radar horizon calculator

What Is the Radar Horizon?

The radar horizon is the farthest distance at which a radar can “see” a target due to line-of-sight geometry. Because Earth is curved, low objects eventually drop below the horizon even if your radar is powerful. This calculator estimates that geometric limit, which is often the first range constraint for marine radar, coastal surveillance systems, and low-altitude air search.

A key point: radar horizon is not the same as radar detection range. A system may have plenty of transmitted power, but still fail to detect beyond the horizon simply because the target is physically hidden by curvature.

Formula Used in This Calculator

Distance to horizon from one height

For a height h above the surface, and effective Earth radius R_e:

d = √(2R_eh + h²)

where R_e = kR, with Earth radius R = 6,371,000 m and atmospheric refraction factor k.

Combined radar-to-target horizon

If radar height is h_r and target height is h_t, then:

d_total = d(h_r) + d(h_t)

• k = 1.0: geometric Earth only (no atmospheric bending)
• k ≈ 1.333: common “standard atmosphere” assumption
• Higher k increases apparent horizon distance

How to Use the Radar Horizon Calculator

Inputs

• Radar antenna height: height of the radar above mean sea level or local surface reference.
• Target height: representative reflecting point of the target (mast top, aircraft altitude, tower top, etc.).
• Height unit: meters or feet.
• Refraction factor k: leave at 1.333 for standard conditions unless you have a site-specific model.

Outputs

• Distance from radar to its own horizon
• Distance from target to its own horizon
• Total line-of-sight radar horizon in kilometers, miles, and nautical miles
• Comparison against purely geometric (k = 1) horizon

Practical Examples

Marine radar on a small vessel

A radar at 15 m and a target with reflective structure near 8 m can be line-of-sight limited much earlier than expected. Raising antenna placement even a few meters can add meaningful range for collision avoidance and navigation.

Coastal surveillance

Shore stations often place antennas on masts or cliffs to push horizon outward. This is usually more effective than only increasing transmit power, because curvature, not power, is the dominant limit against low-altitude or sea-skimming targets.

Low-altitude aircraft tracking

Aircraft near terrain or at low altitude can intermittently drop below radar horizon. Integrating multiple radar sites with overlapping geometry helps reduce blind sectors.

Important Limitations

This tool is intentionally simple and fast. It does not include all real-world propagation and detection effects.

• Terrain masking (hills, islands, buildings) can reduce range dramatically.
• Sea state and multipath can distort returns near the surface.
• Atmospheric ducting and strong gradients may increase or decrease practical range versus standard k.
• Target radar cross-section, clutter environment, and receiver sensitivity determine whether a visible target is actually detected.

Radar Horizon vs Detection Range

Think of horizon as a geometric gate: if the target is below the line-of-sight path, no practical amount of transmit power will fix that. If the target is above the horizon, then radar equation factors (power, gain, wavelength, cross-section, losses, noise figure, processing gain) determine if detection is reliable.

Quick Tips for Better Coverage

• Increase antenna height where feasible and safe.
• Use multiple sensor sites for low-altitude coverage.
• Model local atmospheric statistics if precision matters.
• Combine geometric horizon checks with full radar performance calculations.