Why are there 5280 feet in a mile?
A few years ago I was curious about why there are 5280 feet in a mile. The explanations I found weren’t very convincing. At the time I made some fixes to some elements of the puzzle in Wikipedia, but today noted that even now, if you perform a Google search for “why are there 5280 feet in a mile”, you still get the conventional, largely inconclusive, explanations.
[2014 Update, it’s a little better now, this blog entry comes 4th on Google and 9th on Bing]
Now, I haven’t found any really good sources. And Wikipedia, of course, is not a soap box nor a place for original research. But my blog is my personal soapbox. So I can write whatever I want here.
So here’s the thing: below is my theory of how the mile ended up with 5280 feet. If you have a better one, please point me to it.
First, the conventional version (replicated in various vaguely crowdsourced locations): the mile was originally 5000 feet. It was changed to 5280 feet in Elizabethan times around 1600 (some point to 1592 or 1593) to accommodate the furlong, which was 660 feet. It was easier to fix the mile rather than the furlong for legal reasons, hence, eight furlongs and 5280 feet in a mile. That’s the version you’ll find online, in encyclopedias, etc. It’ll be fleshed out with bells and whistles, including odd theories about horses, but that’s it. Go ahead, look it up.
The problem with these versions is that they don’t explain why this collision between furlong and mile occurred around 1600, and not centuries before. It implies that people suddenly woke up and realized, hey, wait a second, if there’s 660 feet in a furlong … and eight furlongs in a mile … but 5000 feet in a mile …. wait a second !?!
It implies that four-digit multiplication was invented ca 1600. Like a lot of rear-view-mirror takes on history, the “explanation” boils down to: “before time X people were stupid about topic Y, and at time Z they wizened up.”
I have yet to find a proper and complete write-up of the origins. But I’ve pieced together my own theory over the years. And it’s a fun one because the answer (or rather, hypothesis) is simply this: the number 5280 arises out of a collision between organized religion, the military, and taxation. Three powerful historical forces, to be sure, so the fourth pillar to modern society (rationality) obviously had to be the one to compromise!
But wait, there’s more: naked Greeks are involved, and Jesus, and Vikings. In that order.
Our story starts with the “original” mile, the Roman one. The Romans were both practical and militant. Their mile was 1000 paces – a pace being a double step (left foot, right foot) by a soldier in full battle gear. That was a “passus”, and a mile was a “milia passuum”, hence the word “mile”. We still remember this information in our convention of relating pedometers to miles with the relation of 2000 steps to a mile, a trick also used by hikers etc. But we have forgotten that it’s not a “trick”, it’s the whole point. Historically, thus, a mile is defined as 2000 steps.
Furthermore, the Romans had another convention, which was to place stones next to their roads to mark the distance from Rome. Called “milliarium”, these stone obelisks were first erected along the Via Appia, where milestones dating as far back as the second century BC still survive. (The central stone in Rome, from which the “all roads lead to Rome” phrase derives, wasn’t erected until some two centuries later in 20 BC, but is since lost.) Naturally, quite a large number of these stones survived along roads throughout Europe, providing a natural reference point, explaining why their particular measure of a “foot” survives with high accuracy.
It’s worth injecting that the popular notion that Roman roads all had measures of the distance from Rome is a myth: only central Italy and a few exceptions were marked from central Rome, all other roads were measured from the nearest local significant center. The US’ attempt to replicate this myth with the Zero Mile marker in Washington, DC, in 1792 would have a similar destiny, influencing only measurements nearby.
We know very little of the details of how the Roman army used the mile as a practical tool; not a single significant military treatise has survived from Roman times. The one treatise that has survived, the Epitoma rei militaris is not considered authoritative, and the claims (that the army marched 20 miles in 5 summer hours at regular pace and 24 miles at double pace) cannot be checked against any contemporary sources, and seem (very) high.
You can measure yourself to realize that the miles per hour measure is practical for a human: casual walking is 2 mph, easy walk is 3, swift walking is 4. The available number of hours in a day is similarly small, thus making the mental arithmetic simple.
Hence, 5000 feet to the mile, a general measure that survived throughout Europe as roadside reminders of the might of Rome.
