Roman numerals

Roman numerals, the numeric system used in ancient Rome, employs 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, 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 Hindu-Arabic numerals; however this process was gradual, and the use of Roman numerals in some minor applications continues to this day.

Reading Roman numerals

MMXIV

"2014" as a Roman numeral

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

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1,000

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 using subtractive notation as follows:^[3][4]

• the numeral I can be placed before V and X to make 4 units (IV) and 9 units (IX respectively)
• X can be placed before L and C to make 40 (XL) and 90 (XC respectively)
• C can be placed before D and M to make 400 (CD) and 900 (CM) according to the same pattern^[5]

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.

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

• 1954 as MCMLIV (Trailer for the movie The Last Time I Saw Paris)^[6]
• 1990 as MCMXC (The title of musical project Enigma's debut album MCMXC a.D., named after the year of its release.)
• 2014 as MMXIV - the year of the games of the XXII (22nd, Winter) Olympiad (in Sochi)

Alternative forms

The "standard" forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and later use has also been inconsistent.^[7]

Roman inscriptions, especially in official contexts, tended to use additive forms such as IIII and VIIII rather than subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document. "Double subtractives" also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX.^[8][9]

Such variation and inconsistency continued through the medieval period and into modern times, even becoming conventional. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock,^[10][11][12] a practice that goes back to very early clocks such as the Wells Cathedral clock. This is far from being an unvarying convention; the clock in Elizabeth Tower on the Palace of Westminster in London (aka "Big Ben"), for example, uses IV.^[11] Inscribed dates appear in different forms even in the modern era; on Admiralty Arch, London, 1910 is shown as MDCCCCX rather than the “standard” MCMX and on the north entrance to the Saint Louis Art Museum 1903 was inscribed as MDCDIII rather than MCMIII.^[13]

History

Pre-Roman times and Ancient Rome

Although Roman numerals came to be 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.

Hypotheses About the Origin of Roman Numerals

Tally sticks

One hypothesis is that 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.^[14]

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: 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 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 CIƆor CꟾƆ), and half of a thousand or "five hundred" is the right half of the symbol, I) (or IƆor ꟾƆ), and this may have been converted into ⟨D⟩.^[15] 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 ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille "thousand".

Hand signals

Alfred Hooper has an alternative hypothesis for the origin of the Roman numeral system, for small numbers.^[16] 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.

Intermediate symbols deriving from few original symbols

A third hypothesis about the origins states that the basic ciphers were I, X, C and Φ (or ⊕) and that the intermediary ones were derived from taking half of those (half a X is V, half a C is L and half a Φ/⊕ is D).^[17]

Middle Ages and Renaissance

Numeral systems by culture
Hindu–Arabic numerals Western Arabic Eastern Arabic Bengali Burmese Indian family Khmer Lao Mongolian Sinhala Tamil Telugu Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese Counting rods Alphabetic numerals Abjad Armenian Āryabhaṭa Cyrillic Ge'ez Greek Georgian Hebrew Other historical systems Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit Kharosthi Mayan Quipu Roman
Positional systems by base
Decimal (10)
1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 20 24 26 27 32 36 60
Non-standard positional numeral systems
List of numeral systems
v t e

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.^[18][19]

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 they are long out of use.^[20]

Modern number	Medieval abbreviation	Notes
5	A	Resembles an upside-down V. Also said to equal 500.
6	Ϛ	Either a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical value.[21]
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.
80	R
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.[22]
160	T	Possibly derived from Greek tetra, as 4 x 40 = 160.
200	H
250	E
300	B
400	P, G
500	Q	Redundant with D, abbreviation for quingenti, Latin for 500.
2000	Z

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

By the 11th century Hindu–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 (where the actual calculations would have been by abacus). Their eventual almost complete replacement by their more convenient "Arabic" equivalents happened quite gradually, in fact Roman numerals are still used today in several niche contexts. A few examples of their current use are:

• Names of monarchs and Popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers; e.g. "II" is pronounced "the second". This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England only during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage - unless this was a whim of the designer.
• Generational suffixes, particularly seen in the USA, for people who share the same name across generations, for example William Howard Taft IV.
• 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."^[23] Outside reference to the work will use regular Hindu–Arabic numerals.
• Hour marks on timepieces. In this context 4 is usually written IIII.

• The year of construction on building faces and cornerstones.
• Page numbering of prefaces and introductions of books.
• Book volume and chapter numbers.
• Sequels of movies, video games, and other works. (as in Jaws IV).
• Outlines, which use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:
  • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad)
  • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLVII)
  • WrestleMania, the annual professional wrestling event for the WWE (e.g. the forthcoming WrestleMania XXX)

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 musical 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.

