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Roman numerals

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For the Latin names of numbers, seeLatin numerals.

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Roman numeralsare anumeral systemthat originated inancient Romeand remained the usual way of writing numbers throughout Europe well into theLate Middle Ages.Numbers are written with combinations of letters from theLatin alphabet,each letter with a fixed integer value. Modern style uses only these seven:

Roman numerals on stern of the shipCutty Sarkshowingdraughtinfeet.The numbers range from 13 to 22, from bottom to top.
I V X L C D M
1 5 10 50 100 500 1000

The use of Roman numerals continued long after thedecline of the Roman Empire.From the 14th century on, Roman numerals began to be replaced byArabic numerals;however, this process was gradual, and the use of Roman numerals persists. One place they are often seen is onclock faces.For instance, on the clock ofBig Ben(designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notationsIVandIXcan be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as "IIII"on Roman numeral clocks.[1]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs.MCM,signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is writtenMCMXII.For the years of the current (21st) century,MMindicates 2000; this year isMMXXIV(2024).

Description

Roman numerals use different symbols for each power of ten and there is no zero symbol, in contrast with theplace value notationof Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage varied greatly in ancient Rome and became thoroughly chaotic in medieval times. The more recent restoration of a largely "classical" notation has gained popularity among some, while variant forms are used by some modern writers as seeking more "flexibility".[2]Roman numerals may be considered legally binding expressions of a number, as inU.S. Copyright law(where an "incorrect" or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period).[3]

Standard form

The following table displays how Roman numerals are usually written:[4]

Individual decimal places
Thousands Hundreds Tens Units
1 M C X I
2 MM CC XX II
3 MMM CCC XXX III
4 CD XL IV
5 D L V
6 DC LX VI
7 DCC LXX VII
8 DCCC LXXX VIII
9 CM XC IX

The numerals for 4 (IV) and 9 (IX) are written usingsubtractive notation,[5]where the smaller symbol (I) issubtractedfrom the larger one (V,orX), thus avoiding the clumsierIIIIandVIIII.[a]Subtractive notation is also used for 40 (XL), 90 (XC), 400 (CD) and 900 (CM).[6]These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

  •   39 =XXX+IX=XXXIX.
  •  246 =CC+XL+VI=CCXLVI.
  •  789 =DCC+LXXX+IX=DCCLXXXIX.
  • 2,421 =MM+CD+XX+I=MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

  •  160 =C+LX=CLX
  •  207 =CC+VII=CCVII
  • 1,009 =M+IX=MIX
  • 1,066 =M+LX+VI=MLXVI[7][8]

The largest number that can be represented in this manner is 3,999 (MMMCMXCIX), but this is sufficient for the values for which Roman numerals are commonly used today, such as year numbers:

Prior to the introduction of Arabic numerals in the West, ancient and medieval users of Roman numerals used various means to write larger numbers; seelarge numbersbelow.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

Aclock facewith the Roman numerals typical for clocks, inBad Salzdetfurth,Germany

While subtractive notation for 4, 40 and 400 (IV,XLandCD) has been the usual form since Roman times,additive notationto represent these numbers (IIII,XXXXandCCCC)[9]continued to be used, including in compound numbers like 24 (XXIIII),[10]74 (LXXIIII),[11]and 490 (CCCCLXXXX).[12]The additive forms for 9, 90, and 900 (VIIII,[9]LXXXX,[13]andDCCCC[14]) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to theColosseum,IIIIis systematically used instead ofIV,but subtractive notation is used forXL;consequently, gate 44 is labelledXLIIII.[15][16]

Modernclock facesthat use Roman numerals still very often useIIIIfor four o'clock butIXfor nine o'clock, a practice that goes back to very early clocks such as theWells Cathedral clockof the late 14th century.[17][18][19]However, this is far from universal: for example, the clock on thePalace of Westminstertower (commonly known asBig Ben) uses a subtractiveIVfor 4 o'clock.[18][c]

The year number onAdmiralty Arch,London. The year 1910 is rendered asMDCCCCX,rather than the more usualMCMX

Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually writtenMCM). These vary fromMDCCCCXfor 1910 as seen onAdmiralty Arch,London, to the more unusual, if not uniqueMDCDIIIfor 1903, on the north entrance to theSaint Louis Art Museum.[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally writtenIIIIIandXXXXXinstead ofVandL,and there are instances such asIIIIIIandXXXXXXrather thanVIorLX.[22][23]

