Line-of-sight range calculator
The radio horizon is further than the optical one
The atmosphere refracts radio waves and bends them slightly around the curve of the Earth. So the radio horizon is worked out for an equivalent radius of 4/3 of the true one — about 15 % further than the eye can see.
| Transmit antenna height (m) | |
| Receive antenna height (m) | |
| Horizon model | |
| Result | |
| Line-of-sight range | |
📐 The formulas
Range between two antennas:
d = √(h₁² + 2Rk × h₁) + √(h₂² + 2Rk × h₂)
A simplified form (heights in metres, range in kilometres):
d ≈ 4.12 × (√h₁ + √h₂) radio horizon, k = 4/3
d ≈ 3.57 × (√h₁ + √h₂) optical horizon, k = 1
Symbols:
h₁,h₂— antenna heights above ground level [m]R— the radius of the Earth, 6371 kmk— the refraction factor: 4/3 for radio, 1 for none
Where this calculator stops:
- The calculation assumes flat terrain: hills, woodland and buildings shorten the range
- This is a geometric limit, not a guarantee of a contact — you also need an adequate link budget
- Tropospheric propagation, inversions and reflections give contacts far beyond the horizon
- Heights are measured from ground level at the site, not above sea level
🎯 In practice
Typical figures (radio horizon):
| Height | To the horizon |
|---|---|
| 2 m (handheld) | 5.8 km |
| 10 m (rooftop mast) | 13 km |
| 30 m (tall mast) | 22.6 km |
| 100 m (a hill) | 41 km |
| 300 m (a mountain) | 71 km |
Practical advice:
- Raising the lower antenna buys more than raising the higher one: range grows as the square root of height.
- Reaching the horizon is not enough — you also have to clear the Fresnel zone, or the path will clip the signal.
- For a realistic estimate, combine this with the radio link budget: the smaller of the two numbers is your answer.
© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.
How to cite this calculator
UR3PKI. «Line-of-sight range calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/line_of_sight (licence CC BY-NC-SA 4.0).The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.