Signal Visibility Calculator

About the Signal Visibility Calculator

Estimates the maximum distance at which a light or signal is visible, accounting for both the observer's height and the signal's height above the horizon.

How to use

Enter the heights of the signal and the observer in metres, then click Calculate.

Worked example

A 20 m lighthouse seen from a 2 m boat → about 21 km.

How to use this calculator

1. Enter the height of the signal source.
2. Enter the observer height if the tool asks for it.
3. Use the calculator to estimate the distance to the horizon where the signal can still be seen.

The formula explained

• \(d\) = maximum visibility distance
• \(R\) = Earth's radius
• \(h_1\) = height of the light or signal source above the ground
• \(h_2\) = height of the observer above the ground

Step by step method

1. Identify the source height and the viewing height used by the calculator.
2. Apply the horizon-distance formula for each height component.
3. Add the two distances to get the total visibility estimate.

Worked example

Suppose a lighthouse light is 30 meters above sea level and the observer is standing 2 meters above sea level.

1. Use the horizon formula for the light height: \(\sqrt{2Rh_1}\). With Earth radius about 6,371,000 meters and \(h_1 = 30\), this is about \(\sqrt{2 \cdot 6371000 \cdot 30} \approx 19,547\) meters.
2. Use the same formula for the observer height: \(\sqrt{2Rh_2}\). With \(h_2 = 2\), this is about \(\sqrt{2 \cdot 6371000 \cdot 2} \approx 5,048\) meters.
3. Add the two distances: 19,547 + 5,048 = 24,595 meters.
4. Convert to kilometers: 24.595 km.

Tips and common mistakes

• Make sure heights use the same unit, usually meters or feet.
• This estimates visibility to the geometric horizon, not whether weather, haze, or buildings block the signal.
• If the signal is on a hill or tall structure, include that elevation in the source height.
• Do not confuse signal range with transmitter power, which is a different calculation.

Frequently asked questions