Range of Lights Calculator
A lighthouse disappears below the horizon at a distance fixed by geometry, not by how bright it is. The geographic range of a light combines the distance to the horizon for the light's own height with the distance to the horizon for your height of eye. The standard Light List formula uses 1.17 times the square root of each height in feet, summed, to give the range in nautical miles. The distance you actually raise the light is the smaller of this geographic range and the charted luminous range. Enter the light height, your height of eye, and the charted luminous range to compare them.
Geographic range formula
Light horizon = 1.17 x sqrt(light height in feet)
Eye horizon = 1.17 x sqrt(height of eye in feet)
Geographic range = light horizon + eye horizon
Distance raised = min(geographic range, luminous range)
The coefficient 1.17 gives nautical miles from a height in feet, including standard refraction. The light first appears at the lesser of its geographic and luminous ranges.
Range of lights notes
- Geographic range depends only on heights, never on the light's intensity.
- Luminous range depends on intensity and the weather; it falls in haze, fog, or rain.
- The light is raised at whichever range is smaller on the night in question.
- Take the charted height of light and nominal range from the U.S. Coast Guard Light List.
- Heights here are in feet to match the 1.17 coefficient; convert meters first if needed.
Range of lights: frequently asked questions
What is the geographic range of a light?
Geographic range is the greatest distance at which a light can theoretically be seen, limited only by the curvature of the Earth. It depends on the height of the light and the observer's height of eye, not on the brilliance of the light. Beyond this range the light is below the horizon.
What is the formula for geographic range?
Using heights in feet, geographic range in nautical miles equals 1.17 times the square root of the light height plus 1.17 times the square root of the height of eye. The coefficient 1.17 accounts for standard terrestrial refraction. This is the formula used in the U.S. Coast Guard Light List.
What is luminous range and how does it differ?
Luminous range is the distance a light can be seen given its intensity and the prevailing visibility, independent of Earth curvature. The distance you actually see a light is the smaller of its geographic range and its luminous range. In clear weather a powerful light is limited by geography; in haze it is limited by luminous range.
Where do I find the height of a light?
The charted height of a light above the water and its nominal luminous range are published in the U.S. Coast Guard Light List and shown on nautical charts. Enter the charted height of the light and your own height of eye; both are user inputs because they are specific to the light and observer.
Why use height of eye?
An observer raised above the water sees a more distant horizon, so a taller bridge or a higher deck extends the range at which a light first appears. The height of eye term adds your own horizon distance to the light's horizon distance to give the total geographic range.
Official sources
- U.S. Coast Guard Navigation Center: Navigation Center and Light List.
- NOAA Office of Coast Survey: Nautical Charts.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.