Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce a system used today. It is based on certain letters which are given values as numerals.
Roman numerals are commonly used in numbered lists (in outline format), clock faces, pages preceding the main body of a book, chord triads in music analysis, the numbering of movie publication dates, successive political leaders or children with identical names, and the numbering of some annual sport events. See #Modern usage below.
|I||1 (one) (unus)|
|V||5 (five) (quinque)|
|X||10 (ten) (decem)|
|L||50 (fifty) (quinquaginta)|
|C||100 (one hundred) (centum)|
|D||500 (five hundred) (quingenti)|
|M||1000 (one thousand) (mille)|
Multiple symbols may be combined to produce numbers in between these values, subject to certain rules on repetition. In cases where it may be shorter, it is sometimes allowable to place a smaller, subtractive, symbol before a larger value, so that, for example, one may write IV or iv for four, rather than IIII. Sometimes, especially in medical prescriptions, a final i becomes j, such as iij for 3 or vij for 7. This was originally done to prevent forgery. Again, for the numbers not assigned a specific symbol, the above given symbols are combined:
For large numbers (4000 and above), a bar can be placed above a base numeral to indicate multiplication by 1000, although the Romans themselves often just wrote out the M's:
The basic Roman numerals follow a pattern:
Thus I descends not from the letter I but from a notch scored across the stick. Every fifth notch was double cut (i.e. ⋀, ⋁, ⋋, ⋌, etc.), and every tenth was cross cut (X), IIIIΛIIIIXIIIIΛIIIIXII…, much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, IIIIΛIII, or the eighth of a longer series of tallies; either way, it could be abbreviated ΛIII (or VIII), as the existence of a Λ implies four prior notches. By extension, eighteen was the eighth tally after the first ten, which could be abbreviated X, and so was XΛIII. Likewise, number four on the stick was the I-notch that could be felt just before the cut of the Λ (V), so it could be written as either IIII or IΛ (IV). Thus the system was neither additive nor subtractive in its conception, but ordinal. When the tallies were transferred to writing, the marks were easily identified with the existing Roman letters I, V, X.
The tenth V or X along the stick received an extra stroke. Thus 50 was written variously as N, И, K, Ψ, ⋔, etc., but perhaps most often as a chicken-track shape like a superimposed V and I - ᗐ. This had flattened to ⊥ (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter L. Likewise, 100 was variously Ж, ⋉, ⋈, H, or as any of the symbols for 50 above plus an extra stroke. The form Ж (that is, a superimposed X and I) came to predominate. It was written variously as >I< or ƆIC, was then abbreviated to Ɔ or C, with C variant finally winning out because, as a letter, it stood for centum, Latin for "hundred".
The hundredth V or X was marked with a box or circle. Thus 500 was like a Ɔ superposed on a ⋌ or ⊢ — that is, like a Þ with a cross bar,— becoming
D or Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified as the letter D, perhaps as an abbreviation of demi-mille "half-thousand"; this at least was the folk etymology given to it later on.
Meanwhile, 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. In different traditions it then evolved along several different routes. Some variants, such as Ψ and CD (the latter more accurately a mirror image of a D, which is not supported by Unicode, adjacent to a regular D), were historical dead ends, although folk etymology later identified D for 500 as graphically half of Φ for 1000 because of the CD variant. A third line, ↀ, survives to this day in two variants:
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 1/3 and 1/4 than does a system based on ten . On coins, many of which had values that were duodecimal fractions of the unit as, they used a tally-like notational system based on twelfths and halves. A dot • indicated an uncia "twelfth", the source of the English words inch and ounce; dots were repeated for fractions up to five twelfths. Six twelfths (one half) was abbreviated as the letter S for semis "half". Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.
