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.

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Indian family
East Asian numerals
Counting rods
Alphabetic numerals
Greek (Ionian)
Other systems
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…
Entrance to section LII of the Colosseum, with numerals still visible



Symbol Value
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 stems from the medieval use of j as a swash character (a form of i) to end numbers. 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:[1]

The basic Roman numerals follow a pattern:

100 Thousands C CC CCC CD D DC DCC DCCC CM


Although the Roman numerals are now written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used I Λ X 8 ⊕ for I V X L C M, of which only I and X happened to be letters in their alphabet. One folk etymology has it that the V represented a hand, and that the X was made by placing two Vs on top of each other, one inverted. However, the Etrusco-Roman numerals actually appear to derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century.[2]

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 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, , survives to this day in two variants:


In general, the number zero did not have its own Roman numeral, but a primitive form (nulla) was known by medieval computists (responsible for calculating the date of Easter). They included zero (via the Latin word nulla meaning "none") as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, xi, and xxii (written in minuscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525. Only one instance of a Roman numeral for zero is known. About 725, Bede or one of his colleagues used the letter N, the initial of nullae, in a table of epacts, all written in Roman numerals.




Each of these fractions had a name, which was also the name of the corresponding coin:

Fraction Roman Numeral Name (nominative and genitive) Meaning
1/12 uncia, unciae "ounce"
5/12 ••••• or :: quincunx, quincuncis "five-ounce" (quinquae unciaequincunx)
9/12 = 3/4 S••• or S: dodrans, dodrantis
or nonuncium, nonuncii
"less a quarter" (de-quadransdodrans)
or "ninth ounce" (nona uncianonuncium)
or decunx, decuncis
"less a sixth" (de-sextansdextans)
or "ten ounces" (decem unciaedecunx)
11/12 S••••• or S:: deunx, deuncis "less an ounce" (de-unciadeunx)
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:


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 duodeviginti or “two from twenty”; the number 19 was 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.

An inscription on Admiralty Arch, London. The numeral translates to 1910.

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

The Shepherd gate clock with Roman numbers up to XXIII (and 0), in Greenwich

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:

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.


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 numbers on stern of Cutty Sark, Greenwich
Bow of Clipper ship Cutty Sark

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.

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".



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.

Roman numeral I ii iii IV V vi vii°
Scale degree
(major mode)
tonic supertonic mediant subdominant dominant submediant leading tone
Roman numeral i ii° III iv V VI ()VII vii°
Scale degree
(minor mode)
tonic supertonic mediant subdominant dominant submediant subtonic leading tone

Modern non-English-speaking usage

The above uses are customary for English-speaking countries. Although many of them are also maintained in other countries, those countries have additional uses for Roman numerals which are unknown in English-speaking regions.

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.

I 9:30–17:30
II 9:30–19:00
III 9:30–17:30
IV 9:30–17:30
V 9:30–19:00
VI 9:30–13:00

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").

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

Roman Numerals, 16th century

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:

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. 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 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 and CIƆ, respectively.


Base number   CIƆ = 1,000 CCIƆƆ = 10,000 CCCIƆƆƆ = 100,000
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 () 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 ; and 10,000 (CCIƆƆ) was reduced to


Medieval Roman numerals

Most uniquely, during the Middle Ages there came about a unique, more comprehensive shorthand for writing Roman numerals, called today the "medieval Roman numerals." This system used almost every other letter of the Roman alphabet to stand as abbreviations for more longhand numbers (usually those that consisted of repetitions of the same symbol). They are still listed today in most dictionaries, although through disfavor are primarily out of use.[4]

40 F Presumed abbreviation of English forty.
80 R
90 N Presumed abbreviation of nonaginta, Latin for 90.
150 Y Possibly derived from the lowercase y's shape.
200 H
250 E
300 B
400 P, G
800 W More properly, the Greek ω, as W was a fairly new creation.
900 ĵ, ↑ Resembled a crooked up arrow.
2000 Z

Modern Roman numerals

Some "modern" Roman numerals, post-Victorian era, are shown below:

Standard Arabic Notes
none 0 N was used at least once (by Bede about 725).
I 1
II 2
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.
VI 6
VIII 8 IIX was used rarely in the Middle Ages.
IX 9 10-1
X 10 VV was used rarely in the Middle Ages.
XI 11
XII 12
XIV 14
XV 15
XVI 16
XIX 19
XX 20
XXI 21
XXV 25
XXX 30
XL 40 50−10
XLV 45
XLIX 49 Per rule above, IL would not be generally accepted.
L 50
LX 60
LXX 70 The abbreviation for the Septuagint
XC 90 100−10
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".
CL 150
CC 200
CCC 300
CD 400 500−100
D 500
DC 600
DCLXVI 666 Using every symbol except M in descending order gives the beast number.
DCC 700
DCCC 800
CM 900 1000−100
M 1000
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
MM 2000
MMD 2500
MMM 3000
MV 4000 5000−1000, sometimes MMMM
V 5000
VMDCLXVI 6666 This number uses every symbol up to V once.
X 10000
L 50000
C 100000
D 500000
M 1000000

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 ⅯⅭⅯⅬⅩⅩⅩⅧ. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 ( 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.

Table of Roman numerals in Unicode

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.

A longer mnemonic helps to recall the order of Roman numerals from large to small.


  1. Roman numerals: How they work: Larger numbers
  3. W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196
  4. Capelli, A. Dictionary of Latin Abbreviations. 1912.

See also

External links

The ISO basic Latin alphabet

history • palaeography derivations • diacritics punctuation • numerals • Unicode • list of letters