| Nautical leagues (nlea) | Ångströms (Å) |
|---|---|
| 1 Nautical league | 55560000000000 Å |
| 2 Nautical leagues | 111120000000000 Å |
| 3 Nautical leagues | 166680000000000 Å |
| 4 Nautical leagues | 222240000000000 Å |
| 5 Nautical leagues | 277800000000000 Å |
| 10 Nautical leagues | 555600000000000 Å |
| 20 Nautical leagues | 1.1112 × 1015 Å |
| 25 Nautical leagues | 1.389 × 1015 Å |
| 50 Nautical leagues | 2.778 × 1015 Å |
| 100 Nautical leagues | 5.556 × 1015 Å |
| Reference | Nautical leagues (nlea) | Ångströms (Å) |
|---|---|---|
| A sheet of A4 paper (long side) | 0.0000534557 nlea | 2.97 × 109 Å |
| Average adult human height | 0.000305976 nlea | 1.7 × 1010 Å |
| A football pitch (length) | 0.0188985 nlea | 1.05 × 1012 Å |
| A marathon | 7.59449 nlea | 4.2195 × 1014 Å |
| Height of Mount Everest | 1.59269 nlea | 8.849 × 1013 Å |
The nautical league is a unit of length equal to three nautical miles, or exactly 5556 metres. It is longer than the land league by about 728 metres, since it is built from the nautical mile of 1852 metres rather than the statute mile.
The unit belonged to an era when it was the practical measure of coastal jurisdiction. The cannon shot rule, articulated in the seventeenth and eighteenth centuries, held that a state's authority extended as far as it could defend from shore, conventionally taken as three nautical miles. That distance became the standard territorial sea limit and was expressed as one marine league. Many older treaties and statutes define maritime boundaries in leagues for this reason.
The three-mile limit held for centuries before eroding through the twentieth. States progressively claimed wider waters, and the United Nations Convention on the Law of the Sea settled the matter in 1982 by establishing a twelve nautical mile territorial sea and a two hundred mile exclusive economic zone. Both figures are stated in nautical miles rather than leagues, and the older unit fell out of legal use.
Charts and pilot books from the age of sail used the league routinely for describing offshore distances and the visibility of landmarks. Reading those sources accurately requires knowing which league is meant, since the same word could refer to a land league, a marine league or a Spanish or Portuguese variant, and the differences are large enough to matter when reconstructing a historical position.
Today the unit has no navigational role. Charts are marked in nautical miles, and distances at sea are quoted the same way. The nautical league appears only in historical and legal texts.
The unit also underlies a familiar figure in visibility calculations. From a height of about three metres above sea level, the horizon lies roughly one nautical league away, which is why the three-mile limit corresponded loosely to what a lookout could see as well as to what a gun could reach.
One nautical league equals 3 nautical miles, 5556 metres, 5.556 kilometres, or about 3.452 statute miles.
The ångström is a unit of length equal to one ten-billionth of a metre, or 0.1 nanometres. It takes its name from Anders Jonas Ångström, the Swedish physicist who used it in his 1868 map of the solar spectrum. The symbol is Å, a letter borrowed from the Swedish alphabet.
The ångström survives because it matches the scale of atoms. A hydrogen atom has a radius of about 0.5 Å. A carbon-carbon single bond measures roughly 1.5 Å. Expressing these figures in nanometres produces awkward decimals, so crystallographers, spectroscopists and structural biologists continue to prefer the older unit. Protein structures deposited in public databases are still described by their resolution in ångströms, and a structure resolved to better than 2 Å is considered high quality.
Wavelengths of visible light also fall in a convenient range. Red light sits near 7000 Å and violet near 4000 Å. X-ray wavelengths cluster around 1 Å, which is precisely why X-ray diffraction reveals atomic spacing: the probe and the target are the same size.
The ångström is not part of the International System of Units. The BIPM lists it among units that are accepted for use with SI but discourages new applications, preferring the nanometre or picometre. That guidance has had limited effect in the fields where the unit is entrenched. Semiconductor manufacturing offers a clear illustration. Process nodes were named in nanometres for decades, but as features shrank the industry began quoting gate oxide thicknesses in ångströms, and Intel named a generation of its technology the Angstrom era.
Reading older scientific literature requires care. Before the ångström was tied to the metre it was defined against a specific spectral line of cadmium, and figures published in the early twentieth century may differ slightly from modern values. The International Astronomical Union adopted that spectroscopic definition in 1907, and it stood until the metre itself was redefined against krypton in 1960. The discrepancy is small, but it is real, and it matters when comparing historical spectral measurements against current ones.
Converting is straightforward. One ångström equals 10-10 metres, 0.1 nanometres, or 100 picometres. Ten ångströms make a nanometre.