Now, about the furlong. It means “a furrow long” (long as a furrow) and is a practical measure in an agrarian society: it is (approximately) the distance an oxen can plow without resting. That distance was standardized to be 40 “rods”, where a rod (or “pole”) is 5.5 yards (16.5 feet). An “acre” (which means “field”) was 40 rods long and 4 rods wide (4 rods was also called a “chain”). An acre was the surface area that one man and one oxen could till in one day.
At this point, if you’re paying attention, you’ll see that not only do we have the decimal (base 10) concept in the “mile” (one thousand paces), but also in the acre: the proportions of the sides are exactly 10:1.
This tradition of the furlong took root in England between the fall of Rome and the Norman conquest of 1066. With the Normans came the re-introduction of the Roman definition of the foot as 12 inches – a reference foot was carved into one of the pier bases of the new nave in St Paul’s cathedral in London in 1104 (by the son of a banker, interestingly enough).
The Saxon tradition of measuring land had been established in terms of rods, probably based on 20 “natural” feet (i.e. not Roman standard feet but real 9.8-inch feet). 20, of course, was the common “decimal” system prior to the invention of shoes (at which point you can’t see your toes). Vestiges of base-20 remain, notably for our story, in Danish and French. For example, in French you say “soixante-dix” for 70 and in Danish you say “tresindstyve” for 60. So again, we have a “decimal” element here, too; but one that’s older than shoes and technically known as the “vigesimal” system.
The new Norman Kings, with or without shoes, had little interest in imposing a new measurement system. Thus when the Domesday book was assembled in 1086, the basic measure of taxation for the Danelaw counties was the “carucate” which was 120 acres – the amount of land tillable by a team of eight oxen in a plowing season. The measures were very approximate; the Domesday book is not an accurate survey in any modern sense. Danelaw, of course, derives from Danish Viking laws. The eight oxen was the notional “plough team”.
When the Saxon rod was measured with a Norman foot (e.g. the Roman 12-inch foot), it’s 16.5 feet long. If that’s an awkward multiple, the Norman kings didn’t care. The number wouldn’t be used for anything in a regular fashion. Acres were the important measure. There just had to be some official relationship between them: “198 inches in a rod”. It’s sort of like the definition of the second – today it’s defined as “9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”. You probably didn’t know that. But that doesn’t stop you from using seconds all the times. Medieval farmers didn’t measure their farmland using their thumbs any more than you use caesium to catch the bus.
(Edit: I forgot to note that the Norman foot as handed down to us does not appear to exactly correspond to the Roman foot. Estimates of the Roman foot vary between 11.6 and 11.7 modern inches. Versus 12 inches, between two milestones that’s an error of over 100 feet, and not a likely error. More likely, the Normans also had to account for the Saxon yard, and indeed King Edward I around 1300 created the standard yard, and decreed that a foot was a third of it. Likely whatever exact notion of a Norman foot there was around the year 1100, it had to morph a little to fit an exact number of times inside the yard.)
So this left us with the 11th century (tax-and-military) status in England: an acre is 40 by 4 rods, a rod is 16.5 feet, and a foot is 12 inches. There are numerous other measures as well, but I’m trying to keep this simple. (And now you see why there are 43,560 square feet in an acre.)
And so far, we’ve covered the role of the military and taxation. Enter religion.
Between 1382 and 1395, John Wycliffe and friends translated the Bible from the official Latin version (the “Vulgate”) to vernacular English. Now known as “Wyclif’s Bible”, it significantly predated the the King James Version, which was “authorized” and completed in 1611, and was the first complete English language version.
The dilemma is how to translate the greek “stadio”, which of course refers to the standard length of the first Greek Olympic sport, the 200-meter sprint (well, approximately 200 meters, we’re not sure). Consider, for example, Luke 24:13 “And lo! tweyne of hem wenten in that dai in to a castel, that was fro Jerusalem the space of sixti furlongis, bi name Emaws.” Notice the phrase “sixti furlongis”; Wycliffe is translating the Greek “stadio” directly to furlongs. This assumption continued forward to the King James Version (“And, behold, two of them went that same day to a village called Emmaus, which was from Jerusalem about threescore furlongs”).