Each of these fractions had a name, which was also the name of the corresponding coin:
|Fraction||Roman Numeral||Name (nominative and genitive)||Meaning|
|2/12 = 1/6||•• or :||sextans, sextantis||"sixth"|
|3/12 = 1/4||••• or ∴||quadrans, quadrantis||"quarter"|
|4/12 = 1/3||•••• or ::||triens, trientis||"third"|
|5/12||••••• or :•:||quincunx, quincuncis||"five-ounce" (quinquae unciae → quincunx)|
|6/12 = 1/2||S||semis, semissis||"half"|
|7/12||S•||septunx, septuncis||"seven-ounce" (septem unciae → septunx)|
|8/12 = 2/3||S•• or S:||bes, bessis||"twice" (as in "twice a third")|
|9/12 = 3/4||S••• or S:•|| dodrans, dodrantis|
or nonuncium, nonuncii
| "less a quarter" (de-quadrans → dodrans)|
or "ninth ounce" (nona uncia → nonuncium)
|10/12 = 5/6||S•••• or S::|| dextans, dextantis|
or decunx, decuncis
| "less a sixth" (de-sextans → dextans)|
or "ten ounces" (decem unciae → decunx)
|11/12||S••••• or S:•:||deunx, deuncis||"less an ounce" (de-uncia → deunx)|
|12/12 = 1||I||as, assis||"unit"|
The arrangement of the dots was variable and not necessarily linear. Five dots arranged like :·: (as on the face of a die) 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 fractions include:
Likewise, on some buildings it is possible to see MDCCCCX, for example, representing 1910 instead of MCMX – notably Admiralty Arch in London. The Leader Building in Cleveland, Ohio, at the corner of Superior Avenue and E.6th Street, is marked MDCCCCXII, representing 1912. Another notable example is on Harvard Medical School's Gordon Hall, which reads MDCCCCIIII for 1904. In Dubrovnik, Croatia, a commemorative inscription marking the 1000th anniversary of King Tomislav’s coronation (Croatia’s first King), appears as DCCCCXXV - MDCCCCXXV (925 -1925).
Clock faces that are labeled using Roman numerals conventionally show IIII for four o'clock and IX for nine o'clock, using the subtractive principle in one case and not the other. There are many suggested explanations for this, several of which may be true:
This problem manifested in such questions as why 1990 was not written as MXM instead of the universal usage MCMXC, or why 1999 was not written simply IMM or MIM as opposed to the universal MCMXCIX.
However, these rules are not universally followed.
Modern Roman numerals (i.e. under the rule above) are written by expressing each digit separately starting with the left most digit and skipping any digit with a value of zero. To see this in practice, consider the above example of 1990. In Roman numerals 1990 is rendered: 1000=M, 900=CM, 90=XC; resulting in MCMXC. 2008 is written as 2000=MM, 8=VIII; or MMVIII.
These practices faded from general use before the start of the twentieth century, though the cornerstones of major buildings still occasionally use them. Roman numerals are today still used on building faces for dates: 2008 can be represented as MMVIII. They are also sometimes used in the credits of movies and television programs to denote the year of production, particularly programs made by the BBC and CBS.
Roman numerals remained in common use until about the 14th century, when they were replaced by Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century). The Roman number system is generally regarded as obsolete in modern usage, but is still seen occasionally. Classical numbering is often used to suggest importance or timelessness, or in other cases where an alternate numbering system is useful for clarity. Examples of their current use include:
Sometimes the numerals are written using lower-case letters (thus: i, ii, iii, iv, etc.), particularly if numbering paragraphs or sections within chapters, or for the pagination of the front matter of a book.
Undergraduate degrees at British universities are generally graded using I, IIi, IIii, III for first, upper second (often pronounced "two one"), lower second (often pronounced "two two") and third class respectively.
In chemistry, Roman numerals were formerly used to denote the group in the periodic table of the elements. But there was not international agreement as to whether the group of metals which dissolve in water should be called Group IA or IB, for example, so although references may use them, the international norm has recently switched to Arabic numerals. However, Roman numerals are still used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. For example, FeO is iron(II) oxide and Fe2O3 is iron(III) oxide. In contrast, Arabic numerals are used to denote the formal oxidation state (which is not always the same as the oxidation number) of positively or negatively charged atoms. They are also used for naming phases of polymorphic crystals, such as ice.
