Calculate radio tower height or radio distance from the other value with meter, foot, kilometer, and mile unit conversions and formulas.
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Radio Distance Formula
The radio distance calculator uses the standard radio horizon approximation for line-of-sight distance from an antenna or tower height.
D = 3.569 * sqrt(H)
H = (D / 3.569)^2
- D = radio distance to the horizon, in kilometers
- H = height of the radio tower or antenna, in meters
- 3.569 = approximation factor that accounts for Earth curvature and standard atmospheric refraction
If you enter the tower height, the calculator finds the estimated radio distance using D = 3.569 × √H. If you enter the radio distance, it rearranges the same formula to find the required height using H = (D / 3.569)2.
The calculator converts feet to meters before calculating height-based distance, and it converts miles to kilometers before calculating the required tower height. The final result can then be shown in meters, feet, kilometers, or miles depending on the selected output unit.
Common Tower Heights and Estimated Radio Distance
The values below use the same formula as the calculator, with height in meters and distance rounded to two decimal places.
| Tower height | Estimated distance | Estimated distance |
|---|---|---|
| 10 m | 11.29 km | 7.02 mi |
| 25 m | 17.85 km | 11.09 mi |
| 50 m | 25.24 km | 15.68 mi |
| 100 m | 35.69 km | 22.18 mi |
| 250 m | 56.43 km | 35.06 mi |
Unit Conversions Used
| Conversion | Value |
|---|---|
| Feet to meters | 1 ft = 0.3048 m |
| Meters to feet | 1 m = 3.28084 ft |
| Miles to kilometers | 1 mi = 1.60934 km |
| Kilometers to miles | 1 km = 0.621371 mi |
Example Problems
Example 1: Find radio distance from tower height
Given: Tower height = 50 m
D = 3.569 * sqrt(50)
D = 25.2376 km
A 50 meter tower has an estimated radio distance of 25.2376 km, or about 15.682 mi.
Example 2: Find required tower height from radio distance
Given: Radio distance = 30 km
H = (30 / 3.569)^2
H = 70.6418 m
To reach an estimated radio distance of 30 km, the required tower height is about 70.6418 m, or about 231.7657 ft.
FAQ
What does radio distance mean?
Radio distance is the estimated line-of-sight distance from a tower or antenna to the radio horizon. It is mainly based on antenna height and Earth curvature. A taller antenna can usually reach farther because the horizon is farther away.
Does this calculate actual signal range?
No. This calculates an estimated radio horizon distance, not guaranteed signal coverage. Actual radio range can be affected by transmitter power, receiver sensitivity, antenna gain, frequency, terrain, buildings, trees, weather, and interference.
Why does the formula use tower height?
For line-of-sight radio paths, height is important because the Earth blocks signals beyond the horizon. Increasing tower height increases the distance to the horizon, but the relationship is not linear. Distance increases with the square root of height, so doubling the tower height does not double the distance.
