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Radar Horizon Range — result sheet
Estimate the geometric line-of-sight range to a target from radar antenna height, target height, and an effective Earth radius.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: range = √(2Rₑhᵣ + hᵣ²) + √(2Rₑhₜ + hₜ²), where Rₑ = Earth radius × effective-radius factor.
A radar can see a target when the line of sight clears the curved Earth. This calculator adds the antenna-to-horizon leg and target-to-horizon leg using a spherical-Earth model. An effective-radius factor near 4/3 is a conventional normal-refraction planning value; setting it to 1 gives the geometric no-refraction case.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Radar antenna height above surface — m; minimum 1.0E-6; maximum 1000000
- Target height above surface — m; minimum 0; maximum 1000000
- Earth radius — km; minimum 100; maximum 100000
- Effective-radius factor — ×; minimum 0.5; maximum 3
Worked example
| Input | Value |
|---|---|
| Radar antenna height above surface | 30 |
| Target height above surface | 1000 |
| Earth radius | 6371 |
| Effective-radius factor | 1.3333333333 |
About 152.92 km total horizon range under the entered effective-radius model.
Assumptions and limits
- Antenna and target heights are measured above the same smooth reference surface and are small compared with Earth’s radius.
- The radar beam is treated as a straight line over an effective spherical Earth; terrain, antenna tilt, beamwidth, diffraction, clutter, and radar cross-section are not modeled.
- The result is a line-of-sight horizon estimate, not a guaranteed detection range or a link-budget calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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