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Calcimator

Antenna Height Calculator

Calculate the required tower height for line-of-sight coverage over a given distance, accounting for earth curvature and remote antenna height.

About this calculator

Radio line-of-sight is limited by the same horizon that limits how far you can see standing on a beach: the earth curves away underneath the signal path. This calculator uses the standard radio-horizon relationship, distance (km) is proportional to the square root of height (m) times the K-factor, which is the widely used engineering approximation for how far a radio wave can "see" over the curved earth before the ground blocks it. The K-factor adjusts the earth's true geometric radius to an effective radius that accounts for how a standard atmosphere bends radio waves slightly toward the ground -- the commonly used value of 4/3 (about 1.333) reflects typical atmospheric refraction, though it can shift with weather (temperature inversions and unusual humidity gradients can raise or lower the effective K-factor, changing real-world range).

Because Target Distance is split between two horizon distances -- how far the remote antenna's own height reaches toward the tower, and how far the tower must reach the rest of the way -- Required Tower Height responds strongly (and non-linearly, since it depends on the square of the remaining distance) to Target Distance: because the geometry is height ~ distance squared, not height ~ distance, doubling the target coverage distance can increase the required tower height far more than proportionally -- the "roughly quadruples" rule of thumb only holds when remote antenna height is small relative to target distance; when remote height is a significant fraction of the distance (as it is at this calculator's own defaults), the increase can be considerably larger. This calculator estimates pure geometric line-of-sight only; it does not model terrain obstructions, foliage, or Fresnel-zone clearance beyond the reference 2.4 GHz radius reported separately -- a path can be geometrically clear yet still suffer diffraction loss if the first Fresnel zone is obstructed.

Inputs

km
m

Results

Required Tower Height

2.86 m

≈ 19 smartphones

Total LOS Distance

20 km

≈ 61 Eiffel Towers

Tower Horizon Distance6.97 km
Remote Horizon Distance13.03 km
1st Fresnel Zone Radius (2.4 GHz)24.99 m
Max LOS from 30m Tower22.57 km
How to Use This Calculator
  1. Enter the target distance to the remote station.
  2. Set the remote antenna height (m) and K-factor (effective Earth radius multiplier -- 4/3 standard).
  3. Review the required antenna height for line-of-sight clearance and horizon distances from both ends.
  4. Increase antenna height or reduce path length if required height exceeds tower constraints.

How the result changes with Target Distance

Target DistanceRequired Tower HeightTotal LOS Distance
100 m13.03 km
150.23 m15 km
3016.95 m30 km
5080.46 m50 km

What each input means

Target Distance
Desired line-of-sight coverage distance in kilometers
Remote Antenna Height
Height of the remote/client antenna above ground in meters
K-Factor (Earth Radius)
Effective earth radius factor (standard atmosphere: 4/3 ≈ 1.333)

How this is calculated

Formula

h = d² / (2 × k × R_earth)

Worked example, using the default values

  1. Identify Input Parameters
    Target Distance = 20, Remote Antenna Height = 10, K-Factor (Earth Radius) = 1.333 = 3 input(s) provided
  2. Calculate Required Tower Height
    Required Tower Height
    2.86 = 2.86
  3. Calculate Total LOS Distance
    Total LOS Distance
    20 = 20
  4. Calculate Tower Horizon Distance
    Tower Horizon Distance
    6.97 = 6.97
  5. Calculate Remote Horizon Distance
    Remote Horizon Distance
    13.03 = 13.03

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does required tower height grow so much faster than the target distance?

Required Tower Height is proportional to the square of the remaining distance the tower alone must cover after subtracting the horizon reach already provided by the remote antenna's own height. Because it's a squared relationship, not a linear one, doubling your target coverage distance increases the tower height needed by far more than double -- the often-cited "roughly quadruples" rule of thumb only holds when the remote antenna's height is small relative to the target distance; when it isn't, the increase can be considerably steeper than 4x, since the remaining distance the tower must cover grows faster than the target distance itself. This is why long point-to-point radio links favor tall towers and short hops rather than one enormous single link.

What does the K-factor actually represent?

The K-factor scales the earth's true radius to an "effective" radius that accounts for how a standard atmosphere gradually bends radio waves toward the ground, letting them travel slightly farther than a straight geometric line would suggest. The commonly used standard-atmosphere value is 4/3 (about 1.333); it can shift under unusual weather (temperature inversions or humidity gradients), occasionally making paths that work most days unreliable during those conditions.

Does a geometrically clear line-of-sight path guarantee a working radio link?

Not necessarily. This calculator checks pure geometric clearance -- whether the direct line between antennas clears the curved earth -- but a working RF link also needs adequate Fresnel-zone clearance around that line, since diffraction loss can degrade a link even when the direct line itself is unobstructed. The 1st Fresnel Zone Radius this calculator reports (at 2.4 GHz) gives a sense of how much additional clearance around the direct path matters at that frequency.

Why does increasing the remote antenna's height reduce the required tower height?

Total Distance is covered by two horizon reaches added together: the distance the remote antenna's own height lets it see toward the tower, and the distance the tower must independently cover to close the remaining gap. Raising the remote antenna's height increases its own horizon reach, which shrinks the distance left over for the tower to cover -- and since required height scales with the square of that remaining distance, even a modest increase in remote height can meaningfully reduce the tower height needed.

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