What is the k-factor?

The k-factor accounts for atmospheric refraction bending radio waves downward. k = 4/3 (1.333) is the standard for temperate climates. k varies from ~0.7 (extreme sub-refraction) to infinity (ducting).

When does super-refraction occur?

Super-refraction (k > 4/3) happens when warm, dry air overlies cool, moist air — common over warm ocean surfaces. It extends radar range beyond normal but can create blind zones.

Ducting occurs when the atmospheric refractive index decreases so rapidly with height that radio waves are trapped in a layer, bending downward more than the Earth curves. This can extend radar range by hundreds of km — or create complete detection failures at certain altitudes.

Does frequency affect the radar horizon?

The horizon distance is independent of frequency. However, frequency affects diffraction around the horizon, atmospheric absorption, and the Fresnel zone clearance required for practical link design.

How does this differ from the optical horizon?

Radio and optical horizons use the same geometry but different k-factors. For optics, k ≈ 1.06-1.08 (visible light refracts less than microwaves). For radio: k ≈ 4/3.

This calculator assumes a smooth, spherical Earth. Terrain obstructions (hills, buildings) reduce the effective line of sight. For real link planning, use terrain profile tools with digital elevation models.

Radar Horizon Calculator

Calculate radar line-of-sight horizon distance from antenna and target heights. Includes atmospheric refraction (k-factor), Fresnel zone, and target height lookup table.

Height Unit

Antenna Height (m)

Target Height (m)

Refraction Factor k

Frequency (MHz)

Radar Horizon

18.43 km

9.95 NM / 11.45 mi

Antenna Horizon

18.43 km

From antenna to surface

Geometric (k=1)

15.96 km

No refraction

Refraction Gain

15.5%

Beyond geometric horizon

Wavelength

3.19 cm

9400 MHz

Fresnel Zone R₁

12.1 m

At horizon distance

Horizon Range

18.4 km (0-50 km scale)

Max Range vs Target Height

Target Height	Max LoS Range
Surface	18.4 km
10 m	31.5 km
100 m	59.6 km
1000 m	148.8 km
10000 m	430.6 km

Atmospheric Refraction Conditions

Condition	k Factor	Relative Range	Notes
Standard (k=4/3)	1.333	100%	Normal conditions
Sub-refraction (k=1)	1	87%	Dry, stable air
Super-refraction (k=2)	2	122%	Warm air over cool water
Ducting (k→∞)	∞	>>100%	Trapping layer
Geometric (k=1)	1	87%	No refraction

Planning notes, formulas, and examples

About the Radar Horizon Calculator

The radar (or radio) horizon is the maximum distance at which a radar or radio signal can propagate in a straight line from an antenna to a target, limited by the curvature of the Earth. For standard atmospheric conditions, the refraction factor k = 4/3 extends the horizon about 15% beyond the geometric (optical) horizon.

This calculator computes the radar horizon distance from antenna height and target height, accounting for atmospheric refraction via the adjustable k-factor. It also calculates the geometric horizon (k=1) for comparison, the wavelength at the given frequency, and the first Fresnel zone radius at the horizon.

A target height table shows the maximum line-of-sight range for surface, 10m, 100m, 1km, and 10km target heights — essential for understanding detection envelopes. The refraction conditions table explains sub-refraction, standard, super-refraction, and ducting.

This calculator is used by radar engineers, RF link designers, maritime navigators, and ATC planners to determine coverage limits.

When This Page Helps

Use this calculator when antenna height, target height, and atmospheric conditions all affect the usable line of sight. It is handy for radar coverage checks, microwave link planning, and marine or aviation visibility estimates.

The target-height table helps compare surface targets with elevated targets under the same refraction setting, which makes it easier to judge whether the horizon is limiting the link.

How to Use the Inputs

Enter the antenna height above ground level.
Enter the target height (0 for surface targets).
Adjust the refraction factor k (default 4/3 for standard atmosphere).
Optionally enter the radar frequency for wavelength/Fresnel calculations.
Read the radar horizon distance in km, NM, and miles.
Check the target height table for detection ranges at various altitudes.

Formula used

d = √(2·k·Re·h_a) + √(2·k·Re·h_t).
where Re = 6,371 km, k = 4/3 standard.
Geometric (no refraction): k = 1.
Simplified: d(km) ≈ 4.12·(√h_a + √h_t) for k=4/3, h in meters.

Example Calculation

Result: Radar horizon = 18.4 km (9.9 NM)

d = √(2 × 4/3 × 6371000 × 20) = √(339.8×10⁶) = 18,400 m = 18.4 km. With k=1: d = 16.0 km. Refraction adds 15%.

Tips & Best Practices

For quick mental math: horizon (km) ≈ 4.12 × √(height in meters) for standard k.
Doubling antenna height increases horizon by only √2 ≈ 41%.
Maritime: ship radar at 20m can see a surface target at ~18 km, but an aircraft at 10,000m at ~380 km.
For microwave links, ensure the first Fresnel zone (0.6×R₁) is clear of obstructions.
In tropical regions, use k=1.6-2.0 due to high moisture gradients over warm water.

Interpreting k

The k-factor changes the effective Earth radius used in the horizon calculation. A higher value means the atmosphere bends radio waves more strongly downward, which extends the horizon.

Practical Use

For marine radar, use the height of the antenna above the waterline. For land-based links, compare both antenna heights and watch for terrain that may block the first Fresnel zone.

Reference Cases

- k = 1: geometric horizon with no refraction - k = 4/3: standard radio atmosphere - k > 4/3: super-refraction or ducting conditions - k < 1: sub-refraction, which shortens the range

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

The k-factor accounts for atmospheric refraction bending radio waves downward. k = 4/3 (1.333) is the standard for temperate climates. k varies from ~0.7 (extreme sub-refraction) to infinity (ducting).