Epitaph ofcenturionMarcus Caelius, showing "XIIX"

Other subtractive forms

There are numerous historical examples ofIIXbeing used for 8; for example,XIIXwas used by officers of theXVIII Roman Legionto write their number.[24][25]The notation appears prominently on thecenotaphof their seniorcenturionMarcus Caelius(c. 45 BC– 9 AD). On the publicly displayed official Roman calendars known asFasti,XIIXis used for the 18 days to the nextKalends,andXXIIXfor the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, theFasti Antiates Maiores.[26] There are historical examples of other subtractive forms:IIIXXfor 17,[27]IIXXfor 18,[28]IIICfor 97,[29]IICfor 98,[30][31]andICfor 99.[32]A possible explanation is that the word for 18 in Latin isduodeviginti,literally "two from twenty", 98 isduodecentum(two from hundred), and 99 isundecentum(one from hundred).[33]However, the explanation does not seem to apply toIIIXXandIIIC,since the Latin words for 17 and 97 wereseptendecim(seven ten) andnonaginta septem(ninety seven), respectively.

TheROMAN()function inMicrosoft Excelsupports multiple subtraction modes depending on the "Form"setting. For example, the number" 499 "(usuallyCDXCIX) can be rendered asLDVLIV,XDIX,VDIVorID.The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".[34]

Non-standard variants

Padlock used on the northgateof the Irish town ofAthlone."1613" in the date is renderedXVIXIII,(literally "16, 13" ) instead ofMDCXIII.
Excerpt fromBibliothèque nationale de France.[35]The Roman numeral for 500 is rendered asCV,instead ofD.

There are also historical examples of other additive and multiplicative forms, and forms which seem to reflect spoken phrases. Some of these variants may have been regarded as errors even by contemporaries.

  • IIXXwas how people associated with theXXII Roman Legionused to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namelyduo et vice(n)sima(literally "two and twentieth" ) rather than the "regular"vice(n)sima secunda(twenty second).[36]Apparently, at least one ancientstonecuttermistakenly thought that theIIXXof "22nd Legion" stood for 18, and "corrected" it toXVIII.[36]
  • There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 asXVIXIII,corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 asXCVXIXas inFrenchquinze-cent-dix-neuf(fifteen-hundred and nineteen), and similar readings in other languages.[37]
  • In some French texts from the 15th century and later, one finds constructions likeIIIIXXXIXfor 99, reflecting the French reading of that number asquatre-vingt-dix-neuf(four-score and nineteen).[37]Similarly, in some English documents one finds, for example, 77 written as "iiixxxvii"(which could be read" three-score and seventeen ").[38]
  • A medieval accounting text from 1301 renders numbers like 13,573 as "XIII. M. V. C. III. XX. XIII",that is," 13×1000 + 5×100 + 3×20 + 13 ".[39]
  • Other numerals that do not fit the usual patterns – such asVXLfor 45, instead of the usualXLV— may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, "XXX"and"XL"have other connotations in addition to their values as Roman numerals, while"IXL"more often than not is agramogramof "I excel", and is in any case not an unambiguous Roman numeral.[40]

Zero

As a non-positional numeral system,Roman numerals have no "place-keeping" zeros. Furthermore, the system as used by the Romans lacked a numeral for the numberzeroitself (that is, what remains after 1 is subtracted from 1). The wordnulla(theLatinword meaning "none" ) was used to represent 0, although the earliest attested instances are medieval. For instanceDionysius Exiguususednullaalongside Roman numerals in a manuscript from 525 AD.[41][42]About 725,Bedeor one of his colleagues used the letterN,the initial ofnullaor ofnihil(the Latin word for "nothing" ) for 0, in a table ofepacts,all written in Roman numerals.[43]

The use ofNto indicate "none" long survived in the historicapothecaries' systemof measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.[44]

Fractions

Atrienscoin (1⁄3or4⁄12of anas). Note the four dots (····) indicating its value.
Asemiscoin (1⁄2or6⁄12of anas). Note theSindicating its value.

The base "Roman fraction" isS,indicating1⁄2.The use ofS(as inVIISto indicate 71⁄2) is attested in some ancient inscriptions[45]and also in the now rare apothecaries' system (usually in the formSS):[44]but while Roman numerals forwhole numbersare essentiallydecimal,Sdoes not correspond to5⁄10,as one might expect, but6⁄12.

