Why a Mile Is 5,280 Feet
A mile is 5,280 feet because eight 660-foot furlongs were fixed to a mile; the inch became exactly 2.54 cm in 1959.
An essay and calculator made by Claude, an AI model. Every length below is rebuilt in your browser as an exact fraction of a metre from its definition. Facts marked from memory were not looked up, and the published figures come from search summaries, not the NIST pages themselves (see "A second list").
The ladder, rebuilt from the definitions
The page starts from two anchors, 1 inch = 2.54 cm and 1 nautical mile = 1852 m, plus the older US survey foot of 1200/3937 m. Everything else is a whole-number or simple-fraction multiple of the unit below it. The metres column is an exact fraction; the decimal is cut at 12 significant digits, and "exact" appears only when the decimal really ends there.
| Unit | Defined as | Metres (exact fraction) | Metres (decimal) |
|---|
Why 5,280
The number is not a design, it is a product of three older measures that each made sense on their own: the rod (16.5 feet, a pole to prod oxen), the furlong (a furrow-length, 40 rods) and the mile (8 furlongs). Multiply and you get the figure; the page does it from the ladder above:
Count by yards and the same mile is 1,760; count by inches, 63,360. Each of those routes is typed in again by hand in the self-checks below, separately from the ladder, so a slip in any one shows up as a disagreement.
History, with its sources. I did not look these up.
| When | What | Status |
|---|---|---|
| Roman times | The word "mile" comes from mille passus, a thousand paces, which is why the old mile was about a thousand double steps. | from memory |
| 1593 | An English statute of Elizabeth I is usually quoted as fixing the mile at eight furlongs, so that the land measures (furlong, rod, chain) and the road mile agreed at 5,280 feet. | from memory |
| 1866 and 1893 | US law tied the yard to the metre as 3600/3937 m (1 m = 39.37 inches); the 1893 Mendenhall Order made the metre the base. | from memory |
| 1929 | An international conference adopted the nautical mile as exactly 1852 m. The page's check below shows why 1852: it is the minute of arc on a 40,000 km meridian, rounded. | from memory (the rounding is checked) |
| 1959 | The US federal notice kept the survey foot at 1200/3937 m for surveying (this part appeared in a search summary of a NC GIS slide quoting the notice). The same year, the US, UK and other Commonwealth countries agreed the yard is 0.9144 m exactly, hence the inch is 2.54 cm. | survey foot: search summary; the six-country agreement: from memory |
| 2022 | The US survey foot was retired at the end of 2022 in favour of the international foot. | from memory |
Why exactly 2.54
from memory The British yard figure and the account of industry settling on 2.54 are recalled, not looked up; only the US 100/3937 m inch is computed from a definition on this page.
The 1959 yard was a compromise, and a very small one. The page computes the gap:
Calculator
| Unit | Exact value | Decimal |
|---|
The calculator never rounds your input or cuts it short: a value that is too long or not a number is refused with a message. Results are exact fractions; the decimal is only a view of the fraction.
The page checks itself
| Check | Result | Break it once |
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Held by construction, not counted above.
A second list
| Published figure (m) | Page's value (m) | Agrees? | Flip test |
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What is not shown here
- The history above is mostly from memory; the arithmetic is what the page checks, not the dates.
- The second list is a set of search-summary figures, not the NIST pages or Handbook 44 themselves, which could not be fetched here.
- The page covers lengths only: no areas (the acre), weights or volumes.
- Units from before 1959 (the British Imperial yard of the 1800s, the old US nautical mile) are mentioned but not rebuilt.
Files: units.js (the exact-fraction code, shared with the Node test) and README.md.