Roman numerals

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Entrance to section LII (52) of the Colosseum, with numerals still visible

Roman numerals, the numeric system in ancient Rome, uses combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as follows:

I, II, III, IV, V, VI, VII, VIII, IX, and X.

The Roman numeral system is a cousin of Etruscan numerals. Use of Roman numerals continued after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by more convenient Arabic numerals; however this process was gradual, and the use of Roman numerals in some minor applications continues to this day.


Reading Roman numerals

"2013" as a Roman numeral

Roman Numerals, as used today, are based on seven symbols:[1]


Numbers are formed by combining symbols together and adding the values. So II is two ones, i.e. 2, and XIII is a ten and three ones, i.e. 13. There is no zero in this system, so 207, for example, is CCVII, using the symbols for two hundreds, a five and two ones. 1066 is MLXVI, one thousand, fifty and ten, a five and a one.

Symbols are placed from left to right in order of value, starting with the largest. However, in a few specific cases,[2] to avoid four characters being repeated in succession (such as IIII or XXXX) these can be reduced as follows:[3][4]

An example using the above rules would be 1904: this is composed of 1 (one thousand), 9 (nine hundreds), 0 (zero tens), and 4 (four units). To write the Roman numeral, each of the non-zero digits should be treated separately. Thus 1,000 = M, 900 = CM, and 4 = IV. Therefore, 1904 is MCMIV. This reflects typical modern usage: historically Roman numerals were often written rather less consistently.[6]

A common exception to the practice of placing a smaller value before a larger in order to reduce the number of characters, is the use of IIII instead of IV for 4 on clocks; see below. Another, rather peculiar example of the same kind of thing is the representation of 1910 in Roman Numerals on Admiralty Arch, London - where DCCCC is used instead of CM for 900. (see illustration)

An inscription on Admiralty Arch, London. The numeral is 1910, but MCMX would be more conventional

Below are some examples of the modern use of Roman Numerals.


Pre-Roman/Ancient Rome

Although 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, and M, of which only I and X happened to be letters in their alphabet. It has been suggested that the V represented the angle between thumb and forefinger of an open hand ("5"), and that the X was made by placing two Vs on top of each other, one inverted; this theory is questionable if, as has been argued, the Etrusco-Roman numerals actually derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century.[8]

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 and 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: . 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 superimposed 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; an alternative symbol for "thousand" was (I) or CIƆ, and half of a thousand or "five hundred" is the right half of the symbol, I) or IƆ, and this may have been converted into D.[9] This at least was the false 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. Over time, the symbol changed to Ψ and . The latter symbol further evolved into , then , and eventually changed to M under the influence of the Latin word mille "thousand".

Alfred Hooper has an alternative discussion of the origin of the Roman numeral system, for small numbers.[10] Hooper contends that the digits are related to hand signals. For example, the numbers I, II, III, IIII correspond to the number of fingers held up for another to see. V, then represents that hand upright with fingers together and thumb apart. Numbers 6–10, are represented with two hands as follows (left hand, right hand) 6=(V,I), 7=(V,II), 8=(V,III), 9=(V,IIII), 10=(V,V) and X results from either crossing of the thumbs, or holding both hands up in a cross.

A third hypothesis about the origins states that the basic ciphers were I, X, C and Φ (or ⊕) and that the halfthrough ones derived from taking half of those (half a X is V, half a C is L and half a Φ/⊕ is D).[citation needed]

In the early period of Roman history, there was no subtractive principle. 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".[citation needed]

Middle Ages/Renaissance

Minuscule (lower case) letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and lower-case versions of Roman numbers are now also commonly used: i, ii, iii, iv, etc. In the Middle Ages, a j was sometimes substituted for the final i of a number, such as iij for 3 or vij for 7. This j was considered a swash variant of i. The use of a final j is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written.[11][12]

A unique, more comprehensive shorthand for writing Roman numerals was developed during the Middle Ages, which today are called "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.[13]

