Roman numerals

Roman numerals

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.

For arithmetics involving Roman numerals, see Roman arithmetic and Roman abacus.


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:
* 1/8 _la. "sescuncia, sescunciae" (from "sesqui-" + "uncia", i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
* 1/24 _la. "semuncia, semunciae" (from "semi-" + "uncia", i.e. ½ uncia), represented by several variant glyphs deriving from the shape of Greek letter sigma Unicode|Σ, one variant resembling the pound sign Unicode|£ without the horizontal line(s) and another resembling Cyrillic letter Unicode|Є.
* 1/36 _la. "binae sextulae, binarum sextularum" ("two sextulas") or _la. "duella, duellae", represented by ƧƧ, a sequence of two reversed S.
* 1/48 _la. "sicilicus, sicilici", represented by Ɔ, a reversed C.
* 1/72 _la. "sextula, sextulae" (1/6 of an uncia), represented by Ƨ, a reversed S.
* 1/144 _la. "dimidia sextula, dimidiae sextulae" ("half a sextula"), represented by ƨ, a reversed S crossed by a horizontal line.
* 1/288 _la. "scripulum, scripuli", represented by a symbol resembling Cyrillic letter Unicode|Э.
* 1/1728 _la. "siliqua, siliquae", represented by a symbol resembling closing guillemets ».


The notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent "four", because IV represented the Roman god Jupiter, whose Latin name, IVPPITER, begins with IV. The subtractive notation (which uses IV instead of IIII) has become universally used only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for "nine", but IIII for "four". Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses IIII, IV, and IX. Constructions such as IIIII for "five", IIX for "eight" or VV for "10" have also been discovered. Subtractive notation arose from regular Latin usage: the number 18 was _la. "duodeviginti" or “two from twenty”; the number 19 was _la. "undeviginti" or "one from twenty". The use of subtractive notation increased the complexity of performing Roman arithmetic, without conveying the benefits of a full positional notation system.

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).

Calendars and clocks

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:

* Louis XIV, king of France, who preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained. [W.I. Milham, "Time & Timekeepers" (New York: Macmillan, 1947) p. 196]
* Using the standard numerals, two sets of figures would be similar and therefore confuseable by children and others unused to reading clockfaces: IV and the VI; and IX and XI. Since the first pair are additionally upside down on the face, an added level of confuseability would be introduced. Better, then, to make greater character distinction between them by using IIII and VI
* The four-character form IIII creates a visual symmetry with the VIII on the other side, which the character IV would not.
* With IIII, the number of symbols on the clock totals twenty I's, four V's, and four X's, so clock makers need only a single mold with a V, five I's, and an X in order to make the correct number of numerals for their clocks: VIIIIIX. This is cast four times for each clock and the twelve required numerals are separated:
** VIII I IX:The IIX and one of the IX’s are rotated 180° to form XI and XII. The alternative with IV uses seventeen I's, five V's, and four X's, requiring the clock maker to have several different molds.
* Only the I symbol would be seen in the first four hours of the clock, the V symbol would only appear in the next four hours, and the X symbol only in the last four hours. This would add to the clock's radial symmetry.


As it relates to the nomenclature of inorganic compounds. For example MnO2 should be named manganese(IV) oxide; manganese(IIII) oxide is not used.


Rules regarding Roman numerals often state that a symbol representing 10n may not precede any symbol larger than 10n+1. For example, C cannot be preceded by I or V, only by X (or, of course, by a symbol representing a value equal to or larger than C). Thus, one should represent the number "ninety-nine" as XCIX (using decimal places -- 90 (XC) then 9 (IX)), not as the "shortcut" IC.

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.

Year in Roman numerals

In seventeenth-century Europe, using Roman numerals for the year of publication for books was standard; there were many other places it was used as well. Publishers attempted to make the number easier to read by those more accustomed to Arabic positional numerals. On British title pages, there were often spaces between the groups of digits: M DCC LX I (relating to 1000 700 60 1 or 1761) is one example. This may have come from the French, who separated the groups of digits with periods, as: M.DCC.LXI. or M. DCC. LXI. Notice the period at the end of the sequence; many countries did this for Roman numerals in general, but not necessarily Britain. (Periods were also common on each side of numerals in running text, as in "commonet .iij. viros illos".)

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.

Modern usage

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:

* Names of monarchs and Popes are still displayed in Roman numerals, e.g. Elizabeth II, Benedict XVI. These are ordinal numbers; e.g. "II" is pronounced "the second".
* The year and, if any, credits shown at the end of a television show or film, especially in the United Kingdom.
* Some faces of clocks and timepieces show hours in Roman numerals.
* Books (particularly older ones) are dated in Roman numerals, and display preliminary pages in Roman numbers. Volume numbers on spines and chapter numbers can also be in Roman numerals.
* Film series and sequels of novels and video games are often numbered with Roman numerals, typically done in emulation of older books.
* Outlines use I, II, III and i, ii, iii as part of their organizational structure.
* A recurring grand event, such as the Olympic Games, Super Bowl, WrestleMania, or the Sprint All-Star Race.
* Historic events, such as World War II
* Army Corps are typically named using Roman numerals.
* Roman numerals often appear in crossword puzzles. For example, "DLII" could be the answer to clues such as "Ovid's 552" or "half of MCIV".
* Names of cranial nerves.
* Guitar chord diagrams.
* Laws; see e.g. Civil Rights Act of 1964, Controlled Substances Act
* Sports teams can be referred to as the number of players in the squad with Roman numerals. In rugby union, the 1st XV of a particular club would be the 1st and best team the club has, likewise for the XIII in rugby league, and XI for football (soccer), field hockey and cricket.