The original Greek, of course, is “Καὶ ἰδοὺ δύο ἐξ αὐτῶν ἐν αὐτῇ τῇ ἡμέρᾳ ἦσαν πορευόμενοι εἰς κώμην ἀπέχουσαν σταδίους ἑξήκοντα ἀπὸ Ἰερουσαλήμ, ἧ ὄνομα Ἐμμαοῦς,”. The important word here is “στάδιον” meaning stadium.
In the Hellenic system, a stadium (the precise length of which is not known) is 600 “podes”. A “pous” (the singular form) is the Greek foot. The length of a Greek foot varied but was about the same as Roman foot. However, Wycliffe was working off the Latin version – the Vulgate. The Latin (Vulgate) version of Luke 24:13 is “et ecce duo ex illis ibant ipsa die in castellum quod erat in spatio stadiorum sexaginta ab Hierusalem nomine Emmaus”. Notice the use of “stadiorum”? The Vulgate, dating from the 4th Century, presented a straight translation from the Greek. Greek and Roman feet may be the same, but the Roman stadium was 625 feet, not 600. The Greek didn’t have any distance measure corresponding to “mile” so they didn’t worry about 600 not evenly fitting into 5000. The Romans clearly did, and since the Greek foot wasn’t very carefully standardized, rounding up to 625 didn’t matter (I’m guessing here, the details are completely lost in history).
But there is no notion of “stadium” in English. And furlongs were not meant to be an eighth of a mile. Furlongs were 660 feet, for reasons described above. But from Wycliffe’s perspective, none of that mattered. He was on a mission to simplify – he wanted the common man to read the Bible. And whether the stadium distance of the Bible was 600, 625, or 660 feet, he didn’t care. Or so I infer.
(Edit) A curious but relevant item i omitted: the laws of the English kings from 1042 through 1272 were written in Latin. Laws were not written in English until 1488 and onwards.
By the way, “mile” in the sense of the Roman one is mentioned once in the Bible, in Matthew 5:41 (King James Version): “And whosoever shall compel thee to go a mile, go with him twain.” The reason the mile is used here is that the Romans would compel locals to carry their gear for up to one (Roman) mile. So Jesus’ contemporaries would know what was implied. Wycliffe the scholar would surely know this.
Was Wycliffe using the local custom in the late 14th century of fitting eight furlongs into a mile, or was he simply rounding off on his own initiative, knowing full well that there were approximately eight Greek stadia in a Roman (and hence Norman) mile? More on this shortly.
The translation of the Bible into English did not go down well with authorities. In 1428, on order from the Pope, Wycliffe’s body was exhumed, burned, and the ashes scattered, following a proclamation that the translation of the Bible into vernacular English was heresy. Persecution of attempts to spread unauthorized translations continued for well over a century. When William Tyndale became the first man to print the New Testament in English in 1526 (two copies have survived), he had to do so from the continent, and copies smuggled into England were burned, as best as the Church and the Crown were able to. Tyndale himself was eventually burned for his efforts, too.
Tyndale probably didn’t use Wycliffe’s translation at all, but worked from the Greek New Testament. I haven’t found any good quality versions online, but some poorly done OCRs confirm that Tyndale, too, uses “furlong” in his 1526 translation of Luke 24:13 (“And beholde two of them went that same daye to a toune which was from Jerusalem about thre scoore forlonges, called Emaus” – notice how Tyndale inserts the word “about”). Despite the burnings and the “abouts”, a furlong as an eighth of a mile is now in the vernacular.
A clue to what probably happened in this transition comes from Arnold’s Almanac. Written around 1500 and based off earlier, now lost, sources, “Arnold” writes a section on “the Mesur to mete Lande by” he states that “viij furlong make an English myle”, but still considers a mile to be 5000 feet. He mentions rods, but here’s the interesting part: he says they vary, mentioning 18, 20, and 21 feet – other sources use still other measures. This doesn’t matter, however: “but of what lengith soo euer they be C.lx. perches make an akir”. Why not care? Because the accuracy of distance over land is not remotely as important as the accuracy of surface of land.
