Roman numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:
The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.
One place they are often seen is on clock faces. For instance, on the clock of Big Ben, the hours from 1 to 12 are written as:
The notations and can be read as "one less than five" and "one less than ten", although there is a tradition favouring representation of "4" as "" on Roman numeral clocks.
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs., signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written. For the years of this century, indicates 2000. The current year is .
Description
There has never been an officially "binding", or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely "classical" notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved "flexibility".On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law it is desirable to strictly follow the usual modern standardized orthography.
"Standard" form
This section defines a standard form of Roman numerals that is in current, more or less universal use, is unambiguous, and permits only one representation for each value. It does not attempt to either endorse or refute every combination of Roman numeral symbols that has been, could be, or is used.Roman numerals are essentially a decimal or "base 10" number system, with a "digit" for each power of ten – thousands, hundreds, tens and units. Each digit is represented by a fixed symbol or combination of symbols. In the absence of "place keeping" zeros, different symbols are used for each power of ten but each follows the same pattern, as summarised in this table
Thousands | Hundreds | Tens | Units | |
1 | ||||
2 | ||||
3 | ||||
4 | ||||
5 | ||||
6 | ||||
7 | ||||
8 | ||||
9 |
The numerals for 4 and 9 are written using "subtractive notation", where the first symbol is subtracted from the larger one, thus avoiding the clumsier. Subtractive notation is also used for 40 and 90, as well as 400 and 900. These are the only subtractive forms in standard use.
A number containing several decimal digits is built by appending them from highest to lowest, as in the following examples:
- 39 = + = '.
- 246 = + + = '.
- 789 = + + = '.
- 2,421 = + + + = '.
- 160 = + = '
- 207 = + = '
- 1,009 = + = '
- 1,066 = + + = '
- 1776 = + + + = '.
- 1918 = + + + = '
- 1954 = + + + = '
- 2014 = + + = ' Olympic Winter Games )
Variant forms
Forms exist that vary in one way or another from the general "standard" described above.Use of additive notation
While subtractive notation for 4, 40 and 400 has been the usual form since Roman times, additive notation continued to be used, including in compound numbers like,, and. The additive forms for 9, 90, and 900 have also been used, although less frequently.The two conventions could be mixed in the same document or inscription, even in the same numeral. On the numbered gates to the Colosseum, for instance, is systematically used instead of, but subtractive notation is used for other digits; so that gate 44 is labelled. Isaac Asimov speculates that the use of, as the initial letters of IVPITTER, may have been felt to have been impious in this context.
Modern clock faces that use Roman numerals still usually employ for four o'clock but for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century. However, this is far from universal: for example, the clock on the Palace of Westminster tower, "Big Ben", uses a subtractive for 4 o'clock.
, London. The year 1910 is rendered as, rather than the more usual |alt=
Several monumental inscriptions created in the early 20th century use variant forms for "1900". These vary from – a classical use of additive notation for , as seen on Admiralty Arch, London, to the more unusual, if not unique for , on the north entrance to the Saint Louis Art Museum.
Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written and instead of and, and there are instances such as and rather than or.
Irregular subtractive notation
The irregular use of subtractive notation, such as for 17, for 18, for 97, for 98, and for 99 have been occasionally used. A possible explanation is that the word for 18 in Latin is duodeviginti, literally "two from twenty". Similarly, the words for 98 and 99 were duodecentum and undecentum, respectively. However, the explanation does not seem to apply to and, since the Latin words for 17 and 97 were septendecim and nonaginta septem, respectively.Another example of irregular subtractive notation is the use of for 18. It was used by officers of the XVIII Roman Legion to write their number. The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than.
On the publicly displayed official Roman calendars known as Fasti, the numbers 18 and 28 could be represented by XIIX and XXIIX respectively; the XIIX for 18 days to the next Kalends, and XXIIX for the number of days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.
Rare variants
While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.. "1613" in the date is rendered, instead of
- was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely duo et vice'sima rather than the "regular" vice'sima secunda. Apparently, at least one ancient stonecutter mistakenly thought that the of "22nd Legion" stood for 18, and "corrected" it to.
- There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as , corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as as in French quinze-cent-dix-neuf, and similar readings in other languages.
- In some French texts from the 15th century and later one finds constructions like for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf. Similarly, in some English documents one finds, for example, 77 written as "".
- Another medieval accounting text from 1301 renders numbers like 13,573 as "", that is, "13×1000 + 5×100 + 3×20 + 13".
- Other numerals that do not fit the usual patterns – such as for 45, instead of the usual — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.