The Romans used aduodecimalrather than a decimal system forfractions,as thedivisibilityof twelve(12 = 22× 3)makes it easier to handle the commonfractionsof1⁄3and1⁄4than does a system based on ten(10 = 2 × 5).Notation for fractions other than1⁄2is mainly found on survivingRoman coins,many of which had values that were duodecimal fractions of the unitas.Fractions less than1⁄2are indicated by a dot (·) for eachuncia"twelfth", the source of the English wordsinchandounce;dots are repeated for fractions up to five twelfths. Six twelfths (one half), isSforsemis"half".Unciadots were added toSfor fractions from seven to eleven twelfths, just as tallies were added toVfor whole numbers from six to nine.[46]The arrangement of the dots was variable and not necessarilylinear.Five dots arranged like (⁙) (as on the face of adie) are known as aquincunx,from the name of the Roman fraction/coin. The Latin wordssextansandquadransare the source of the English wordssextantandquadrant.

Each fraction from1⁄12to12⁄12had a name in Roman times; these corresponded to the names of the related coins:

Fraction Roman numeral Name (nominative and genitive singular) 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··orS: Bes,bessis "Twice" (as in "twice a third" )
9⁄12=3⁄4 S···orS∴ Dodrans,dodrantis
ornonuncium, nonuncii 		"Less a quarter" (de-quadrans→dodrans)
or"ninth ounce" (nona uncia→nonuncium)
10⁄12=5⁄6 S····orS∷ Dextans, dextantis
ordecunx, decuncis 		"Less a sixth" (de-sextans→dextans)
or"ten ounces" (decem unciae→decunx)
11⁄12 S·····orS⁙ Deunx, deuncis "Less an ounce" (de-uncia→deunx)
12⁄12= 1 I As,assis "Unit"

Other Roman fractional notations included the following:

Fraction Roman numeral Name (nominative and genitive singular) Meaning
1⁄1728=12−3 𐆕 Siliqua,siliquae
1⁄288 ℈ Scripulum, scripuli "scruple"
1⁄144=12−2 Ƨ Dimidia sextula, dimidiae sextulae "half a sextula"
1⁄72 Ƨ Sextula,sextulae "1⁄6of an uncia "
1⁄48 Ↄ Sicilicus, sicilici
1⁄36 ƧƧ Binae sextulae, binarum sextularum
(Exceptionally, these are plural forms.) 		"two sextulas" (duella,duellae)
1⁄24 Σor𐆒orЄ Semuncia,semunciae "1⁄2uncia "(semi-+uncia)
1⁄8 Σ·or𐆒·orЄ· Sescuncia, sescunciae "1+1⁄2uncias "(sesqui-+uncia)

Large numbers

The Romans developed two main ways of writing large numbers, theapostrophusand thevinculum,further extended in various ways in later times.

Apostrophus

"1630" on theWesterkerkin Amsterdam. "M"and"D"are given archaicapostrophusform.

Using theapostrophusmethod,[47]500 is written asIↃ,while 1,000 is written asCIↃ.[20]This system of encasing numbers to denote thousands (imagine theCs andↃs as parentheses) had its origins in Etruscan numeral usage.

Each additional set ofCandↃsurroundingCIↃraises the value by a factor of ten:CCIↃↃrepresents 10,000 andCCCIↃↃↃrepresents 100,000. Similarly, each additionalↃto the right ofIↃraises the value by a factor of ten:IↃↃrepresents 5,000 andIↃↃↃrepresents 50,000. Numerals larger thanCCCIↃↃↃdo not occur.[48]

Page from a 16th-century manual, showing a mixture ofapostrophusandvinculumnumbers (see in particular the ways of writing 10,000).
  • IↃ= 500CIↃ= 1,000
  • IↃↃ= 5,000CCIↃↃ= 10,000
  • IↃↃↃ= 50,000CCCIↃↃↃ= 100,000

SometimesCIↃ(1000) is reduced toↀ,IↃↃ(5,000) toↁ;CCIↃↃ(10,000) toↂ;IↃↃↃ(50,000) toↇ;andCCCIↃↃↃ(100,000) toↈ.[49]It is likelyIↃ(500) reduced toDandCIↃ(1000) influenced the laterM.

John Wallisis often credited with introducing the symbol forinfinity⟨∞⟩,and one conjecture is that he based it onↀ,since 1,000 washyperbolicallyused to represent very large numbers.

