Radar Horizon Calculator (4/3 Earth radius, antenna and target height)

Understanding the radar horizon calculator — concept and principle

This calculator finds how far a radar can see a target before the curvature of the Earth hides it, using the standard 4/3 effective Earth radius to allow for atmospheric refraction. It gives the maximum range in km and nautical miles, each terminal's horizon distance, the geometric range without refraction and how much refraction adds. It is used in radar, maritime and radio-link planning.

Each height has its own horizon; add the two, and bending of radio waves (k = 4/3) stretches the total.

How it is calculated

Effective radius a_e = k × 6,370 km (k = 4/3 gives about 8,493 km)

Horizon distance d = √(2 a_e h)

Maximum range d_max = √(2 a_e h_radar) + √(2 a_e h_target)

Heights in metres; with k = 4/3 this is about 4.12 (√h₁ + √h₂) km.
1 nautical mile = 1.852 km.

The principle

Radio waves in the lower atmosphere bend slightly downwards because the air gets thinner with height. Radio engineers handle this by drawing straight rays over a larger, flatter Earth. The radar's horizon and the target's horizon are each the distance at which a straight line from them grazes that Earth; the target is visible while the two horizons touch. Beyond that distance, it hides below the horizon unless unusual conditions such as ducting bend the waves more.

Worked example

Default inputs: antenna 30 m, target 10 m, k = 1.333333.

a_e = 1.333333 × 6,370 = 8,493 km.
Radar horizon = √(2 × 8,493 × 0.03) = 22.57 km; target horizon = √(2 × 8,493 × 0.01) = 13.03 km.
Maximum range = 22.57 + 13.03 = 35.61 km = 19.23 nautical miles.
Without refraction: 30.84 km, so refraction adds 15.5%.

Each point is the calculator re-run with only “Effective Earth radius factor k” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Effective Earth radius factor k	Maximum radar range to the target (km)
0.333	17.8
0.667	25.18
1	30.84
1.33	35.61
1.67	39.81
2	43.61
2.67	50.36

How to read the result

This is a line-of-sight limit only. Whether the radar actually detects the target also depends on transmitter power, antenna gain, target size and clutter. Raising the antenna helps, but range grows only with the square root of height: four times the height gives twice the horizon.

Common mistakes

Using the geometric Earth radius and underestimating range.
Adding heights instead of horizon distances.
Assuming the result guarantees detection.

Keep in mind: Atmospheric conditions vary, and ducting or sub-refraction can greatly change real ranges. Use this for planning, not for safety-critical decisions.

Frequently asked questions

Why 4/3 Earth radius?

It reproduces the average downward bending of radio waves in a standard atmosphere.

How far is the horizon from a 100 m mast?

About 41 km with k = 4/3.

Can radar see beyond the horizon?

Sometimes, through ducting or diffraction, or with special over-the-horizon radars.

Why does target height matter?

A taller target has its own horizon, extending the range at which it can be seen.

Sources: Recommendation ITU-R P.528-4 (08/2019), Annex 2

Checked 9 Nov 2026. Recommendation ITU-R P.528-4 (08/2019), Annex 2: effective Earth radius a_e = 8,493 km (k = 4/3, surface refractivity 301 N-units, a₀ = 6,370 km), horizon distance d = √(2a_eh) (Eq. 27/31) and maximum line-of-sight distance d_ML = d₁ + d₂ (Eq. 4). 1 nautical mile = 1.852 km (standard).

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