Radar Horizon Calculator

Calculate an estimated radar line-of-sight (horizon) distance from antenna height on a smooth Earth, with optional atmospheric refraction using a k-factor and an optional target height for maximum range.

How to use our Radar Horizon Calculator

1. Choose Calculation type: Radar only for one antenna height, or Radar + target to include a target height and get a total line-of-sight limit.
2. Enter Radar antenna height above surface (m) (height above the local ground or sea right at the radar).
3. If you chose Radar + target, enter Target height above surface (m). Use 0 for a ground or sea-level target.
4. Pick a Refraction setting (k-factor). If you are unsure, use Standard (k = 4/3). k = 1 means no refraction.
5. Select an Output distance unit (km, mi, or nmi).
6. Optional: Open Advanced options to set a Custom k-factor, change Earth radius R (km), choose Formula choice (Auto/exact/approx), add Surface or clutter height at horizon (m), or force a Number display style.
7. Click Calculate.
8. Sanity-check the results: if you multiply a height by 4, the horizon should be about 2x (square-root behavior). Also, the Geometric horizon (k = 1) should be shorter than the refracted result when k is greater than 1.

Definitions

Radar horizon distance: The farthest straight-line distance from the radar to a surface target (target height = 0) before Earth curvature blocks line of sight.

Target horizon distance: The target-side horizon distance based on target height. This is only used in Radar + target mode.

Maximum line-of-sight distance: The two-height estimate for radar-to-target line of sight, computed as radar horizon + target horizon.

k-factor: A unitless multiplier used to model atmospheric refraction by using an effective Earth radius. k = 1 means no refraction (pure geometry). A common standard approximation is k = 4/3.

Effective Earth radius: The radius used in the math after refraction is applied: R_eff = k * R. A larger effective radius means a farther horizon.

Surface/clutter height: An optional simple adjustment that reduces the usable height near the horizon (for example, waves, trees, buildings, or terrain). The calculator uses effective height = max(0, height - clutter).

Geometric horizon (k = 1): The horizon distance computed with k = 1 using the same input heights, shown so you can compare refraction vs no refraction.

Nautical mile (nmi): Exactly 1852 meters. [3]

Methodology

What this calculator estimates

This calculator estimates a line-of-sight limit set by Earth curvature using a smooth spherical Earth. It can also apply a refraction shortcut using a k-factor (effective Earth radius). Real radar detection can be shorter or longer because of terrain, obstacles, clutter, antenna patterns, and weather.

1) Optional clutter adjustment (per end)

h_eff = max(0, h - h_clutter)

All heights (radar, target, clutter) are entered in meters. If clutter is larger than the height, that side uses h_eff = 0 and contributes 0 horizon distance (and the calculator should show a note).

2) Effective Earth radius

Earth radius R is entered in kilometers (default 6371 km) and converted to meters for the distance calculation. [1] The effective Earth radius is:

R_eff = k * R

k is chosen from the refraction setting (or Custom). k = 1 is no refraction. k greater than 1 increases the modeled horizon distance.

3) Horizon distance from one height

The exact tangent-to-sphere geometry gives horizon distance d from height h_eff: [1]

d = sqrt(2*R_eff*h_eff + h_eff^2)

The common near-surface approximation (good when h_eff is tiny compared to Earth radius) is:

d ~= sqrt(2*R_eff*h_eff)

If you pick Auto, the calculator can switch to the exact formula when heights are large enough that the approximation could noticeably drift.

4) Radar + target mode (two heights)

If you include a target height, compute each side separately and add them:

D_total = d(h_r_eff) + d(h_t_eff)

Geometric vs refracted comparison

The calculator shows the chosen-k result and also a comparison result with k = 1 (using the same effective heights). The refraction gain is:

gain_percent = 100 * (d_k - d_k1) / d_k1

Mini example

Radar only:

radar height h = 20 m, clutter = 0 m, Earth radius R = 6371 km [1], and k = 4/3. Convert R to meters using 1 km = 1000 m [2], compute R_eff = k*R, then compute d using the exact formula above. For the geometric comparison, repeat with k = 1 and compute the percent gain.

Assumptions and limits

1) Smooth Earth sphere: no terrain profile, no buildings, and no Earth ellipsoid corrections. 2) k-factor is a simplified refraction model and can be very different in unusual weather. 3) Heights are above the local surface at each end, not a detailed sea-level profile along the whole path. 4) This is only a line-of-sight geometry limit, not a guaranteed detection range.

Sources