In Tarot, Roman numerals (with zero) are also used to denote the cards of the Major Arcana.

Modern non-English-speaking usage

Capital Roman numerals are still occasionally used to denote centuries (e.g., XVIII refers to the eighteenth century) in English. This style is much more widely followed in continental Europe.

In many European countries mixed Roman and Hindu-Arabic numerals are used to record dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals while the day is in Hindu-Arabic numerals: 14. VI. 1789 is 14 June 1789.

In parts of Europe it is conventional to employ Roman numerals to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,^[24] 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.

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
VII	—

In several European countries Roman numerals are used for floor numbering.^[25][26] For instance, apartments in central Amsterdam are indicated as 138-III, with both an Hindu-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 Italy, where roads outside built-up areas have kilometer signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX | 17 thus marks km. 17·900.

Special values

Zero

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.^[27][28] 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.^[29]

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 (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.^[30]

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"
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 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 the following:

• 1/8 sescuncia, sescunciae (from sesqui- + uncia, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
• 1/24 semuncia, semunciae (from semi- + uncia, i.e. ½ uncia), represented by several variant glyphs deriving from the shape of the Greek letter Sigma (Σ), one variant resembling the pound sign (£) without the horizontal line(s) and another resembling the Cyrillic letter (Є).
• 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by (ƧƧ), a sequence of two reversed Ss.
• 1/48 sicilicus, sicilici, represented by (Ɔ), a reversed C.
• 1/72 sextula, sextulae (1/6 of an uncia), represented by (Ƨ), a reversed S.
• 1/144 = 12⁻² dimidia sextula, dimidiae sextulae ("half a sextula"), represented by (ƻ), a reversed S crossed by a horizontal line.
• 1/288 scripulum, scripuli (a scruple), represented by the symbol (℈).
• 1/1728 = 12⁻³ siliqua, siliquae, represented by a symbol resembling closing guillemets (»).

Large numbers

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:

• I for one thousand
• V for five thousand
• |I| for one hundred thousand
• |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. 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 IƆ 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 = 1,000	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 ↀ 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 ↁ; CCIƆƆ for 10,000 to ↂ; IƆƆƆ for 50,000 to ↇ; and CCCIƆƆƆ for 100,000 to ↈ.

See also

• Etruscan numerals
• Kharosthi
• Roman abacus
• Roman numerals in Unicode
• Urnfield culture numerals

References

• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8. 

External links

Look up Appendix:Roman numerals or roman numeral in Wiktionary, the free dictionary.

Wikimedia Commons has media related to Roman numerals.

• FAQ No. 1 Why do clocks with Roman numerals use "IIII" instead of "IV"?:
• Child friendly roman numerals webquest
• French book with 841 chapters, numbered up to DCCCXLI
• Roman ad Arabic numerus racio et vice versa
• CESCNC - a handy and easy-to use numeral converter
• Online converter of Roman numerals into Arabic numbers with check of correct notation and random tests

The ISO basic Latin alphabet v t e
Aa	Bb	Cc	Dd	Ee	Ff	Gg	Hh	Ii	Jj	Kk	Ll	Mm	Nn	Oo	Pp	Qq	Rr	Ss	Tt	Uu	Vv	Ww	Xx	Yy	Zz
Related
Derivations Diacritics History ISO/IEC 646 List of letters Numerals Palaeography Punctuation Unicode

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reassigned) Thai & Lao (Japanese vowels) Tibetan Turkish Ukrainian Vietnamese Welsh Yugoslav Reordered scripts Algerian Braille (obsolete) Frequency-based scripts American Braille (obsolete) Independent scripts Japanese Korean Two-Cell Chinese Eight-dot scripts Luxembourgish Kanji Gardner–Salinas braille codes (GS8) Symbols in braille Braille music Canadian currency marks Gardner–Salinas braille codes (GS8/GS6) International Phonetic Alphabet (IPA) Nemeth braille code Braille technology Braille e-book Braille embosser Braille translator Braille watch Mountbatten Brailler Optical braille recognition Perforation Perkins Brailler Refreshable braille display Slate and stylus Persons Louis Braille Charles Barbier Valentin Haüy Thakur Vishva Narain Singh Sabriye Tenberken William Bell Wait Organisations Braille Institute of America Braille Without Borders Japan Braille Library National Braille Association Blindness organizations Schools for the blind American Printing House for the Blind Other tactile alphabets Decapoint Moon type New York Point Night writing Vibratese Related topics Accessible publishing Braille literacy RoboBraille