Radar Horizon Calculator

Calculate the maximum line-of-sight distance for radar signals based on antenna height and target height, accounting for atmospheric refraction.

TOTAL RADAR HORIZON
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Antenna Horizon (km)
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Target Horizon (km)
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Total (nmi)
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Total (miles)
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What Is the Radar Horizon?

The radar horizon is the maximum distance at which a radar system can detect a target, limited by the curvature of the Earth. Unlike optical line-of-sight, radar waves experience atmospheric refraction that bends them slightly toward the Earth's surface, effectively extending the horizon beyond the geometric limit.

This concept is critical in air traffic control, maritime navigation, military surveillance, and weather radar operations. The radar horizon depends on the heights of both the antenna and the target above the surface, as well as atmospheric conditions that affect refraction.

Radar Horizon Formula

d = sqrt(2 × k × R × h)
Total Horizon = sqrt(2kR ×hantenna) + sqrt(2kR × htarget)

Where k is the refraction factor (typically 4/3 = 1.333 for standard atmosphere), R is Earth's radius, and h is the height above the surface.

Typical Radar Ranges

Antenna HeightTarget at Sea LevelTarget at 10 km
10 m13 km378 km
30 m23 km388 km
100 m41 km406 km
500 m92 km457 km

Atmospheric Refraction

  • Standard atmosphere (k=4/3): Normal conditions where temperature decreases with altitude at the standard lapse rate.
  • Sub-refraction (k<4/3): Occurs in dry, arid conditions. Radar horizon shrinks.
  • Super-refraction (k>4/3): Occurs with temperature inversions. Radar waves bend more, extending range.
  • Ducting (k→infinity): Extreme refraction traps signals in an atmospheric duct, enabling detection at extreme ranges.

Frequently Asked Questions

Why is the radar horizon farther than the optical horizon?

Radar waves at microwave frequencies experience greater atmospheric refraction than visible light. The standard refraction factor of 4/3 means radar waves travel as if the Earth's radius were 33% larger, extending the horizon by about 15% compared to the geometric (optical) line-of-sight.

How does the 4/3 Earth radius model work?

Instead of calculating complex refraction physics, engineers use an effective Earth radius of k times the actual radius (k=4/3). This transforms the curved ray path into a straight line over a larger sphere, greatly simplifying calculations while maintaining accuracy for standard atmospheric conditions.

Can radar see beyond the horizon?

Over-the-horizon (OTH) radar systems use HF frequencies that reflect off the ionosphere, achieving ranges of 1,000-3,500 km. However, conventional microwave radar is limited to the line-of-sight horizon described by this calculator. Atmospheric ducting can occasionally extend microwave radar range well beyond normal limits.