Vinculum

Using thevinculum,conventional Roman numerals are multiplied by 1,000 by adding a "bar" or "overline", thus:[49]

  • IV= 4,000
  • XXV= 25,000

Thevinculumcame into use in thelate Republic,[50]and it was a common alternative to the apostrophic ↀ during the Imperial era around the Roman world (M for '1000' was not in use until the Medieval period).[51] [52]It continued in use in the Middle Ages, though it became known more commonly astitulus,[53]and it appears in modern editions of classical and medieval Latin texts.[54][55]

In an extension of thevinculum,a three-sided box (now sometimes printed as two vertical lines and avinculum) is used to multiply by 100,000,[56][50]thus:

Vinculumnotation is distinct from the custom of adding an overline to a numeral simply to indicate that it is a number. Both usages can be seen on Roman inscriptions of the same period and general location, such as on theAntonine Wall.[57][58]

Origin

The system is closely associated with the ancientcity-stateof Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

Etruscan numerals

Main article:Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from theEtruscan number symbols:⟨𐌠⟩,⟨𐌡⟩,⟨𐌢⟩,⟨𐌣⟩,and⟨𐌟⟩for 1, 5, 10, 50, and 100 (they had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus, the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 sinceEtruscanwas written from right to left.)[59]

The symbols⟨𐌠⟩and⟨𐌡⟩resembled letters of the Etruscan alphabet, but⟨𐌢⟩,⟨𐌣⟩,and⟨𐌟⟩did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers ( "three from twenty", etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.[59]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones:⟨𐌠⟩,⟨𐌢⟩,and⟨𐌟⟩.The symbols for 5 and 50 changed from⟨𐌡⟩and⟨𐌣⟩to⟨V⟩and⟨ↆ⟩at some point. The latter had flattened to⟨⊥⟩(an inverted T) by the time ofAugustus,and soon afterwards became identified with the graphically similar letter⟨L⟩.[48]

The symbol for 100 was written variously as⟨𐌟⟩or⟨ↃIC⟩,and was then abbreviated to⟨Ↄ⟩or⟨C⟩,with⟨C⟩(which matched the Latin letterC) finally winning out. It might have helped thatCwas the initial letter ofCENTUM,Latin for "hundred".

The numbers 500 and 1000 were denoted byVorXoverlaid with a box or circle. Thus, 500 was like aƆsuperimposed on a⋌or⊢,making it look likeÞ.It becameDorÐby the time of Augustus, under the graphic influence of the letterD.It was later identified as the letterD;an alternative symbol for "thousand" was aCIↃ,and half of a thousand or "five hundred" is the right half of the symbol,IↃ,and this may have been converted intoD.[20]

The notation for 1000 was a circled or boxedX:Ⓧ,⊗,⊕,and by Augustan times was partially identified with the Greek letterΦphi.Over time, the symbol changed toΨandↀ.The latter symbol further evolved into∞,then⋈,and eventually changed toMunder the influence of the Latin wordmille"thousand".[48]

According to Paul Kayser, the basic numerical symbols wereI,X,𐌟andΦ(or⊕) and the intermediate ones were derived by taking half of those (half anXisV,half a𐌟isↆand half aΦ/⊕isD). Then 𐌟 and ↆ developed as mentioned above.[60]

Entrance to sectionLII(52) of theColosseum,with numerals still visible

Classical Roman numerals

TheColosseumwas constructed in Rome in CE 72–80,[61]and while the original perimeter wall has largely disappeared, the numbered entrances fromXXIII(23) toLIIII(54) survive,[62]to demonstrate that in Imperial times Roman numerals had already assumed their classical form:as largely standardised in current use.The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation - whileXLis used for 40,IVis avoided in favour ofIIII:in fact, gate 44 is labelledXLIIII.

Use in the Middle Ages and Renaissance

Lower case,orminuscule,letters were developed in the Middle Ages, well after the demise of theWestern Roman Empire,and since that time lower-case versions of Roman numbers have also been commonly used:i,ii,iii,iv,and so on.

13th century example ofiiij.

