| Radar Height (m) | Target Height (m) | k | Estimated Max Range (km) |
|---|---|---|---|
| 30 | 10 | 1.3333 | 34.98 |
| 60 | 0 | 1.3333 | 39.57 |
| 15 | 25 | 1.0000 | 28.52 |
The radio horizon can be modeled by using an effective Earth radius to represent atmospheric bending. For an antenna height h, the horizon distance is:
If both radar and target heights are known, the maximum line-of-sight range becomes:
- Enter the radar antenna height and choose its unit.
- Enter the target height, or set it to zero.
- Select a refraction factor or provide a custom value.
- Confirm Earth radius and pick your output unit.
- Press Calculate to see results above the form.
1) What the radar horizon represents
Radar range horizon is the geometric limit created by Earth curvature and atmospheric refraction. It is the furthest distance where a straight ray can still clear the surface. This is not the same as detection range, which also depends on transmitter power, antenna gain, target RCS, clutter, and noise.
2) Why height matters so strongly
Horizon distance grows with the square root of antenna height. Doubling height does not double range; it increases range by about 41%. Small height changes near sea level can still matter, especially for coastal navigation radar or low‑altitude surveillance where the first few meters remove a lot of curvature loss.
3) Effective Earth radius and k‑factor
Refraction bends radio waves slightly downward in the lower atmosphere. Engineers often model this with an “effective Earth radius,” using a refraction factor k. Standard conditions commonly use k = 4/3, which extends the horizon beyond the optical line of sight. This calculator lets you compare k scenarios quickly.
4) Standard, no‑bending, and ducting cases
With k = 1, you get a conservative, no‑bending estimate. With k = 4/3, you get a typical maritime or terrestrial estimate. Under stronger bending or ducting, k can be larger and the horizon can expand dramatically. Ducting can also cause uneven coverage, false echoes, and unexpected long‑range contacts.
5) Radar‑to‑target geometry
When both radar and target heights are known, the maximum line‑of‑sight range is approximated by adding each horizon distance. This is useful for ship‑to‑ship, tower‑to‑aircraft, or coastal‑to‑vessel planning. For very long distances, terrain, atmospheric layers, and Earth ellipsoid variations can become noticeable.
6) Unit choices used in operations
Kilometers are common for engineering and maps, while nautical miles are standard in marine navigation. Miles may be preferred in some aviation or regional contexts. This tool converts internal meter calculations into your chosen unit, keeping the underlying geometry consistent.
7) Interpreting results with real systems
A horizon estimate tells you where detection becomes unlikely, not impossible. Targets can appear beyond the horizon due to anomalous propagation, super‑refraction, or elevated targets. Conversely, clutter, sea state, precipitation, and interference can reduce practical range well before the horizon limit.
8) Good practice for planning and reporting
Use measured antenna heights, not mast height from deck plans. If your environment is stable and humid, test multiple k values to bracket outcomes. Record settings in exported CSV/PDF for traceability. When safety‑critical, validate with trials or local propagation data rather than relying on a single estimate.
1) Is radar horizon the same as maximum detection range?
No. Horizon is a geometry limit. Detection also depends on power, antenna gain, target size, receiver sensitivity, clutter, weather, and processing settings.
2) What k value should I use for typical conditions?
A common engineering default is k = 4/3. It represents average atmospheric refraction for many near‑surface radar cases, especially maritime and temperate conditions.
3) Why does the calculator ask for target height?
Because elevated targets have their own horizon distance. Adding radar and target horizons estimates the maximum line‑of‑sight separation for two raised points.
4) Can I set the target height to zero?
Yes. Zero models a sea‑level or ground‑level target, giving a one‑sided radar horizon estimate without extra elevation on the far end.
5) Does frequency change the horizon distance?
In this simplified model, horizon depends on geometry and refraction, not frequency. Frequency affects clutter, attenuation, ducting likelihood, and detection performance.
6) Why might real coverage be less than the horizon result?
Sea clutter, terrain masking, rain, multipath fading, interference, or low target reflectivity can reduce usable detection range even when the target is above the geometric horizon.
7) When should I use a custom Earth radius?
Use custom radius for specialized studies, regional geoid assumptions, or teaching comparisons. For most practical planning, the mean radius value is sufficient.