Free · Physics models
Geometric and Refracted Radar Horizon
Estimate line-of-sight distances from radar and target height using spherical Earth and a conventional refraction approximation.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
With radar and target each 10 m high, geometric visibility is about 22.576 km; the four-thirds-Earth estimate is about 26.069 km.
dgeometric = √(h² + 2Re h); drefraction ≈ √(2 × 4Re/3 × h).
Worked example
Enter these known values and leave the other values blank.
- Radar system height
- .01 km
- Target height
- .01 km
- Radar horizon (with refraction)
- 13.034 km
- Target visibility (with refraction)
- 13.034 km
- Maximum distance (with refraction)
- 26.07 km
Assumptions and limitations
- Earth radius is retained as 6,371,009 m. Heights are nonnegative above the local spherical surface.
- The refracted branch uses the small-height four-thirds-effective-Earth approximation, omitting the h² term.
- Terrain, obstacles, antenna pattern and anomalous refraction can change practical detection range.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.