Eighteen Miles of Light

How far can you see a lighthouse? There are two answers and you only ever get the shorter one. One is set by the curve of the Earth, the other by how much light is left when it reaches your eye. And the second one, it turns out, is being turned down on purpose.

Stand on a boat at night and look for a light. It can fail to reach you in two completely different ways. It can be below your horizon: the sea bulges up between you and the lamp, and no amount of brightness gets through rock and water. Or it can be too faint: above the horizon, in plain line of sight, but spread so thin by distance and eaten so much by the air that what arrives is less than an eye can notice. Every light therefore has two ranges, the geographic range and the luminous range, and what you see is whichever is smaller.

The two ranges · pick a real light or build your own
Geographic range
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Luminous range
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You see it to
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The side view is drawn in the standard surveyor's frame where light travels in straight lines over an Earth enlarged to allow for ordinary refraction; heights are stretched against distance, and the stretch is printed on the picture. The luminous range is IALA's form of Allard's law with the night threshold of 2×10−7 lux, the illuminance a candle gives at about 2.2 km with nothing in the air between.

Try Beachy Head, the default. Its lamp is 31 m above high water and its published intensity is 21,500 candela. From a small boat with your eye 5 m up, the horizon lets you see it to about 16.1 nautical miles, and on a standard night the light itself carries about 16. The two ranges are nearly the same number, which is not a coincidence you should read anything into, but it is a good place to feel how they trade: climb to a ship's bridge at 15 m and the horizon moves out past 19 miles while the light still dies at 16; let the haze in to 5 miles of visibility and the light is gone by 10.

What a mile costs

The horizon grows with the square root of height, which is gentle. The luminous range is not gentle at all. Light spreads over the square of the distance, and on top of that every mile of air takes a fixed fraction of what is left: with 10 miles of visibility each mile passes about 74% of the light. That second factor compounds, so the far miles are ruinously expensive. One candela, a candle, carries about a mile. A thousand candela carries 9.4. A million carries 25.7. Ten million, 31.9.

Candela needed for each mile of nominal range, and what 60 lights publish
IALA band: candela that rounds to each milelight on its bandlight off its band

Tap a dot.

To double Beachy Head's 16 miles you would need about 480 times the light. To go from 18 miles to 24 costs about 11 times the light. That arithmetic is the whole story of the next two sections.

The constant the lights keep

The yellow band above is not something I drew to fit the dots. It is the table in IALA Recommendation E-200-2, which the engine on this page regenerates from the one formula and two constants (every printed boundary to within the table's own three-figure rounding): an eye needs 2×10−7 lux, and the air is assumed to allow 10 miles of visibility. A light's published nominal range is supposed to be exactly that computation, rounded to the mile.

Trinity House, which runs the lights of England, Wales and the Channel Islands, prints an intensity and a range on each light's page. 32 of the 60 pages that carry both give exactly the range the formula gives for their own candela; 48 are within a mile. Run it backwards, asking each light what threshold its own two numbers imply, and the median answer is 2.01×10−7 lux. The standard's constant can be recovered from the lighthouses' own web pages, without reading the standard.

Most of the misses are a mile or two, and most lean the cautious way: 21 of the 28 pages promise less range than their candela would give. The table shows every light off by three miles or more. Two of them promise far more than their candela can deliver, and for both the formula is what caught it.

LightPublished candelaPublished rangeFormula saysWhat the record says

A web page's intensity field and range field are two numbers someone typed; neither is a measurement you can take from here. What the formula can do is say that they cannot both be right, and it can do it for every light at once.

Eighteen

In 2020 the three General Lighthouse Authorities of the United Kingdom and Ireland (Trinity House, the Northern Lighthouse Board and the Commissioners of Irish Lights) published their review of every aid to navigation they run. Among the conclusions, set down as a bullet point:

A maximum nominal range of 18 miles is considered sufficient for most lighted Visual Aids to Navigation.General Lighthouse Authorities, Aids to Navigation Review 2020 to 2025, section 3.6, among the principles applied

and, in the section on LEDs:

Off the shelf omnidirectional LED AtoN lights can currently provide a nominal range of around 18nM.same document, 4C.5

The review's own appendix lists every light with its range. Here are the 352 that are not buoys:

Nominal ranges of the non-buoy lights in the GLA review appendix (2020)

Eighteen miles is the commonest range on the coast, and the lights above it are being brought down to it. Each change goes out as a Notice to Mariners, and Trinity House keeps them online:

LightNoticeRangeSame light in the US NGA List of Lights, fetched 2026-09-26

Read the last column. The United States' National Geospatial-Intelligence Agency publishes a worldwide List of Lights, free, and it is what a great many chart plotters and apps and web pages quietly draw on. Seven years after Portland Bill went to 18 miles it still prints 25, with the old flash lengths. The latest Notice to Mariners number on that record is 14/2015. Of the 70 Trinity House lights I could match to NGA by position and character, 67 carry the same range in both; the three that do not are three of the four cuts in this table. (Berry Head's stale 19 is shared by Trinity House's own page, so it does not count as a disagreement.)

What does the cut mean in light? From 25 miles to 18 is about 16 times less intensity; from 21 to 18, about 3 times. The review marked more: Flamborough Head (24), Bishop Rock (20), St Catherine's and Trevose "reduce to 18", Nash Point "possible", and it says range reductions will generally be done "as part of the normal Enginering Projects programme" (their spelling), when a station is next re-engineered. Trinity House's own pages still give Flamborough 24 and Bishop Rock 20 today, so those two have not happened yet, or have not reached the pages.

Why would anyone dim a lighthouse? The review's first principle is that lights are now "complementary to and an essential back-up system to" satellite navigation, its third that "having one AtoN in view is acceptable", and 18 miles is what the off-the-shelf LED gives. Put it back into the first instrument: Portland Bill at 43 m, seen from a 5 m eye, drops below the horizon at 18.2 miles. For a small boat the new range and the horizon are nearly the same distance, and most of what was cut was light that only a high bridge could ever have seen. From 15 m up, the horizon is at 21.6 miles and the old light was reaching you; the new one stops at 18.

Not for navigation. Nominal range is a design number: night, no background lights, a point source, 10 miles of visibility, and an observer who only has to detect the light, not read its rhythm. Real luminous range on a given night depends on the actual visibility (which you can move above), on town lights behind the lamp (IALA multiplies the threshold by 10 or 100 for those), and on your eyes. The horizon distance assumes ordinary refraction (coefficient 0.13, the value that gives the familiar 2.07 √h); on a night of strong inversion light bends further, as Light Leans Toward the Cold shows, and lights are seen from beyond their geographic range. None of that is in the numbers here.

The check

Verifier: verify-how-far-can-you-see-a-lighthouse.mjs. It runs from an empty folder against this page's own engine and data; with --live it re-fetches the Trinity House pages and the NGA volumes.