Non-numeric combinations
Zero
The number zero did not originally have its own Roman numeral, but the word nulla was used by medieval scholars to represent 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525. About 725, Bede or one of his colleagues used the letter, the initial of nulla or of nihil for 0, in a table of epacts, all written in Roman numerals.Fractions
Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve makes it easier to handle the common fractions of and than does a system based on ten On coins, many of which had values that were duodecimal fractions of the unit, quadrantis"Quarter" = ···· or ∷Triens, trientis"Third"····· or ⁙, dodrantisor nonuncium, nonuncii"Less a quarter"
or "ninth ounce" = ···· or ∷Dextans, dextantis
or decunx, decuncis"Less a sixth"
or "ten ounces" ····· or ⁙Deunx, deuncis"Less an ounce" = 1As "Unit"
The arrangement of the dots was variable and not necessarily linear. Five dots arranged like are known as a quincunx, from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.
Other Roman fractional notations included the following:
- sescuncia, sescunciae, represented by a sequence of the symbols for the semuncia and the uncia.
- semuncia, semunciae, represented by several variant glyphs deriving from the shape of the Greek letter sigma, one variant resembling the pound sign without the horizontal line and another resembling the Cyrillic letter.
- binae sextulae, binarum sextularum or duella, duellae, represented by a sequence of two reversed Ss.
- sicilicus, sicilici, represented by a reversed C.
- sextula, sextulae, represented by a reversed S.
- = 12^{−2} dimidia sextula, dimidiae sextulae, represented by a reversed S crossed by a horizontal line.
- scripulum, scripuli, represented by the symbol.
- = 12^{−3} siliqua, siliquae, represented by a symbol resembling closing guillemets.
Large numbers
Apostrophus
One of these was the apostrophus, in which 500 was written as, while 1,000, was written as instead of "". This is a system of encasing numbers to denote thousands, which has its origins in Etruscan numeral usage. The and used to represent 500 and 1,000 most likely preceded, and subsequently influenced, the adoption of "" and "" in conventional Roman numerals.In this system, an extra denoted 500, and multiple extra s are used to denote 5,000, 50,000, etc. For example:
Base number | = 1,000 | = 10,000 | = 100,000 | |
1 extra | = 500 | = 1,500 | = 10,500 | = 100,500 |
2 extra s | = 5,000 | = 15,000 | = 105,000 | |
3 extra s | = 50,000 | = 150,000 |
Sometimes was reduced to for 1,000. John Wallis is often credited for introducing the symbol for infinity, and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, for 5,000 was reduced to ; for 10,000 to ; for 50,000 to ; and for 100,000 to.
Vinculum
Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a "bar" or "overline". Although mathematical historian David Eugene Smith disputes that this was part of ancient Roman usage, the notation was certainly in use in the Middle Ages. Although modern usage is largely hypothetical it is certainly easier for a modern user to decode than the Apostrophus,- ' = 4,000
- ' = 4,627
- ' = 25,000
- ' = 25,459
- ' for 80,000
- ' for 200,000
Origin of the system
The system is closely associated with the ancient city-state of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.Etruscan numerals
Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.The Roman numerals, in particular, are directly derived from the Etruscan number symbols: "?", "?", "?", "?", and "?" for 1, 5, 10, 50, and 100. As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = ???????
The symbols "?" and "?" resembled letters of the Etruscan alphabet, but "?", "?", and "?" did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as "?????", "????", and ???, mirroring the way they spoke those numbers ; and similarly for 27, 28, 29, 37, 38, etc. However they did not write "??" for 4, and wrote "???", "????" and "?????" for 7, 8, and 9, respectively.
Early Roman numerals
The early Roman numerals for 1, 10, and 100 were the Etruscan ones: "", "", and "". The symbols for 5 and 50 changed from and "?" to and ↆ at some point. The latter had flattened to by the time of Augustus, and soon afterwards became identified with the graphically similar letter.The symbol for 100 was written variously as or, was then abbreviated to or, with finally winning out. It may have helped that is the initial of centum, Latin for "hundred".
The numbers 500 and 1000 were denoted by or overlaid with a box or circle. Thus 500 was like a superimposed on a. It became or by the time of Augustus, under the graphic influence of the letter. It was later identified as the letter ; an alternative symbol for "thousand" was a, and half of a thousand or "five hundred" is the right half of the symbol,, and this may have been converted into.
The notation for 1000 was a circled or boxed : Ⓧ,,, and by Augustinian times was partially identified with the Greek letter phi. Over time, the symbol changed to and. The latter symbol further evolved into, then, and eventually changed to under the influence of the Latin word mille "thousand".
According to Paul Kayser, the basic numerical symbols were,, and and the intermediate ones were derived by taking half of those.
Use in the Middle Ages and Renaissance
, minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used:,,,, and so on.Since the Middle Ages, a "" has sometimes been substituted for the final "" of a "lower-case" Roman numeral, such as "" for 3 or "" for 7. This "" can be considered a swash variant of "". The use of a final "" is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written.
Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one, while others serve as abbreviations for compound numerals. Although they are still listed today in some dictionaries, they are long out of use.