Since the Middle Ages, a "j"has sometimes been substituted for the final"i"of a" lower-case "Roman numeral, such as"iij"for 3 or"vij"for 7. This"j"can be considered aswashvariant of "i".Into the early 20th century, the use of a final"j"was still sometimes used inmedical prescriptionsto prevent tampering with or misinterpretation of a number after it was written.[63]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one (such as "A"for"V",or"Q"for"D"), while others serve as abbreviations for compound numerals ("O"for"XI",or"F"for"XL"). Although they are still listed today in some dictionaries, they are long out of use.[64]

A superscript "o" (sometimes written directly above the symbol) was sometimes used as anordinal indicator.[65]

Number Medieval
abbreviation 		Notes and etymology
5 A Resembles an upside-down V. Also said to equal 500.
6 ↅ Either from aligatureofVI,or fromdigamma(ϛ), the Greek numeral 6 (sometimes conflated with theστligature).[48]
7 S,Z Presumed abbreviation ofseptem,Latin for 7.
9.5 X̷ Scribal abbreviation, an x with a slash through it. Likewise,IX̷represented 8.5
11 O Presumed abbreviation ofonze,French for 11.
40 F Presumed abbreviation of Englishforty.
70 S Also could stand for 7, with the same derivation.
80 R
90 N Presumed abbreviation ofnonaginta,Latin for 90. (Ambiguous withNfor "nothing" (nihil)).
150 Y Possibly derived from the lowercase y's shape.
151 K Unusual, origin unknown; also said to stand for 250.[66]
160 T Possibly derived from Greektetra,as 4 × 40 = 160.
200 H Could also stand for 2 (see also 𐆙, the symbol for thedupondius). From a barring of twoI's.
250 E
300 B
400 P,G
500 Q Redundant withD;abbreviatesquingenti,Latin for 500. Also sometimes used for 500,000.[67]
800 Ω Borrowed fromGothic.
900 ϡ Borrowed from Gothic.
2000 Z

Chronograms,messages with dates encoded into them, were popular during theRenaissanceera. The chronogram would be a phrase containing the lettersI,V,X,L,C,D,andM.By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe fromal-Andalus,by way ofArabtraders 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 made using anabacus). Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

Spanish Real usingIIIIinstead ofIVas regnal number of CharlesIVof Spain.

Specific disciplines

Inastronautics,United States rocketmodel variants are sometimes designated by Roman numerals, e.g.Titan I,Titan II,Titan III,Saturn I,Saturn V.

Inastronomy,thenatural satellitesor "moons" of theplanetsaredesignatedby capital Roman numerals appended to the planet's name. For example,Titan's designation isSaturnVI.[69]

Inchemistry,Roman numerals are sometimes used to denote thegroupsof theperiodic table,but this has officially been deprecated in favour of Arabic numerals.[70]They are also used in theIUPAC nomenclature of inorganic chemistry,for theoxidation numberofcationswhich can take on several different positive charges. They are also used for namingphasesofpolymorphiccrystals,such asice.

Ineducation,school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, "gradeIX"is sometimes seen for" grade 9 ".

Stylised "IX"represents" 9 "in unit emblem of9th Aero SquadronAEF, 1918.

Inentomology,the broods of the thirteen- and seventeen-yearperiodical cicadasare identified by Roman numerals.

Ingraphic designstylised Roman numerals may represent numeric values.

Inlaw,Roman numerals are commonly used to help organize legal codes as part of analphanumeric outline.

Inmathematics(includingtrigonometry,statistics,andcalculus), when a graph includes negative numbers, its quadrants are named usingI,II,III,andIV.These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

Inmilitaryunit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example, the American XVIII Airborne Corps or the Nazi III Panzerkorps) with Arabic numerals being used for divisions and armies.

Inmusic,Roman numerals are used in several contexts:

Inpharmacy,Roman numerals were used with the now largely obsoleteapothecaries' systemof measurement: includingSSto denote "one half" andNto denote "zero".[44][71]

Inphotography,Roman numerals (with zero) are used to denote varying levels of brightness when using theZone System.

Inseismology,Roman numerals are used to designate degrees of theMercalli intensity scaleof earthquakes.

Example of postage stamp from Ireland (Éire) franked using Roman numeral for the month

Insportthe team containing the "top" players and representing a nation or province, aclubor a school at the highest level in (say)rugby unionis often called the "1stXV",while a lower-rankingcricketorAmerican footballteam might be the "3rdXI".

Intarot,Roman numerals (with zero) are often used to denote the cards of theMajor Arcana.

