Radar Horizon Calculator

Determine the maximum distance a radar can detect a target over the Earth's surface.

This tool calculates the geometric and effective radar horizon based on the heights of the radar antenna and the target.

Practical Examples

Load an example to see how the calculator works with different scenarios.

Maritime Surveillance

Maritime Surveillance

A ship-based radar detecting a small boat on the horizon.

Radar Height: 25 m

Target Height: 5 m

Refraction (k): 1.33

Unit: Metric

Air Traffic Control

Air Traffic Control

An airport radar tower tracking an aircraft at a low altitude.

Radar Height: 150 ft

Target Height: 10000 ft

Refraction (k): 1.33

Unit: Imperial

Coastal Defense

Coastal Defense

A coastal radar identifying an incoming surface vessel.

Radar Height: 50 m

Target Height: 15 m

Refraction (k): 1.33

Unit: Metric

Microwave Link

Microwave Link

Calculating the line-of-sight for a microwave communication link between two towers.

Radar Height: 300 ft

Target Height: 300 ft

Refraction (k): 1.33

Unit: Imperial

Other Titles
Understanding the Radar Horizon Calculator: A Comprehensive Guide
Explore the principles behind radar line-of-sight, the factors influencing detection range, and the practical applications of this calculator.

What is the Radar Horizon?

  • The Concept of Line-of-Sight
  • Geometric vs. Radar Horizon
  • The Role of Earth's Curvature
The radar horizon is the maximum distance at which a radar can detect an object. Due to the Earth's curvature, this 'line-of-sight' is a curve, not a straight line. The geometric horizon is the true line-of-sight in a vacuum, while the radar horizon accounts for the fact that radar waves bend slightly as they travel through the atmosphere, allowing them to 'see' a bit further over the curve of the Earth.
Why Bending Occurs: Atmospheric Refraction
Radar waves bend due to changes in atmospheric density with altitude, a phenomenon called refraction. This bending, or 'ducting,' effectively increases the Earth's radius from a radar's perspective. The standard model uses an effective Earth radius that is 4/3 of the actual radius, which is why the refraction coefficient 'k' defaults to 1.33.

Step-by-Step Guide to Using the Radar Horizon Calculator

  • Entering Input Values Correctly
  • Selecting Units of Measurement
  • Interpreting the Results
Input Fields Explained
1. Radar Antenna Height: Enter the height of your radar antenna from the surface. 2. Target Height: Input the altitude of the object you wish to detect. 3. Refraction Coefficient (k): Use the default 1.33 for standard atmospheric conditions, or adjust if you have specific data. 4. Unit: Choose between Metric (meters/km) and Imperial (feet/miles) for all inputs and outputs.
Understanding the Output
The calculator provides two key distances: the geometric horizon (a straight line, no atmosphere) and the radar horizon (a bent line, with atmosphere). The total line-of-sight is the sum of the horizon distance from the radar and the horizon distance from the target.

Real-World Applications of Radar Horizon Calculations

  • Maritime Navigation and Safety
  • Aviation and Air Traffic Control
  • Military and Defense Operations
Calculating the radar horizon is critical in many fields. In maritime navigation, it determines the range for detecting other ships and coastal features. In aviation, it helps air traffic controllers manage airspace safely. Military operations rely on it for early-warning systems, surveillance, and missile defense to maintain situational awareness and a tactical advantage.
Telecommunications and Broadcasting
The same principles apply to line-of-sight for microwave communication links and broadcasting towers. Engineers must calculate the horizon to ensure that signals can travel between two points without being obstructed by the Earth's curvature.

Common Misconceptions and Correct Methods

  • Radar Can't See 'Through' the Earth
  • Weather Effects on Refraction
  • The Myth of 'Over-the-Horizon' Radar
A common misconception is that powerful radars can see indefinitely. In reality, unless special conditions create significant atmospheric ducting, detection is limited by the horizon. While Over-the-Horizon (OTH) radars exist, they do not use line-of-sight; instead, they bounce signals off the ionosphere to detect targets at great distances, a completely different principle.
Variable Refraction
The k-factor of 4/3 is an average. Actual atmospheric conditions (temperature, pressure, humidity) can cause 'k' to vary, leading to sub-refraction (k < 1), super-refraction (k > 4/3), or even ducting, where waves are trapped and can travel much further than the calculated horizon.

Mathematical Derivation and Formulas

  • The Geometric Horizon Formula
  • The Radar Horizon Formula with Refraction
  • Combining Radar and Target Horizons
The Core Formula
The basic formula for the line-of-sight distance (d) to the horizon from a height (h) is derived from the Pythagorean theorem: (R+h)² = R² + d². For small heights, this simplifies to d ≈ √(2Rh). To account for atmospheric refraction, we use an effective Earth radius, R' = k R. The formula becomes: d ≈ √(2 k R h).
Total Line-of-Sight
To find the maximum distance between a radar at height h1 and a target at height h2, we calculate the horizon for each and add them together: D_total ≈ √(2kRh1) + √(2kRh2). This calculator performs this calculation for you.