Number | Medieval abbreviation | Notes and etymology |
5 | Resembles an upside-down V. Also said to equal 500. | |
6 | ↅ | Either from a ligature of, or from digamma, the Greek numeral 6. |
7 | , | Presumed abbreviation of septem, Latin for 7. |
9.5 | Scribal abbreviation, an x with a slash through it. Likewise, represented 8.5 | |
11 | Presumed abbreviation of onze, French for 11. | |
40 | Presumed abbreviation of English forty. | |
70 | Also could stand for 7, with the same derivation. | |
80 | ||
90 | Presumed abbreviation of nonaginta, Latin for 90.. | |
150 | Possibly derived from the lowercase y's shape. | |
151 | Unusual, origin unknown; also said to stand for 250. | |
160 | Possibly derived from Greek tetra, as 4 × 40 = 160. | |
200 | Could also stand for 2. From a barring of two 's. | |
250 | ||
300 | ||
400 | , | |
500 | Redundant with ; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000. | |
800 | Borrowed from Gothic. | |
900 | Borrowed from Gothic. | |
2000 |
Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters,,,,,, and. By putting these letters together, the reader would obtain a number, usually indicating a particular year.
Modern use
By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records. Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:- Names of monarchs and popes, e.g. Elizabeth of the United Kingdom, Pope Benedict. These are referred to as regnal numbers and are usually read as ordinals; e.g. is pronounced "the second". This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs seem to have preferred the use of instead of on their coinage.
- Generational suffixes, particularly in the US, for people sharing the same name across generations, for example William Howard Taft.
- In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year when this calendar was introduced to the year when it was abandoned.
- The year of production of films, television shows and other works of art within the work itself. It has been suggested – by BBC News, perhaps facetiously – that this was originally done "in an attempt to disguise the age of films or television programmes." Outside reference to the work will use regular Arabic numerals.
- Hour marks on timepieces. In this context, 4 is often written.
- The year of construction on building faces and cornerstones.
- Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
- Book volume and chapter numbers, as well as the several acts within a play.
- Sequels to some films, video games, and other works.
- Outlines that use numbers to show hierarchical relationships.
- Occurrences of a recurring grand event, for instance:
- * The Summer and Winter Olympic Games
- * The Super Bowl, the annual championship game of the National Football League
- * WrestleMania, the annual professional wrestling event for the WWE. This usage has also been inconsistent.
Specific disciplines
In chemistry, Roman numerals are often used to denote the groups of the periodic table.
They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.
In education, school grades are sometimes referred to by a Roman numeral; for example, "grade " is sometimes seen for "grade 9".
In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.
In advanced mathematics, when a graph includes negative numbers, its quadrants are named using,,, and. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.
In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals with Arabic numerals being used for divisions and armies.
In music, Roman numerals are used in several contexts:
- Movements are often numbered using Roman numerals.
- In music theory, the diatonic functions are identified using Roman numerals.
- Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.
In photography, Roman numerals are used to denote varying levels of brightness when using the Zone System.
In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.
In sport the team containing the "top" players and representing a nation or province, a club or a school at the highest level in rugby union is often called the "1st ", while a lower-ranking cricket or American football team might be the "3rd ".
In tarot, Roman numerals are used to denote the cards of the Major Arcana.
In theology and biblical scholarship, the Septuagint is often referred to as, as this translation of the Old Testament into Greek is named for the legendary number of its translators.
Modern use in continental Europe
Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe. For instance:Capital or small capital Roman numerals are widely used in Romance languages to denote, e.g. the French and the Spanish siglo XVIII mean "18th century". Slavic languages in and adjacent to Russia similarly favor Roman numerals. On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes "18." before the local word for "century".
's signature, dated 10 November 1988, rendered as 10..1988.
Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates. The is written in Roman numerals, while the day is in Arabic numerals: "14..1789" and ".14.1789" both refer unambiguously to 14 June 1789.
Roman numerals are sometimes used to represent the in hours-of-operation signs displayed in windows or on doors of businesses, and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by. Sunday is represented by. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. In the example case, the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.
Roman numerals may also be used for floor numbering. For instance, apartments in central Amsterdam are indicated as 138-, with both an Arabic numeral and a Roman numeral. The apartment on the ground floor is indicated as 138-huis.
In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from to for the smaller intervals. The sign " | 17" thus marks 17.9 km.
A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals are generally used in contexts where Roman numerals would be used elsewhere.
Unicode
The "Number Forms" block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188. This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12. One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that "or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters".The block also includes some apostrophus symbols for large numbers, an old variant of "L" similar to the Etruscan character, the Claudian letter "reversed C", etc.
Symbol | ↀ | ↁ | ↂ | ↅ | ↆ | ↇ | ↈ |
Value | 1,000 | 5,000 | 10,000 | 6 | 50 | 50,000 | 100,000 |