InIreland,Roman numerals were used until the late 1980s to indicate the month on postageFranking.In documents, Roman numerals are sometimes still used to indicate the month to avoid confusion over day/month/year or month/day/year formats.

Intheologyandbiblical scholarship,theSeptuagintis often referred to asLXX,as this translation of theOld Testamentinto Greek is named for the legendary number of its translators (septuagintabeing Latin for "seventy" ).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts ofcontinental Europeand in other regions (e.g.Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used inRomance languagesto denotecenturies,e.g. the FrenchXVIIIesiècle[72]and the Spanishsigloxviii(notxviiisiglo) for "18th century". Some Slavic and Turkic languages (especially in and adjacent to Russia) similarly favor Roman numerals (e.g. RussianXVIII век,AzeriXVIII əsror Polishwiek XVIII[73]). On the other hand, inTurkishand someCentral EuropeanSlavic languages, like mostGermanic languages,one writes "18." (with a period) before the local word for "century" (e.g. Turkish18. yüzyıl,Czech18. století).

Boris Yeltsin's signature, dated 10 November 1988, rendered as 10.XI.'88.

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). Themonthis written in Roman numerals, while the day is in Arabic numerals: "4.VI.1789 "and"VI.4.1789 "both refer unambiguously to 4 June 1789.

Business hours table on a shop window inVilnius,Lithuania.

Roman numerals are sometimes used to represent thedays of the weekin hours-of-operation signs displayed in windows or on doors of businesses,[74]and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented byI.Sunday is represented byVII.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. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and isclosed on Sundays.Note that the listing uses 24-hour time.

Sign at 17.9 km on route SS4Salaria,north of Rome, Italy.

Roman numerals may also be used forfloor numbering.[75][76]For instance, apartments in centralAmsterdamare 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 as138-huis.

In Italy, where roads outside built-up areas havekilometre signs,major roads and motorways also mark 100-metre subdivisionals, using Roman numerals fromItoIXfor the smaller intervals. The sign⁠IX/17⁠thus marks 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of theItalianParliamentfrom 2018 to 2022 (elected in the2018 Italian general election) is called theXVIII Legislature of the Italian Republic(or more commonly the "XVIII Legislature" ).

A notable exception to the use of Roman numerals in Europe is in Greece, whereGreek numerals(based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The "Number Forms"block of theUnicodecomputer character set standard has a number ofRoman numeral symbolsin the range ofcode pointsfrom U+2160 to U+2188.[77]This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ orXII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that "[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters".[78] The block also includes someapostrophussymbols for large numbers, an old variant of "L"(50) similar to the Etruscan character, theClaudian letter"reversed C", etc.[79]

See also

References

Notes

  1. ^Without theorising about causation, it may be noted thatIVandIXnot only have fewer characters thanIIIIandVIIII,but are less likely to be confused (especially at a quick glance) withIIIandVIII.
  2. ^This is the Coordinated Universal Time (UTC) year in which Wikipedia's cache of this page was last updated, so may be a few hours out of date.
  3. ^Isaac Asimovonce mentioned an "interesting theory" that Romans avoided usingIVbecause it was the initial letters ofIVPITER,the Latin spelling ofJupiter,and might have seemedimpious.[20]He did not say whose theory it was.
  4. ^XIII= 13 x 100,000 = 1,300,000 andXXXII= 32 x 1000 = 32,000, so 'XIIIXXXII= 1,332,000.p.is a common abbreviation forpassus,paces, the Romans counting a pace as two steps.