Today, we consider accuracy of distance as inseparable from accuracy in surface. But these vagaries were intellectually sound prior to the onslaught of the early Renaissance. The revolution in Mathematics was just beginning: Luca Pacioli published the Summa de arithmetica, geometria, proportioni et proportionalita in Venice in 1494 and Gerolamo Cardano published Ars Magna in 1540. A genuine marriage of algebra and geometry would of course have to wait until Descartes and La Géométrie in 1637, but nevertheless the broadening of the mathematics of measurement in England in the sixteenth century must have been dramatic.
Thus our next and final point in history is when our current standardization to 5280 became official under Elizabeth I in an act of parliament in 1592. At this point, the popular perception of a furlong was well established that it was an eighth of a mile. Of course, the concept of “acre” could not be changed since it was inherent in the management of land and taxation. The military at this point didn’t do that much marching and didn’t care much about the Roman mile: England was a marine power and ships don’t navigate by counting footsteps. By the time of Elizabeth’s reform, the Age of Exploration was a century old, and navigation at sea was highly developed.
So the furlong was 660 feet because the Saxon foot was smaller than the Roman, and because Oxen apparently tire easily, and because Danish Vikings were good at taxation, and because the Greeks liked running. Naked. And why are there eight of these things in a mile? Because the Bible says so. If English was good enough for Jesus, it’s good enough for us.
Well that was a long story. So, why, exactly, did we get stuck with 5280 feet in the mile? The short answer is that there is no short answer. But it’s not because people were stupid. Let me try a “summary”:
- The Romans standardized their mile to be 1000 paces, each defined as 5 feet, each foot was 12 (Roman) inches. Since milestones survived throughout Europe after the fall of Rome, and these were marked with distances to local centers, this provided a surviving reference point.
- After the fall of the Roman Empire and up to the Norman conquest of 1066, Britain was ruled by Angles, Saxons, Jutes, and Danish viking invaders. The Saxons introduced the “rod” (or “perch”), which is believed to have been 20 “natural” feet of about 9.8 or 9.9 inches. A rod, in other words, is the distance measured out by your feet as you count off all your fingers and toes (and is likely a very ancient measure of distance).
- During this period, and up to this day, and “acre” was defined as an area 40 rods long and 4 rods wide, or 160 “perches” (one perch/rod square), and corresponded to a practical surface definition for a simple (and practical) farming society: the length was about the distance an oxen could plow before taking a break, and the total area was about the amount of land that a single man with one oxen could plow in one work day. The length, 40 rods, was thus called furlong (“one furrow long”).
- The acre became the basis for legal agreements, deeds, taxation, borders, etc throughout Britain, so once established, was there to stay (and still is the same).
- When the Normans invaded in 1066, they brought back the Roman system, notably the Roman foot, which was about 11.65 of today’s inches vs the Saxon foot of about 9.9 inches. This led the Norman Kings to define the rod as 16.5 Roman feet, as opposed to 20 Saxon feet. By this time rods weren’t measured with actual human feet anymore, but with defined reference rods, so the discrepancy no longer mattered. The Norman foot, probably closer to the 11.6-11.7 inches that is the Roman foot, had to stretch a little to fit an even three times into the Saxon yard, and was so defined by 1300.
- Around 1400 the movement to translate the Bible to vernacular English brought a need to translate the New Testament use of the Greek word for “stadium”. The furlong was close enough, so the translations would variously insert the word “about” in their texts; nevertheless, the literary equivalence between the stadium and the furlong was established by default in the 1400s.
- The discrepancies between different definitions of distance were well understood prior to the sixteenth century. But the accuracy of distance was not as important as the accuracy of surface
- The early part of the Renaissance leads to a dramatic growth in the depth and width of mathematical learning in the sixteenth century.
- Finally, with a 1592 act of Parliament under Elizabeth I, the various discrepant measurement systems were sorted through and standardized. With various versions of the mile in use throughout the kingdom, the Biblical equivalence of a furlong with a stadium well established, and the definition of an acre important to keep constant, the mile itself was the most malleable. This left us with the furlong of 660 feet (40 times 16.5) and eight furlongs make 5280 feet.
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