Lighthouse geographic range calculator
A light 40 m above the sea, seen from an eye height of 2 m, first rises over the horizon at about 14.9 nautical miles. Enter both heights to get this Earth-curvature limit in nautical miles, kilometres or miles. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Lighthouse height
- 40
- Observer height
- 2
- Height unit
- M
- Distance unit
- Nmi
- Lighthouse height m
- 40
- Observer height m
- 2
- Earth radius
- 6,371,000
- Earth radius unit
- M
How far away can a mariner first see a lighthouse light over open water? Geographic range answers that Earth-curvature question from two heights alone: the elevation of the light (focal plane) above sea level and the height of the observer’s eye on the bridge, deck, or shore. This lighthouse geographic range calculator sums the geometric horizon of the light with the geometric horizon of the observer, optionally scaling Earth radius for atmospheric refraction, and returns the maximum separation in nautical miles, kilometres, or other length units.
What geographic range means and how two horizons add
On a spherical Earth a light of height H above the surface cannot send a straight geometric ray beyond the tangent that just grazes the sphere. Elementary right-triangle geometry yields the light’s geometric horizon distance as the square root of two times effective radius times H plus H squared. An observer of eye height h has a symmetric horizon of the same form.
The light becomes just visible when the vessel’s ground range equals the sum of those two horizons: the light’s ray meets the common horizon circle from the tower side and the observer’s line of sight meets it from the sea. That sum is the geographic range of the light for the given eye height—the classic quantity tabulated on light lists alongside luminous (nominal) range. Geographic range depends only on geometry and optional refraction; luminous range depends on candlepower, atmospheric transmissivity, and the threshold of the human eye.
Setting observer height to zero recovers the single-object distance to the sea horizon for the light alone. Setting both heights equal models two identical towers facing each other. Real coasts have haze, swell, cliffs, and islands, so planners treat geographic range as a clear-air upper bound over open water, not a guarantee that the flash will be seen at that distance on a foggy night.
Where the lighthouse range calculation helps
Coastal navigation education uses a lighthouse geographic range calculator so students can turn light-list elevations and bridge eye height into the Earth-curvature limit before discussing luminous range and meteorology. Passage-planning tools estimate when a listed light should rise over the geometric horizon for a given freeboard or bridge height on approach. Chart and content publishers that rank for lighthouse geographic range calculator, lighthouse visibility distance, or how far can you see a lighthouse benefit from a live free browser tool whose math matches the automation path byte for byte.
Search-and-rescue and coastal-watch training convert tower height and vessel freeboard into a planning radius for visual contact over open water. Keep requests small, pin the cleaned floats in tests, and you get reproducible geographic ranges for lessons, apps, and edge workers without standing up a full atmospheric-optics or radio-propagation stack of your own.
What you can do with it
Light-list and passage planning
Convert listed light elevation and bridge eye height into geometric geographic range in nautical miles for approach notes and training.
Maritime classroom demos
Show how raising the light or the observer stretches visibility with the square-root horizon law over open water.
Coastal SAR and watch training
Estimate the clear-air visual contact radius between a tower light height and a vessel freeboard for briefing materials.
FAQ
What is the difference between geographic range and luminous (nominal) range?
Geographic range is the Earth-curvature line-of-sight limit from two heights. Luminous or nominal range depends on light intensity, atmosphere, and eye threshold. A light may be geometrically above the horizon yet still too dim to see.
What height should I use for the lighthouse?
Use the height of the light (focal plane) above mean sea level as published on the light list or chart, not necessarily the top of the tower masonry.
What observer eye height should I enter?
Use bridge or deck eye height above the waterline for a vessel, or standing eye height above the water or beach for a shore observer. Typical bridge values are often several metres; standing adults are often about 1.5–1.8 m.
What refraction factor should I use?
Leave it at 1, the default, for pure geometry. Coastal optical work sometimes uses about 1.15 to 1.33, and radio planners often use 4/3; a higher factor stretches both horizons a little.
Will I really see the light at that distance?
Only in clear air over open water. Geographic range is an upper bound set by the Earth's curve; haze, swell, cliffs, islands or fog can hide the flash well before that point, and the light's brightness sets a separate limit.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/travel/lighthouse-geographic-range \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"lighthouse_height":40,"observer_height":2}'const res = await fetch("https://api.kit.forhosting.com/travel/lighthouse-geographic-range", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"lighthouse_height": 40,
"observer_height": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/travel/lighthouse-geographic-range",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"lighthouse_height": 40,
"observer_height": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/travel/lighthouse-geographic-range", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"lighthouse_height":40,"observer_height":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"lighthouse_height":40,"observer_height":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/travel/lighthouse-geographic-range", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"lighthouse_height": 40,
"observer_height": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "travel.lighthouse_geographic_range",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Failed validation is not billed; successful calls use prepaid KIT balance at the published base price.
Input contract, refraction, units, and response shape
Example: a forty-metre light and a two-metre eye height with default Earth radius and k equals one yield a geographic range of roughly fourteen point nine nautical miles. POST a JSON body with two required non-negative finite numbers: lighthouse_height, the focal-plane or light elevation above mean sea level or the local water surface, and observer_height, the eye height of the mariner or lookout above the same reference. Optional height_unit defaults to metres and accepts m, ft, km, mi, or nmi for both heights together. Optional earth_radius defaults to six million three hundred seventy-one thousand metres, the common mean Earth radius, with optional earth_radius_unit. Optional refraction_k defaults to one for a pure geometric sphere; coastal optical work sometimes uses about one point one five to one point three three, and radio planners often use four thirds. Optional distance_unit defaults to nautical miles, the usual unit on charts and light lists. On success the body echoes the heights and units, reports lighthouse_height_m and observer_height_m, earth_radius_m, refraction_k, and effective_radius_m, returns lighthouse_horizon, observer_horizon, and geographic_range in the chosen distance unit, and always includes geographic_range_m, geographic_range_km, geographic_range_mi, and geographic_range_nmi for multi-unit UIs, plus a formula string and a short assumptions note. Missing fields, negative heights, non-positive radius or k, non-finite values, and unknown unit strings fail with invalid_input naming the problem and are not billed.
Technical questions
How is lighthouse geographic range calculated?
Each height gets a geometric horizon d=sqrt(2·R_eff·height+height²). Geographic range is d(lighthouse_height)+d(observer_height). R_eff is refraction_k times the planetary radius (default mean Earth, k=1).
What does the lighthouse geographic range calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.