In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals, at first by order from the center of the planet, as the four Galilean satellites of Jupiter are numbered, and later by order of discovery; e.g., Callisto was "Jupiter IV" or "J IV". This is particularly amusing in the case of Callisto, because, as mentioned above, the notation IV was mostly disused by the Romans for its similarity to the first two letters of Jupiter. With recent discoveries—Jupiter currently has 63 known satellites—as well as computerization, this is somewhat disparaged for the minor worlds, at least in computerized listings.
Also in music theory, individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings. For example I signifies the E string on the violin and the A string on the viola and cello, these being the highest strings, respectively, on each instrument. They are also sometimes used to signify position. In this case, the number in Roman numerals corresponds with the position number. For example, III means third position and V means fifth.
|Scale degree |
|Scale degree |
The Catalan, French, Hungarian, Italian, Portuguese, Polish, Romanian, Russian and Spanish languages use capital Roman numerals to denote centuries. For example, XVIII refers to the eighteenth century, so as to avoid confusion between the 18th century and the 1800s. (The Italians also take the opposite approach, basing names of centuries on the digits of the years; quattrocento for example is a common Italian name for secolo XV, the fifteenth century.) Some scholars in English-speaking countries have adopted the former method.
In Italy, Poland, Russia, Central Europe, and in Portuguese, Romanian and Serbian languages, mixed Roman and Arabic numerals are used to record dates (usually on tombstones, but also elsewhere, such as in formal letters and official documents). Just as an old clock recorded the hour by Roman numerals while the minutes were measured in Arabic numerals, the month is written in Roman numerals while the day is in Arabic numerals: 14-VI-1789 is 14 June 1789. This is how dates are inscribed on the walls of the Kremlin, for example. This method has the advantage that days and months are not confused in rapid note-taking, and that any range of days or months can be expressed without confusion. For instance, V-VIII is May to August, while 1-V-31-VIII is May 1 to August 31.
In Eastern Europe, especially the Baltic nations, Roman numerals are used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses. Monday is represented by I, which is the initial day of the week. Sunday is represented by VII, which is the final day of the week. 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. The following example hours-of-operation table would be for a business whose hours of operation are 9:30AM to 5:30PM on Mondays, Wednesdays, and Thursdays; 9:30AM to 7:00PM on Tuesdays and Fridays; and 9:30AM to 1:00PM on Saturdays; and which is closed on Sundays.
Since the French use capital Roman numerals to refer to the quarters of the year (III is the third quarter), and this has become the norm in some European standards organisation, the mixed Roman–Arabic method of recording the date has switched to lowercase Roman numerals in many circles, as 4-viii-1961. (ISO has since specified that dates should be given in all Arabic numerals, in ISO 8601 formats.)
In geometry, Roman numerals are often used to show lines of equal length.
In Romania and Serbia to lesser extent, Roman numerals are used for floor numbering. Likewise apartments in central Amsterdam are indicated as 138-III, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as '138-huis'.
In Poland, Roman numerals are used for ordinals in names of some institutions. In particular high schools ("V Liceum Ogólnokształcące w Krakowie" - 5th High School in Kraków), tax offices ("II Urząd Skarbowy w Gdańsku" - 2nd Office of Treasury in Gdańsk) and courts ("I Wydział Cywilny Sądu Okręgowego" - District Court, 1st Civil Division) - use Roman numerals. Institutions that use "Instutition nr N" notation always use Arabic numerals. These include elementary ("Szkoła Podstawowa nr 5") and middle schools ("Gimnazjum nr 5").
In the Middle Ages, Latin writers used a horizontal line above a particular numeral to represent one thousand times that numeral, and additional vertical lines on both sides of the numeral to denote one hundred times the number, as in these examples:
Sometimes 500, usually D, was written as I followed by an apostrophus (which resembles a backwards C, i.e. Ɔ), while 1,000, usually M, was written as CIƆ. This is believed to be a system of encasing numbers to denote thousands (imagine the Cs as parentheses). This system has its origins from Etruscan numeral usage. The D and M symbols to represent 500 and 1,000 were most likely derived from IƆ and CIƆ, respectively.
