Radar Horizon Calculator — Line-of-Sight Range
Enter the radar antenna height and the target altitude to find the maximum detection range imposed by Earth's curvature — using the standard 4/3-effective-Earth-radius atmospheric model.
m
m
≈ 12.2 nautical miles
- 1
Antenna radar horizon
4.12 × √30 = 22.566 kmThe 4.12 factor comes from the 4/3-effective-Earth-radius atmospheric model. - 2
Total radar range
4.12 × √30 = 22.6
How does this calculator work?
Radar range is limited by Earth's curvature. Using the 4/3-effective-Earth-radius model for standard atmospheric refraction, maximum radar range = 4.12 × (√h₁ + √h₂) km, where h₁ is antenna height and h₂ is target height in metres. A 30 m antenna can see a surface target (h₂ = 0) to about 22.6 km.
Formula
How this is calculated
Radar signals travel in approximately straight lines and are blocked by Earth's curvature — targets below the geometric horizon cannot be detected regardless of transmitter power. However, in a standard atmosphere, radio waves are slightly bent (refracted) downward by the decreasing air density gradient, effectively extending the visible range. Engineers model this by replacing the true Earth radius (Re = 6 371 km) with an effective radius of (4/3) × Re = 8 495 km. The resulting radar-horizon coefficient is √(2 × 8 495 × 1 000 / 1 000) ≈ 4.12 km per √metre.
For an antenna at height h₁ (m) and a target at height h₂ (m), the maximum one-way radar horizon is d = 4.12 × (√h₁ + √h₂) km. When the target is at sea level (h₂ = 0), this simplifies to d = 4.12 × √h₁ km. The geometric (unrefracted) horizon uses the coefficient 3.57 instead of 4.12 and represents the absolute minimum range in a near-vacuum.
Limitations: the 4/3 model assumes a standard atmosphere (15 °C, 1 013 hPa at sea level with a constant lapse rate). In sub-refractive conditions (dry desert air) the effective range shrinks; in super-refractive or ducting conditions (tropical maritime air) it can be much longer than predicted. The model also assumes flat terrain — hills, terrain masking and terrain clutter are not accounted for.
Frequently asked questions
In a standard atmosphere, air density decreases with altitude and bends radio waves slightly toward Earth. This downward refraction makes the waves behave as if travelling over a larger, flatter Earth. The factor 4/3 is the commonly accepted approximation for a standard atmosphere; real atmospheric conditions cause this factor to vary.
A higher target is visible from further away because it rises above the horizon sooner. The contributions add as square roots: a target at 100 m altitude adds 4.12 × √100 = 41.2 km to the range, regardless of the antenna height.
They are calculated the same way — the 4/3-Earth model applies to all centimetre- and metre-band radar and VHF/UHF radio links. "Radar horizon" typically means one-way propagation to a target, while "radio horizon" is used for point-to-point communication links. The formula and coefficient (4.12) are identical.
Also known as
TG we-Calculate Editorial Team. (2026). Radar Horizon Calculator — Line-of-Sight Range [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/radar-horizon-calculator
TG we-Calculate Editorial Team. "Radar Horizon Calculator — Line-of-Sight Range." TG we-Calculate. 2026. https://we-calculate.com/calculator/radar-horizon-calculator.
TG we-Calculate Editorial Team, "Radar Horizon Calculator — Line-of-Sight Range," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/radar-horizon-calculator
@misc{wecalculate_radar_horizon_calculator, title = {Radar Horizon Calculator — Line-of-Sight Range}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/radar-horizon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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