Citations

  1. ^Judkins, Maura (4 November 2011)."Public clocks do a number on Roman numerals".The Washington Post.Archived fromthe originalon 15 November 2020.Retrieved13 August2019.Most clocks using Roman numerals traditionally use IIII instead of IV... One of the rare prominent clocks that uses the IV instead of IIII is Big Ben in London.
  2. ^Adams, Cecil (23 February 1990)."What is the proper way to style Roman numerals for the 1990s?".The Straight Dope.
  3. ^abHayes, David P."Guide to Roman Numerals".Copyright Registration and Renewal Information Chart and Web Site.
  4. ^Reddy, Indra K.; Khan, Mansoor A. (2003). "1 (Working with Arabic and Roman numerals)".Essential Math and Calculations for Pharmacy Technicians.CRC Press. p. 3.ISBN978-0-203-49534-6.Table 1-1 Roman and Arabic numerals (table very similar to the table here, apart from inclusion of Vinculum notation.
  5. ^Dehaene, Stanislas (1997).The Number Sense: How the Mind Creates Mathematics.Oxford University Press.ISBN9780199723096.288 pages.
  6. ^Hazewinkel, Michiel, ed. (1990)."Numbers, Representations of".Encyclopaedia of Mathematics.Vol. 6. Springer. p. 502.ISBN9781556080050.546 pages.
  7. ^Dela Cruz, M. L. P.; Torres, H. D. (2009).Number Smart Quest for Mastery: Teacher's Edition.Rex Bookstore, Inc.ISBN9789712352164.
  8. ^Martelli, Alex; Ascher, David (2002).Python Cookbook.O'Reilly Media Inc.ISBN978-0-596-00167-4.
  9. ^abGaius Iulius Caesar.Commentarii de bello Gallico, Book II, Section 4(in Latin) – viaWikisource.
    Book II, Section 4: "... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia;..."
    Book II, Section 8: "... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit..."
    Book IV, Section 15: "Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt."
    Book VII, Section 4: "...in hiberna remissis ipse se recipit die XXXX Bibracte."
  10. ^Rocca, Angelo (1612).De campanis commentarius.Rome: Guillelmo Faciotti.Title of a Plate:"Campana a XXIIII hominibus pulsata" ( "Bell to be sounded by 24 men" ).
  11. ^Gerard Ter Borch (1673):Portrait of Cornelis de Graef.Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII".
  12. ^Gaius Plinius Secundus.Naturalis Historia, Book III(in Latin) – viaWikisource.Book III: "Saturni vocatur, Caesaream Mauretaniae urbemCCLXXXXVIIp[assum]. traiectus. reliqua in ora flumen Tader... ortus in Cantabris haut procul oppido Iuliobrica, perCCCCLp. fluens..."
    Book IV: "Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII."
    Book VI: "tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur."
  13. ^Bennet, Thomas (1731).Grammatica Hebræa, cum uberrima praxi in usum tironum... Editio tertia.T. Astley. p. 24.Copy in the British Library; 149 pages.
    Page 24: "PRÆFIXA duo suntviz.Heemphaticum vel relativum (de quo Cap VI Reg. LXXXX.) &ShincumSegalsequenteDagesh,quod denotat pronomen relativum..."
  14. ^Della Mirandola, Pico (1486).Conclusiones sive Theses DCCCC[Conclusions, or 900 Theses] (in Latin).
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  16. ^"Paul Lewis".Roman Numerals...How they work.13 November 2021.
  17. ^Milham, W.I. (1947).Time & Timekeepers.New York: Macmillan. p. 196.
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  19. ^Adams, Cecil; Zotti, Ed (1988).More of the straight dope.Ballantine Books. p.154.ISBN978-0-345-35145-6.
  20. ^abcAsimov, Isaac (1966).Asimov on Numbers(PDF).Pocket Books, a division of Simon & Schuster, Inc. p. 12.
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  22. ^Reynolds, Joyce Maire; Spawforth, Anthony J. S. (1996)."numbers, Roman".In Hornblower, Simon; Spawforth, Anthony (eds.).Oxford Classical Dictionary(3rd ed.). Oxford University Press.ISBN0-19-866172-X.
  23. ^Kennedy, Benjamin Hall (1923).The Revised Latin Primer.London: Longmans, Green & Co.
  24. ^Adkins, Lesley; Adkins, Roy A (2004).Handbook to life in ancient Rome(2 ed.). Facts On File. p. 270.ISBN0-8160-5026-0.
  25. ^Boyne, William (1968).A manual of Roman coins.p. 13.
  26. ^Degrassi, Atilius,ed. (1963).Inscriptiones Italiae.Vol. 13: Fasti et Elogia. Rome: Istituto Poligrafico dello Stato. Fasciculus 2: Fasti anni Numani et Iuliani.
  27. ^Lundorphio, Michaele Gaspar (1621).Acta publica inter invictissimos gloriosissimosque&c.... et Ferdinandum II. Romanorum Imperatores...(in Latin). Ian-Friderici Weissii. p. 123.
    Page 123: "Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX".
