Coverage Radius Estimation by Terrain Type
The Radio Horizon Formula
The theoretical radio horizon for a single antenna at height h metres above a smooth spherical earth, accounting for standard atmospheric refraction (the 4/3-earth model), is:
d (km) = 3.574.12 × √h_m (radio horizon, 4/3-earth refraction)For a link between two antennas at heights h₁ and h₂ the total radio horizon is:
d_total (km) = 3.574.12 × (√h₁ + √h₂)Note: the purely geometric (optical) line-of-sight horizon uses the coefficient 3.57 × √h. The 4.12 coefficient adds the standard 4/3-earth refraction correction and is the value used for radio horizon throughout this book (consistent with the mountain-and-complex-terrain and repeater-placement pages). There is no latitude term in this formula.
This is the maximum possible range on a flat, unobstructed earth.earth - a theoretical ceiling,
not a usable-coverage promise. Real terrain, vegetation, and buildings reduce this significantly.
The formula provides the ceiling; terrain obstruction factors bring it down to a realistic estimate.
Terrain Obstruction Factors
Apply these multipliers to the radio-horizon distance to get a realistic coverage radius:radius. The
factor bands below are illustrative planning heuristics, not measured constants - no Tier-1
standard assigns these exact multipliers to named terrain classes. The underlying propagation
behaviour is described in ITU-R P.526 (diffraction), P.833 (vegetation), and P.1411
(urban/suburban short-range); use those for rigorous modelling.
| Environment Type | Obstruction Factor | Effective Coverage (%) | Notes |
|---|---|---|---|
| Flat open (farmland, desert, water) | 0.85 - 1.00 | 85 - 100% | Near-theoretical range; ground reflections can help at low angles |
| Gentle rolling terrain | 0.65 - 0.80 | 65 - 80% | Moderate ridge shadowing; elevated repeaters mitigate well |
| Suburban (low-rise, gardens) | 0.50 - 0.65 | 50 - 65% | Houses and trees add 5 - 15 dB of excess loss (ITU-R P.1411 range) |
| Dense forest / jungle | 0.35 - 0.55 | 35 - 55% | Vegetation |
| Urban (mid-rise, 3 - 8 floors) | 0.30 - 0.50 | 30 - 50% | Building diffraction dominates; rooftop-to-rooftop paths much better |
| Dense urban (high-rise, canyons) | 0.15 - 0.30 | 15 - 30% | Multipath + shadowing severe; per-block coverage planning needed |
| Mountainous / complex terrain | 0.20 - 0.60 | 20 - 60% | Highly variable; valleys may have near-zero coverage from a single site |
Worked Examples
The coverage areas below are theoretical maxima derived from the radio-horizon ceiling times an obstruction factor. They are not the usable coverage you should plan around. In practice a single well-placed repeater at ~30 m AGL delivers on the order of 300 - 800 km² of reliable coverage in flat/rolling terrain, and far less in forest or urban settings - see the repeater-placement-principles and repeater-grid pages for realistic per-terrain planning densities. Treat the figures here as "maximum, not expected."
Example 1 - 30 m Tower on Flat Land
A community group installs a repeater at the top of a 30 m self-supporting tower in flat agricultural land. The mobile clients they serve have antennas at 1.5 m AGL.
Radio horizon (tower): 3.574.12 × √30 = 3.574.12 × 5.48 = 19.22.6 km
Radio horizon (client): 3.574.12 × √1.5 = 3.574.12 × 1.22 = 4.45.0 km
Total radio horizon: 19.22.6 + 4.45.0 = 24.027.6 km
Obstruction factor (flat open): 0.90
RealisticTheoretical coverage radius: 24.027.6 × 0.90 ≈ 21.624.8 km
CoverageTheoretical area:coverage area (ceiling): π × 21.6²24.8² ≈ 1,466930 km²
WithThat ~1,930 km² is the radio-horizon ceiling, not a usable-coverage guarantee. Realistic
usable coverage from a single well-sited tower,rural thistower repeateris comfortablyfar coverslower a- circletypically on the order of
about300 1,500- 800 km² -once roughlyreal-world fading, foliage, and link-margin requirements are accounted for.
Plan around the sizeusable offigure, anot mid-sizedthe US county.ceiling.
Example 2 - 10 m Mast in Suburbs
A volunteer mounts a repeater on a 10 m mast attached to their house in a typical American suburb (one-storey houses, trees). Mobile clients at 1.5 m.