5AResembles an upside-down V. Also said to equal 500.
6ϚEither a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical value.[14]
7S, ZPresumed abbreviation of septem, Latin for 7.
11OPresumed abbreviation of (e.g.) onze, French for 11.
40FPresumed abbreviation of English forty.
70SAlso could stand for 7, and has same etymology.
90NPresumed abbreviation of nonaginta, Latin for 90.
150YPossibly derived from the lowercase y's shape.
151KThis unusual abbreviation's origin is unknown; it has also been said to stand for 250.[15]
160TPossibly derived from Greek tetra, as 4 x 40 = 160.
400P, G
500QRedundant with D, abbreviation for quingenti, Latin for 500.

Chronograms, messages with a numbers encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern usage

Roman numbers on stern of Cutty Sark, Greenwich, showing draft in feet.

Roman numerals remained in common use until about the 14th century, when they were outmoded by Hindu-Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century) in practically all mathematical and economical applications.[citation needed] Roman numerals are still used today in several niche contexts. A few examples of their current use are:

In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals.

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

In music theory, the diatonic functions are identified using roman numerals. See: Roman numeral analysis.

In performance practice, 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 (with zero) are used to denote varying levels of brightness when using the Zone System.

Modern non-English-speaking usage

Capital Roman numerals are used to denote centuries (e.g., XVIII refers to the eighteenth century) in Bulgarian, Croatian, French, Hungarian, Italian, Polish, Portuguese, Romanian, Russian, Serbian, Georgian, and Spanish languages. This use has largely been replaced by Arabic numerals (e.g. 18.) in Czech and Slovak languages.

Boris Yeltsin's autograph, November 10, 1988. The month is specified by Roman numerals.

In Central Europe, Italy, Russia, and in Bulgarian, Croatian, 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). The month is written in Roman numerals while the day is in Arabic numerals: 14.  VI. 1789 is June 14, 1789. This use has largely been replaced by Arabic numerals (e.g. 14.06.1789) in Czech, Slovene, Slovak, Polish, Portuguese and Russian languages.

In the Baltic and Eastern Europe 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, and also sometimes in railway and bus timetables. 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 9:30 AM to 5:30 PM on Mondays, Wednesdays, and Thursdays; 9:30 AM to 7:00 PM on Tuesdays and Fridays; and 9:30 AM to 1:00 PM on Saturdays; and which is closed on Sundays.


In Rome, Greece, Romania, and other European countries to a 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'.

Special values


The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval computists in lieu of 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525.[17][18] About 725, Bede or one of his colleagues used the letter N, the initial of nulla, in a table of epacts, all written in Roman numerals.[19]


A triens coin (1/3 or 4/12 of an as). Note the four dots •••• indicating its value.
A semis coin (1/2 or 6/12 of an as). Note the S indicating its value.

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 (12 = 3 × 2 × 2) makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten (10 = 2 × 5). 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:

FractionRoman NumeralName (nominative and genitive)Meaning
1/12uncia, unciae"ounce"
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" (quinque unciaequincunx)
6/12 = 1/2Ssemis, semissis"half"
7/12S•septunx, septuncis"seven-ounce" (septem unciaeseptunx)
8/12 = 2/3S•• or S:bes, bessis"twice" (as in "twice a third")
9/12 = 3/4S••• or Sdodrans, dodrantis
or nonuncium, nonuncii
"less a quarter" (de-quadransdodrans)
or "ninth ounce" (nona uncianonuncium)
10/12 = 5/6S•••• or S::dextans, dextantis
or decunx, decuncis
"less a sixth" (de-sextansdextans)
or "ten ounces" (decem unciaedecunx)
11/12S••••• or S:·:deunx, deuncis"less an ounce" (de-unciadeunx)
12/12 = 1Ias, 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 following:

Large numbers

1630 on the Westerkerk in Amsterdam
Roman numerals, 16th century

In the Middle Ages, a horizontal line was used 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 original |Ɔ, while 1,000, usually M, was written as original C|Ɔ. This is a system of encasing numbers to denote thousands (imagine the Cs and Ɔs as parentheses), which has its origins in Etruscan numeral usage. The D and M used to represent 500 and 1,000 were most likely derived from and CIƆ, respectively, and subsequently influenced by assumed abbreviations.