    Page 126, end of the same document: "Dabantur Pragæ 17 Decemb. M. DC. IIXX".
  28. ^Sulpicius à Munscrod, Raphael (1621).Vera Ac Germana Detecto Clandestinarvm Deliberationvm(in Latin). p. 16.
    Page 16, line 1: "repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX".
    Page 41, upper right corner: "Decemb. A. C. MDC.IIXX".Page 42, upper left corner:"Febr. A. C. MDC.XIX".Page 70:"IIXX. die Maij sequentia in consilio noua ex Bohemia allata....".
    Page 71: "XIX. Maij.
  29. ^Tentzel, Wilhelm Ernst (1699).Als Ihre Königl. Majestät in Pohlen und...(in German). p. 39.
    Page 39: "... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC [1699]."
  30. ^Posner, Johann Caspar (1698).Mvndvs ante mvndvm sive De Chao Orbis Primordio(in Latin).
    Title page: "Ad diem jvlii A. O. R. M DC IIC".
  31. ^Tentzel, Wilhelm Ernst (1700).Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten...(in German). p. 26.
    Page 26: "Die Revers hat eine feine Inscription:SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT [year 1698 day 18 oct]."
  32. ^Piccolomini, Enea Silvio(1698).Opera Geographica et Historica(in Latin) (1st ed.). Helmstadt: J. M. Sustermann.Title page of first edition: "Bibliopolæ ibid. M DC IC".
  33. ^Kennedy, Benjamin H. (1879).Latin grammar.London: Longmans, Green, and Co. p.150.ISBN9781177808293.
  34. ^"ROMAN function".support.microsoft.com.
  35. ^L' Atre périlleux et Yvain, le chevalier au lion.1301–1350.
  36. ^abMalone, Stephen James (2005).Legio XX Valeria Victrix: A Prosographical and Historical Study(PDF)(Thesis). Vol. 2. University of Nottingham.
    On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22.
    The footnote on that page says: "The form IIXX clearly reflecting the Latinduo et vicensima'twenty-second': cf. X5398,legatus I[eg II] I et vicensim(ae) Pri[mi]g;VI 1551,legatus leg] IIXX Prj;III 14207.7,miles leg IIXX;and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' – surely here the stonecutter's hypercorrection for IIXX PR.
  37. ^abGachard, M. (1862)."II. Analectes historiques, neuvième série (nosCCLXI-CCLXXXIV) ".Bulletin de la Commission royale d'Historie.31(3): 345–554.doi:10.3406/bcrh.1862.3033.
    Page 347:Lettre de Philippe le Beau aux échevins..., quote: "Escript en nostre ville de Gand, le XXIIIImede febvrier, l'an IIIIXXXIX [quatre-vingt-dix-neuf = 99]."
    Page 356:Lettre de l'achiduchesse Marguerite au conseil de Brabant..., quote: "... Escript à Bruxelles, le dernier jour de juing anno XVcXIX [1519]."
    Page 374:Letters patentes de la rémission... de la ville de Bruxelles, quote:"... Op heden, tweentwintich ['twenty-two'] daegen in decembri, anno vyfthien hondert tweendertich['fifteen hundred thirty-two']... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich [1532] vorschreven."
    Page 419:Acte du duc de Parme portant approbation..., quote: "Faiet le XVmede juillet XVchuytante-six [1586].".
  38. ^Salter, Herbert Edward (1923).Registrum Annalium Collegii Mertonensis 1483–1521.Vol. 76. Oxford Historical Society.544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iiixxxvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.
  39. ^de Wailly; Delisle (1865) [1301]. "E Duo Codicibus Ceratis Johannis de Sancto Justo" [From Two Texts in Wax by John of St Just].Recueil des historiens des Gaules et de la France. Par Martin Bouquet: Contenant la deuxieme livraison des monumens des regnes de saint Louis, de Philippe le Hardi, de Philippe le bel, de Louis X, de Philippe V et de Charles IV... Jusqu'en MCCCXXVIII. Tome Vingt-Deuxième.Recueil des Historiens des Gaules et de la France(in Latin). Vol. 22. p. 530:SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d.[Sum total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers.]
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Sources

Further reading

Library resourcesabout
Roman numerals
  • Aczel, Amir D. 2015.Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers.1st edition. New York: Palgrave Macmillan.
  • Goines, David Lance.A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals.Boston: D.R. Godine, 1982.
  • Houston, Stephen D. 2012.The Shape of Script: How and Why Writing Systems Change.Santa Fe, NM: School for Advanced Research Press.
  • Taisbak, Christian M. 1965. "Roman numerals and the abacus."Classica et medievalia26: 147–60.
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