Radar Horizon Calculator

How to use this radar horizon calculator

What this calculator does. This tool estimates how far a radar and an elevated target can be separated before Earth curvature blocks a direct geometric radio path. It reports the Radar horizon contributed by the antenna height, the Target visibility contributed by the target height, and their sum as Maximum distance. It can apply the conventional 4/3 effective-Earth-radius approximation for standard atmospheric refraction. It does not model transmitter power, receiver sensitivity, radar cross-section, terrain masking, clutter, ducting, precipitation attenuation, or antenna beam shape, so the answer is a horizon limit rather than a promise that a real radar will detect a particular target.

When to use it. Use it to compare a ground radar with an elevated radar site, estimate the curvature-limited line of sight to a low-flying aircraft or vessel mast, explore how antenna height changes coverage, or perform a quick communications/radar planning check before moving to a full propagation model. NOAA explains that radar uses transmitted radio energy and returned echoes to determine target range; see its radar overview and NEXRAD resources.

How to calculate

1. The calculator opens with a ready-to-use demonstration: standard refraction enabled, a radar height of 9,150 m, and a target height of 122 m. The results and a validated example XLSX are available immediately.
2. Choose Atmospheric refraction? Select “Yes – standard 4/3 Earth” for the common effective-radius approximation, or “No – geometric” for a purely spherical-Earth line-of-sight calculation.
3. Replace Radar system height and Target height with non-negative finite values. Use Height unit to switch both heights between meters and feet; the current values are converted rather than merely relabeled.
4. Read Maximum distance first, then use Radar horizon, Target visibility, the distance breakdown, and the Horizon components table to understand how each height contributes.
5. Select Download Excel to export the current validated inputs and results as a real XLSX workbook. Reset clears the demonstration values and calculated state; after Reset, Excel export stays disabled until both required heights form a complete valid state again.

Input guide

Atmospheric refraction? is a required two-state control. “Yes” uses a dimensionless effective-Earth factor of 4/3; “No” uses 1. Use “Yes” for a conventional standard-atmosphere planning estimate and “No” when you specifically want pure geometry. The ITU describes downward radio-wave refraction and notes that a typical effective-Earth-radius factor of 4/3 is often used at VHF and higher frequencies under standard conditions in its Ground Wave Propagation handbook. A common mistake is treating 4/3 as universal: unusual atmospheric gradients can produce different propagation.

Radar system height is required and accepts a plain non-negative decimal, such as 9,150 m or its converted value in feet. It represents antenna height above the same reference surface used for the target. Increasing it increases the radar's horizon approximately with the square root of height. Do not enter a slant range, building floor number, or height below the chosen reference surface.

Target height is required and follows the same numeric rules, for example 122 m. Higher targets remain geometrically visible farther beyond the radar's own surface horizon. Zero is valid and represents a target on the reference surface. A frequent mistake is mixing above-ground height for one object with above-sea-level height for the other when the terrain elevations differ.

Height unit is a required mode control with Meters and Feet. Changing it converts both entered heights using 1 ft = 0.3048 m while keeping the physical scenario unchanged. Results remain in kilometers. If you type values after switching, interpret them in the currently displayed unit.

Output guide

Radar horizon is the radar-height contribution to line of sight in kilometers. Target visibility is the same horizon calculation applied to the target height. Maximum distance is their exact sum in this model. A zero component means that object is on the reference surface; a larger value means curvature allows a longer direct path. These are estimates based on a spherical Earth and the selected refraction model, not measured detection ranges. The Radar contribution and Target contribution percentages in the breakdown and Share of maximum table column show each component divided by the maximum distance. The Effective Earth factor is 1.3333× with standard refraction and 1.0000× without it. In the Horizon components table, Height repeats the current physical height in the active unit and Horizon distance repeats the canonical component result.

Worked example

The demonstration uses a radar at 9,150 m and a target at 122 m with standard refraction. Using Earth mean radius R = 6,371.009 km and k = 4/3, the standard low-altitude approximation is d = √(2 × k × R × h), with height h converted to kilometers. For the radar, √(2 × 4/3 × 6,371.009 × 9.150) = 394.27 km. For the target, √(2 × 4/3 × 6,371.009 × 0.122) = 45.53 km. Adding the two produces the first-open Maximum distance of 439.80 km. NASA/JPL lists Earth's mean radius at about 6,371.0084 km in its planetary physical parameters, consistent with the rounded radius used here.

Learn more

For operational context, the National Weather Service's Radar Basics training material explains the broader radar system beyond geometry. Remember that real coverage can be shorter or occasionally longer than this simple horizon because terrain, anomalous refraction, ducting, clutter, antenna elevation, and signal-to-noise limits are outside the model.