| Leagues (lea) | Ångströms (Å) |
|---|---|
| 1 League | 48280320000000 Å |
| 2 Leagues | 96560640000000 Å |
| 3 Leagues | 144840960000000 Å |
| 4 Leagues | 193121280000000 Å |
| 5 Leagues | 241401600000000 Å |
| 10 Leagues | 482803200000000 Å |
| 20 Leagues | 965606400000000 Å |
| 25 Leagues | 1.207008 × 1015 Å |
| 50 Leagues | 2.414016 × 1015 Å |
| 100 Leagues | 4.828032 × 1015 Å |
| Reference | Leagues (lea) | Ångströms (Å) |
|---|---|---|
| A sheet of A4 paper (long side) | 0.0000615157 lea | 2.97 × 109 Å |
| Average adult human height | 0.00035211 lea | 1.7 × 1010 Å |
| A football pitch (length) | 0.021748 lea | 1.05 × 1012 Å |
| A marathon | 8.73959 lea | 4.2195 × 1014 Å |
| Height of Mount Everest | 1.83284 lea | 8.849 × 1013 Å |
The league is a unit of length equal to three miles, 24 furlongs, or exactly 4828.032 metres. It is obsolete in every practical sense, surviving mainly in literature and in historical documents.
The unit originated as a measure of how far a person could walk in an hour, which explains both its rough magnitude and its variability. Ancient and medieval leagues differed widely between regions. The Roman leuga was about 2.2 kilometres. French, Spanish and Portuguese leagues each had their own values, and the Spanish legua used in colonial land grants in the Americas differed again, complicating the interpretation of old property records in Texas and the American southwest.
English usage settled on three miles, a figure that was never especially precise in practice because it depended on the mile in force at the time. Since the mile itself was fixed at 5280 feet in 1593, the league inherited that definition, giving the modern value of 4828.032 metres.
Its cultural persistence far exceeds its practical use. Jules Verne's Twenty Thousand Leagues Under the Seas measures a journey rather than a depth, a distinction frequently lost in casual reference: twenty thousand leagues is roughly 96,000 kilometres, more than twice the circumference of the Earth and vastly greater than any ocean depth. Seven-league boots appear in French fairy tales as a device for covering ground in single strides. Tennyson's Charge of the Light Brigade opens with half a league onward.
The unit was formally abolished for trade in the United Kingdom long ago and has no legal standing. It appears occasionally in nautical contexts, where the marine league of three nautical miles is a separate and slightly longer unit.
Because the unit is so variable across languages and centuries, translations of older works can mislead badly. A distance given in leagues in a Spanish colonial document, a French medieval chronicle and an English statute may differ by a factor of two, and historians working with such sources generally convert to modern units and state which league they have assumed.
One league equals 3 miles, 4828.032 metres, or 4.828032 kilometres. A brisk hour's walk covers rather less than one.
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.