Radar Horizon Distance Calculator

Overview

Radar horizon distance estimates how far a radar beam can travel before Earth curvature hides the target. It helps operators plan sensor placement, mast height, and expected contact range for ships, towers, and coastal sites.

Height and curvature

Because the horizon grows with the square root of height, small height gains can noticeably improve range. With mean Earth radius 6371 km, a common approximation for geometric horizon is d(km) ≈ 3.57 × √h(m). When standard atmospheric bending is assumed (k = 4/3), the coefficient is about 4.12, giving longer reach.

Inputs and unit handling

This calculator accepts radar height and target height, both in meters or feet. It also lets you set Earth radius in kilometers or miles, then converts internally to meters for the core geometry. Output can be shown in kilometers, statute miles, or nautical miles for navigation reporting.

Refraction factor k

Refraction factor k models how the atmosphere bends the path downward. k = 1.0 is purely geometric and is a conservative baseline. k = 4/3 is widely used for “standard” radio conditions, especially over water. Higher k values can represent super-refraction and ducting, which sometimes extend detection beyond normal expectations.

Combined horizon

The tool computes the horizon from the radar and from the target separately, then adds them. This matters because an elevated target “sees” farther too. For example, with k = 4/3, a 30 m radar has about 22.6 km horizon and a 10 m target has about 13.0 km, yielding about 35.6 km combined.

Worked numbers

Try another quick check: a 100 m radar and a 20 m target give roughly 59.6 km combined under k = 4/3. Switching to k = 1.0 reduces the estimate and provides a lower-bound for cautious planning. Internally the calculator uses d = √((R_eff + h)² − R_eff²) with R_eff = k·R.

Practical limits

For small heights, √(2·k·R·h) gives similar results. Choose 1–2 decimals for field use, but keep 3–4 decimals when comparing scenarios across missions. Remember the horizon is a clear-path limit, not a guaranteed detection range. Sea clutter, terrain masking, antenna tilt, target radar cross-section, and interference can reduce real performance. Use the export buttons to store assumptions, compare k values, and document range briefs for operations.

FAQs

1) What is radar horizon distance?

It is the maximum clear line-of-sight distance before Earth’s curvature blocks the path. This tool estimates it from heights, Earth radius, and refraction factor k.

2) Should I always use k = 4/3?

It is a common “standard” assumption, especially over water. For conservative planning, also compare with k = 1.0. If you suspect ducting, test a slightly higher k.

3) How do I measure antenna height?

Use the antenna phase-center height above mean sea level when available. Otherwise use height above local terrain and keep your target height referenced the same way for consistent geometry.

4) Why does target height change the answer?

The target has its own horizon. A taller target can be seen from farther away, so the combined horizon increases because the calculator adds both horizon distances together.

5) Why offer nautical miles?

Nautical miles match many maritime and aviation charts. The calculator converts the same distance into km, miles, or nmi so your reports align with operational standards.

6) Is horizon range a guaranteed detection range?

No. It is a geometry and propagation limit. Real detection depends on radar power, antenna gain, clutter, sea state, interference, and the target’s radar cross section and aspect.