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

Base number CIƆ = 1,000CCIƆƆ = 10,000CCCIƆƆƆ = 100,000
1 extra ƆIƆ = 500CIƆƆ = 1,500CCIƆƆƆ = 10,500CCCIƆƆƆƆ = 100,500
2 extra ƆsIƆƆ = 5,000 CCIƆƆƆƆ = 15,000CCCIƆƆƆƆƆ = 105,000
3 extra ƆsIƆƆƆ = 50,000  CCCIƆƆƆƆƆƆ = 150,000

(Sometimes (CIƆ) was reduced to () for 1,000. John Wallis is often credited for introducing the symbol for infinity (modern ()), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, (IƆƆ) for 5,000) was reduced to (); (CCIƆƆ) for 10,000 to (); and similarly () and ().)

"IIII" on clocks

A typical clock face with Roman numerals in Bad Salzdetfurth, Germany
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:

The IIX and one of the IXs are rotated 180° to form XI and XII. The alternative with IV uses seventeen Is, five Vs, and four Xs, requiring the clock maker to have several different patterns.

See also


  1. ^ Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN 0520050797.
  2. ^ Reddy, Indra K. & Khan, Mansoor A. (2003). CRC Press.
  3. ^ Dela Cruz, M.L.P. & Torres, H.D. (2009). Rex Bookstore, Inc..
  4. ^ Martelli, Alex & Ascher, David (2002). Python Cookbook. O'Reilly Media Inc..
  5. ^ Stroh, Michael. Trick question: How to spell 1999? Numerals: Maybe the Roman Empire fell because their computers couldn't handle calculations in Latin. The Baltimore Sun, December 27, 1998.
  6. ^ Adams, Cecil (February 23, 1990). "The Straight Dope". The Straight Dope.
  7. ^ Hayes, David P.. "Guide to Roman Numerals". Copyright Registration and Renewal Information Chart and Web Site.
  8. ^ Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley & Sons.
  9. ^ Asimov, Issac (1966, 1977). Asimov On Numbers. Pocket Books, a division of Simon & Schuster, Inc. p. 9.
  10. ^ Alfred Hooper. The River Mathematics (New York, H. Holt, 1945).
  11. ^ Sturmer, Julius W. Course in Pharmaceutical and Chemical Arithmetic, 3rd ed. (LaFayette, IN: Burt-Terry-Wilson, 1906). p25 Retrieved on 2010-03-15.
  12. ^ Bastedo, Walter A. Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582 Retrieved on 2010-03-15.
  13. ^ Capelli, A. Dictionary of Latin Abbreviations. 1912.
  14. ^ Perry, David J. Proposal to Add Additional Ancient Roman Characters to UCS.
  15. ^ Bang, Jørgen. Fremmedordbog, Berlingske Ordbøger, 1962 (Danish)
  16. ^ Owen, Rob (2012-01-13). "TV Q&A: ABC News, 'Storage Wars' and 'The Big Bang Theory'". Pittsburgh Post-Gazette. Retrieved 2012-01-13.
  17. ^ Faith Wallis, trans. Bede: The Reckoning of Time (725), Liverpool: Liverpool Univ. Pr., 2004. ISBN 0-85323-693-3.
  18. ^ Byrhtferth's Enchiridion (1016). Edited by Peter S. Baker and Michael Lapidge. Early English Text Society 1995. ISBN 978-0-19-722416-8.
  19. ^ C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.
  20. ^ Paul Lewis, Clocking the fours: A new theory about IIII; see the clock
  21. ^
  22. ^ W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196
  23. ^ FAQ: Roman IIII vs. IV on Clock Dials – Donn Lathrop's page on IIII vs. IV.

External links