Radio horizon (mast): 3.574.12 × √10 = 3.574.12 × 3.16 = 11.313.0 km
Radio horizon (client): 3.574.12 × √1.5 = 3.574.12 × 1.22 = 4.45.0 km
Total radio horizon: 11.313.0 + 4.45.0 = 15.718.0 km
Obstruction factor (suburban): 0.55
RealisticTheoretical coverage radius: 15.718.0 × 0.55 ≈ 8.69.9 km
CoverageTheoretical area:coverage area (ceiling): π × 8.6²9.9² ≈ 232308 km²
This is a solid community repeater covering roughly the footprint of a small city.city, However,though pocketsthe
308 km² figure is again a ceiling - expect meaningfully less usable coverage. Pockets of shadow
behind larger buildings will exist. A wardriving survey is recommended after installation to
confirm actual coverage.
Example 3 - Rooftop in Dense Urban
A repeater is placed on the flat roof of a 7-storey (21 m) apartment building in a dense city. Surrounding buildings average 6 storeys (18 m). Mobile clients at street level (1.5 m).
Radio horizon (roof): 3.574.12 × √21 = 3.574.12 × 4.58 = 16.418.9 km
Radio horizon (client): 3.574.12 × √1.5 = 3.574.12 × 1.22 = 4.45.0 km
Total radio horizon: 16.418.9 + 4.45.0 = 20.823.9 km
Obstruction factor (dense urban): 0.25
RealisticTheoretical coverage radius: 20.823.9 × 0.25 ≈ 5.26.0 km
CoverageTheoretical area:coverage area (ceiling): π × 5.2²6.0² ≈ 85113 km²
Only 25% of the theoretical range is realised because the repeater barely clears the
surrounding roofline. EvenRaising the antenna by 3 additional storeys of height (to 30 m) would raiselifts the obstruction factorhorizon
to ~27.6 km and, at an improved ~0.35 andobstruction expandfactor, the ceiling rises to a radius of
~9.7 km - roughly π × 9.7² ≈ 295 km² (still a theoretical maximum, with usable coverage towell
~120below km².that). In dense urban networks, rooftop height relative to surroundings matters enormously.
Coverage Overlap: The 20 - 30% Rule
When planning adjacent repeaters, their coverage footprints should overlap by 20 - 30% of the coverage radius. This is a rule of thumb borrowed from cellular and WLAN cell-planning practice (which commonly calls for 15 - 30% overlap). It ensures:
- No gap corridor between repeaters where nodes lose connectivity
- Sufficient signal margin at the cell edge for reliable forwarding (not just barely detectable signals)
- Redundancy: a node in the overlap zone can reach two repeaters
If repeater A has a coverage radius of 8 km and repeater B also has 8 km, place the two sites
noabout more than 1312 - 1413 km apart (leavingto 2keep ~20 - 30% overlap (a single shared lens-shaped zone roughly
3 - 4 km of overlap on each side). Placing them 16 km
apart creates a 0 - 2 km gap corridorwide in the middle - not "on each side"). At exactly 16 km the two cells are tangent:
they just touch, with zero overlap margin and zero gap. Only beyond ~16 - 18 km does a real
gap corridor open up where nodes may lose one or both repeaters.
Link Budget Margin: Target >10 dB
Coverage radius estimates are not hard boundaries - they define the distance at which the link margin drops to zero. In practice, a link operating at exactly the sensitivity floor is unreliable. Fading, multipath, vegetation sway, and atmospheric changes will cause it to fail intermittently.
Target at least 10 dB of margin at the cell edge for reliable operation. This means planning for a coverage radius at which the received signal is 10 dB above the receiver sensitivity floor. The 10 dB figure is a standard engineering convention (see any link-budget reference); the margin you actually need scales with the environment - budget more in heavy-fading or foliage-dense paths.
For Meshtastic on SF12 / BW125,BW125 (the Long Slow preset), receiver sensitivity is approximately
−137 dBm.dBm with the SX1262's Rx Boosted gain enabled (standard gain is ~3 - 4 dB worse).
Note that LongFast (SF11 / BW250) has a sensitivity closer to −131 dBm, not −137. A link
budget target of −127 dBm at the coverage boundary gives 10 dB margin.of margin relative to the
SF12/BW125 floor. Links measured below −127 dBm at normal operating distances should be
treated as marginal and either reinforced with a relay node or deprioritised until a better
repeater site is available.
Quick field check: If a node reports RSSI < −125 dBm or SNR < −10 dB when communicating with its nearest repeater, that link is at or below the 10 dB margin boundary. Plan to add a relay or move the repeater closer.