Radar Line of Sight Calculator

Calculator Inputs

Radar antenna height

Common values: 10–60 m (ship/shore), 100+ m (tower).

Radar height unit

Target height

For aircraft, use altitude above sea level.

Target height unit

Refraction preset

k adjusts effective Earth radius: R_eff = k · R.

k-factor (custom)

Tip: standard radio horizon often uses k = 4/3.

Earth radius

km

Default is 6371 km (mean Earth radius).

Output units

Rounding (decimal places)

Optional: link distance to check

Checks whether the link is within maximum LOS.

Link distance unit

Reset

This tool estimates the maximum clear-Earth line of sight. Mountains, buildings, and local weather can reduce real coverage.

Radar height (m)	Target height (m)	k-factor	Max LOS (km)	Notes
20	2	4/3	~24	Small surface target near sea level
30	300	4/3	~92	Low aircraft improves range greatly
50	50	1	~50	Geometric horizon without refraction
100	100	4/3	~82	Two elevated towers, standard conditions

Values are approximate and depend on Earth model and k-factor.

This calculator models Earth curvature using an effective Earth radius: R_eff = k · R. The horizon distance from a height h (meters) is:

d = √(2 · R_eff · h + h²)
For two endpoints: d_max = d₁ + d₂

For small heights where h ≪ R, a common approximation is d ≈ √(2 · k · R · h), which leads to quick “radio horizon” rules of thumb.

Enter the radar antenna height and select its unit.
Enter the target height (or altitude) and its unit.
Select a refraction preset, or choose custom and set k.
Keep Earth radius at 6371 km unless you need a different model.
Press Calculate to view horizons and total line of sight.
Optionally enter a link distance to check if it fits within LOS.
Use the download buttons to export the last result.

Practical Guide

1) What “line of sight” means in radar planning

Radar coverage is often limited by Earth curvature, not transmitter power. When the target drops below the geometric horizon, returns weaken fast. This calculator estimates the maximum clear-Earth path between two heights, giving a realistic first-pass range.

2) Earth radius and why 6,371 km is used

The mean Earth radius is about 6,371 km, which works well for engineering estimates. Local terrain and ellipsoidal effects can shift results slightly, but radius changes are usually smaller than weather-driven refraction changes.

3) k-factor: standard atmosphere versus “no refraction”

Radio waves typically bend slightly downward, extending the horizon. A common standard is k = 4/3 (≈1.3333), which increases effective radius and range. Setting k = 1.0 gives purely geometric line of sight for comparison. In practice, k can swing from about 0.8 to 2.0, shifting predicted range by roughly 10–30%.

4) Typical height inputs you can try

Ship radars are often 10–40 m above sea level, small coastal towers 30–80 m, and tall structures 100–300 m. Targets vary widely: 2 m for a small boat, 10 m for a large vessel, and hundreds of meters for low aircraft. Use sea-level heights for best consistency always.

5) Example outcomes with real numbers

With a 30 m radar and a 2 m target at k = 4/3, total line of sight is roughly 25 km. Keep the radar at 30 m but raise the target to 300 m and the total can jump to about 90+ km. Height matters more than small parameter tweaks.

6) Units that match navigation workflows

Maritime users often think in nautical miles: 1 nmi = 1.852 km. Aviation or land users may prefer miles. This tool can show km, mi, and nmi together, so you can copy results into route plans without extra conversion steps.

7) Using the link-distance check for quick validation

If you already know the separation between radar and target, enter it as “link distance.” The calculator reports whether the path is within the predicted maximum LOS and shows the margin. This is useful for deciding if more height is needed.

8) Important limits and what to do next

This model assumes a smooth Earth and does not include hills, buildings, ducting layers, or clutter. After this estimate, confirm with terrain profiles, antenna patterns, and operational constraints. Use k presets to explore best-case and conservative scenarios.

FAQs

1) Is this the same as radar horizon?

Yes. It computes horizon from each height and adds them. That sum is the maximum clear-Earth line of sight between the radar and the target.

2) Which k-factor should I choose?

Start with k = 4/3 for typical conditions. Use k = 1 for geometric-only checks. Try higher k for super-refraction, and lower values if you want a conservative estimate.

3) Why can aircraft be detected much farther?

Because the target horizon increases with the square root of height. Even a few hundred meters of altitude adds tens of kilometers to total line of sight.

4) Does this include terrain and buildings?

No. It models Earth curvature only. Obstacles can reduce range significantly, so use terrain data or a path-profile tool for detailed site planning.

5) What is the difference between miles and nautical miles?

A statute mile is 1.609 km. A nautical mile is 1.852 km and is tied to latitude minutes, which is why it is standard for marine and aviation navigation.

6) Can I use feet for height inputs?

Yes. Select feet for radar or target heights. The calculator converts to meters internally before applying the horizon equations.

7) Why does the result change when I change Earth radius?

Horizon distance depends on √(R). A different radius slightly shifts range. In most cases, k-factor and height dominate more than small radius adjustments.