraction extends the radar horizon by approximately 15% compared to the geometric calculation. This is because the atmosphere bends radar waves slightly downward, effectively increasing the "visible" range. Some radar systems use a "4/3 Earth radius" model to account for this.
What's a typical radar horizon for ships?
A typical ship's radar antenna at 10-15 m height can detect sea-level targets up to about 11-13 km away. For detecting other ships (which also have height), the range extends to 15-20 km depending on both ships' heights. This is why ships need to post lookouts and use other detection methods in addition to radar.