An extra Ɔ denoted 500, and multiple extra Ɔs are used to denote 5,000, 50,000, etc. For example:
|Base number||CIƆ = 1,000||CCIƆƆ = 10,000||CCCIƆƆƆ = 100,000|
|1 extra Ɔ||IƆ = 500||CIƆƆ = 1,500||CCIƆƆƆ = 10,500||CCCIƆƆƆƆ = 100,500|
|2 extra Ɔs||IƆƆ = 5,000||CCIƆƆƆƆ = 15,000||CCCIƆƆƆƆƆ = 105,000|
|3 extra Ɔs||IƆƆƆ = 50,000||CCCIƆƆƆƆƆƆ = 150,000|
Sometimes CIƆ was reduced to an lemniscate symbol (ↀ) for denoting 1,000. John Wallis is often credited for introducing this symbol to represent infinity (∞), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, 5,000 (IƆƆ) was reduced to ↁ; and 10,000 (CCIƆƆ) was reduced to ↂ
In medieval times, before the letter j emerged as a distinct letter, a series of letters i in Roman numerals was commonly ended with a flourish; hence they actually looked like ij, iij, iiij, etc. This proved useful in preventing fraud, as it was impossible, for example, to add another i to vij to get viij. This practice is now merely an antiquarian's note; it is never used.
|5||A||Resembles an upside-down V. Also said to equal 500.|
|7||S, Z||Presumed abbreviation of septem, Latin for 7.|
|11||O||Presumed abbreviation of (e.g.) onze, French for 11.|
|40||F||Presumed abbreviation of English forty.|
|70||S||Also could stand for 7, and has same etymology.|
|90||N||Presumed abbreviation of nonaginta, Latin for 90.|
|150||Y||Possibly derived from the lowercase y's shape.|
|151||K||This unusual abbreviation's origin is unknown; it has also been said to stand for 250.|
|160||T||Possibly derived from Greek tetra, as 4 x 40 = 160.|
|500||Q||Redundant with D, abbreviation for quingenti, Latin for 500.|
|800||W||More properly, the Greek ω, as W was a fairly new creation.|
|900||ĵ, ↑||Resembled a crooked up arrow.|
|none||0||N was used at least once (by Bede about 725).|
|IV||4||IIII is still used on clock and Tarot card faces. See Calendars and clocks above.|
|V||5||IIIII was used rarely in the Middle Ages.|
|VIII||8||IIX was used rarely in the Middle Ages.|
|X||10||VV was used rarely in the Middle Ages.|
|XLIX||49||Per rule above, IL would not be generally accepted.|
|LXX||70||The abbreviation for the Septuagint|
|XCIX||99||As opposed to the "shortcut" way IC seen above.|
|C||100||This is the origin of using the slang term "C-bill" or "C-note" for "$100 bill".|
|DCLXVI||666||Using every symbol except M in descending order gives the beast number.|
|MCDXLIV||1444||Smallest pandigital number (each symbol is used)|
|MDCLXVI||1666||Largest efficient pandigital number (each symbol occurs exactly once)|
|MCMXCIX||1999||Shortcuts like IMM and MIM disagree with the rule stated above|
|M||4000||5000−1000, sometimes MMMM|
|MDCLXVI||6666||This number uses every symbol up to once.|
An accurate way to write large numbers in Roman numerals is to handle first the thousands, then hundreds, then tens, then units.
Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is VIII.
Put it together: MCMLXXXVIII.
The characters in the range U+2160–217F are present only for compatibility with other character set standards which provide these characters. For ordinary uses, the standard Latin letters are preferred. Displaying these characters requires a program that can handle Unicode and a font that contains appropriate glyphs for them.
The following mnemonics recall the order of Roman numeral values above ten, with L being 50, C being 100, D being 500, and M being 1000.
A longer mnemonic helps to recall the order of Roman numerals from large to small.
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