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.

Science fiction, and not astronomy "per se", has adopted the use for numbering the planets around a star; e.g., Planet Earth is called "Sol III".

In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone system.

In earthquake seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale.

Music theory

In music theory, while scale degrees are typically represented with Arabic numerals, often modified with a caret or circumflex, the triads that have these degrees as their roots are often identified by Roman numerals (as in chord symbols). See also diatonic functions. Upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads, as the following chart illustrates. Lower-case Roman numerals with a degree symbol indicate diminished triads. For example, in the major mode the triad on the seventh scale degree, the leading tone triad is diminished.

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.

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 ' _nl. 138-huis'.

In Poland, Roman numerals are used for ordinals in names of some institutions. In particular high schools (" _pl. V Liceum Ogólnokształcące w Krakowie" - "5th High School in Kraków"), tax offices (" _pl. II Urząd Skarbowy w Gdańsku" - "2nd Office of Treasury in Gdańsk") and courts (" _pl. I Wydział Cywilny Sądu Okręgowego" - "District Court, 1st Civil Division") - use Roman numerals. Institutions that use " _pl. Instutition nr N" notation always use Arabic numerals. These include elementary (" _pl. Szkoła Podstawowa nr 5") and middle schools (" _pl. Gimnazjum nr 5").

Roman numerals are rarely used in Asia. The motion picture rating system in Hong Kong uses categories I, IIA, IIB, and III based on Roman numerals.

Alternate forms

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:
*overline|I for one thousand
*overline|V for five thousand
*|overline|I| for one hundred thousand
*|overline|V| for five hundred thousand

The same overline was also used with a different meaning, to clarify that the characters were numerals. Sometimes both underline and overline were used, e. g. overline|MCMLXVII, and in certain (serif) typefaces, particularly Times New Roman, the capital letters when used without spaces simulates the appearance of the under/over bar, e.g. MCMLXVII.

Sometimes 500, usually D, was written as unicode|I followed by an "apostrophus" (which resembles a backwards C, i.e. unicode|Ɔ), while 1,000, usually M, was written as unicode|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 unicode|IƆ and unicode|CIƆ, respectively.

An extra unicode|Ɔ denoted 500, and multiple extra unicode|Ɔs are used to denote 5,000, 50,000, etc. For example:

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.


Unicode has a number of characters specifically designated as Roman numerals, as part of the "Number Forms" range from [ U+2160 to U+2183] . For example, MCMLXXXVIII could alternatively be written as unicode|ⅯⅭⅯⅬⅩⅩⅩⅧ. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 (unicode|Ⅻ or XII), mainly intended for the clock faces for compatibility with large East-Asian character sets such as JIS X 0213 that provide these characters. The pre-combined glyphs should only be used to represent the individual numbers where the use of individual glyphs is not wanted, and not to replace compounded numbers. Additionally, glyphs exist for alternate forms of 1000, 5000, and 10000.

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.


After the Renaissance, the Roman system could also be used to write chronograms. It was common to put in the first page of a book some phrase, so that when adding the I, V, X, L, C, D, M present in the phrase, the reader would obtain a number, usually the year of publication. The phrase was often (but not always) in Latin, as chronograms can be rendered in any language that utilises the Roman alphabet.

Mnemonic devices

There are several mnemonics that can be useful in remembering the Roman numeral system.

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.
*Lucky Cows Drink Milk
*Lucy Can't Drink Milk
*Lazy Cows Don't Moo
*Little Cats Drink Milk
*LCD Monitor

A longer mnemonic helps to recall the order of Roman numerals from large to small.
* My Dear Cat Loves eXtra Vitamins Intensely



See also

* Kharoṣṭhī numerals

External links

* [ Conversion algorithm and demonstration program (with java source code)] for numbers up to 3,999
* [ Conversion program (with javascript source code)] for numbers up to 3,999,999
* [ FAQ #1 Why do clocks with Roman numerals use "IIII" instead of "IV"?: ]
* [ Online Converter] for Decimal/Roman Numerals (JavaScript, GPL)
* [ Roman Numeral Conversion Exercises] (Java)
* [ "Romance in Numbers"] by Paul Niquette
* [ Simple Roman Numeral Converter in C] (C)
* [ Web Based Converter - Decimal to Roman Numerals]
* [ Minor history of the rules of Roman Numerals and an Arabic to Roman Numeral Converter]

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