Roman numerals

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Roman numerals on stern of the ship Cutty Sark showing draught in feet. The numbers range from 13 to 22, from bottom to top.
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Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven:

I V X L C D M
1 5 10 50 100 500 1000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big 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 notations IV and IX can 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 written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXIV (2024).

Description

Roman numerals use different symbols for each power of ten and no zero symbol, in contrast with the place value notation of 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. Even the post-renaissance restoration of a largely "classical" notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved "flexibility".[2] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an "incorrect" or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)[3] it is desirable to strictly follow the usual style described below.

Roman numeric system

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 using "subtractive notation",[5] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier IIII and VIIII.[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:

  • 1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
  • 1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
  • 1944 = M + CM + XL + IV = MCMXLIV (erroneous copyright notice of the 1954 movie The Last Time I Saw Paris)[3]
  • 2024 = MMXXIV (this year)[b]

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

Standard form

The modern era has seen the emergence of a standardized orthography for Roman numerals, which permits only one permutation for any given value. This system may be described as a decimal pattern, as above, but also as a logical set of rules. While exceptions can be made (notably IIII instead of IV on clockfaces), the modern convention is widely recognized and adhered to, and may be prescribed by the following ruleset:[9][10][11][12][13][14][15][16][17][18][19]

Basic Rules
  1. Powers of ten are dealt with separately, ordered from greatest to smallest and from left to right, with numerals either added or subtracted.
  2. Repeated 'tens' numerals (I, X, C, M) are added together, with up to three (3) permitted in sequence (subtraction allows an additional non-sequential repetition once per power).
  3. 'Fives' numerals (V, L, D) may only be added once per power (not repeated nor subtracted).
  4. Numerals placed to the right of a greater value are added, while those placed to the left are subtracted; if placed between two larger numerals, the 'tens' value is subtracted (i.e. subtraction takes precedence).
  5. Only one (1) 'tens' numeral may be subtracted from a single numeral per power, and this must be by 1/5 or 1/10 (i.e. the next lower 'tens' numeral).
  6. Addition must be less than subtraction for any given numeral (i.e. the added value to the right must be less than the subtractor).
  7. Any subtracted 'tens' numeral must either be first, or be preceded by a numeral at least ten times (10x) greater.

The above describes the basic pattern of integers from 1 - 3,999.

Examples

Following the above rules:
90 must be XC. It cannot be LXXXX because that would break rule 2 (up to three in sequence), and it cannot be LXL because that would break rule 3 ('fives' not repeated).
45 must be XLV. It cannot be VL because that would break rule 3 ('fives' not subtracted).
99 must be XCIX. It cannot be IC because that would break rule 5 (subtract by one fifth or tenth).
18 must be XVIII. It cannot be IIXX or IXIX because these would break rule 5 (subtract once per power).
19 must be XIX. It cannot be IXX because that would break either rule 5 (subtract by one fifth or tenth) or rule 6 (subtract>add).
10 must be X. It cannot be IXI because that would break rule 6 (subtract>add).
14 must be XIV. It cannot be IXV because that would break rule 6 (subtract>add), and it cannot be VIX because that would break rule 7 (at least 10x).

1894 is MDCCCXCIV. Consider how this agrees with the rules: powers of ten are arranged properly (rule 1), C is used three times sequentially and a fourth time non-sequentially (rule 2), 'fives' numerals D and V are added once each (rule 3), X and I are subtracted by being placed to the left of larger values while the rest are added (rule 4), they are subtracted once per power by one tenth and one fifth respectively (rule 5), IV is less than X (rule 6), and C is 10x X and 100x I (rule 7).

Fractions & Vinculums

The following rules extend the system further:

  • Fractions may only be added once to the right of all numerals (not subtracted), without redundancy, and are duodecimal.
  • Beginning at 6/12, the S (semi) is used, followed by marks (unciae) for additional quantities up to 11/12.
  • Placing a bar (vinculum) over a numeral multiplies it x1000.
  • The vinculum is used for values of 4,000 and greater (it is not used up to 3,999), and may be iterated up to three (3) times.
  • Starting at 4,000, and at the next two powers of a thousand thereafter, a new vinculum is added, with the pattern beginning at IV.
  • Once vinculums are employed, the higher power is modified in preference to the lower (eg IV, not MV).
  • Vinculums are always contiguous and are placed leftmost (ie no broken overlines or lower powers to the left per basic rule 1).

Thus, 2 2/3 would be rendered as IIS••, while 6,986 would be (VI)CMLXXXVI. Note that the symbol V is used more than once in that example, this is only permissible with the vinculum setting them apart. Also note that while M is used, 7,000 would be (VII).

(I), (II), and (III) are not used, with M, MM, MMM being preferred under 4,000. SS is never used in place of I (ss is sometimes seen as a variant of semi, but this is strictly pharmaceutical notation).

With fractions and vinculums employed, the lowest possible value is • or 1/12, while the highest is (((MMMCMXCIX)))((CMXCIX))(CMXCIX)CMXCIX or 3,999,999,999,999 (within standard usage). Four trillion, rendered as (((MMMM))), would be non-standard since it breaks basic rule 2, although the four M's can be used as a variant form, and it is more aesthetically pleasing as a maximum figure. Another alternative is ((((IV)))), but since the general principle is three sequential iterations, this should also apply to vinculums. The reason for the three-rule is that the eye can readily distinguish between one, two, or three marks, while four or greater become illegible. Thus, 4 M's are preferable as a variant form.

Other forms

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

Other additive forms

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

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation to represent these numbers (IIII, XXXX and CCCC)[20] continued to be used, including in compound numbers like XXIIII,[21] LXXIIII,[22] and CCCCLXXXX.[23] The additive forms for 9, 90, and 900 (VIIII,[20] LXXXX,[24] and DCCCC[25]) 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 the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII.[26][27]

Modern clock faces that use Roman numerals still very often use IIII for four o'clock but IX for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.[28][29][30] However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive IV for 4 o'clock.[29]

Isaac Asimov once mentioned an "interesting theory" that Romans avoided using IV because it was the initial letters of IVPITER, the Latin spelling of Jupiter, and might have seemed impious.[31] He did not say whose theory it was.

The year number on Admiralty Arch, London. The year 1910 is rendered as MDCCCCX, rather than the more usual MCMX

Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.[32]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.[33][34]

Other subtractive forms

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be "compressed". The best known example of this is the ROMAN() function in Microsoft Excel, which can render "499" (usually CDXCIX) into LDVLIV, XDIX, VDIV or ID depending on the "Form" setting.[c] [35] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

Epitaph of centurion Marcus Caelius, showing "XIIX"

There is, however, some historic use of subtractive notation other than that described in the above "standard": in particular IIIXX for 17,[36] IIXX for 18,[37] IIIC for 97,[38] IIC for 98,[39][40] and IC for 99.[41] A possible explanation is that the word for 18 in Latin is duodeviginti, literally "two from twenty", 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).[42] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.[43][44] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.[45]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.

Padlock used on the north gate of the Irish town of Athlone. "1613" in the date is rendered XVIXIII, (literally "16, 13") instead of MDCXIII.
  • IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely duo et vice(n)sima (literally "two and twentieth") rather than the "regular" vice(n)sima secunda (twenty second).[46] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of "22nd Legion" stood for 18, and "corrected" it to XVIII.[46]
Excerpt from Bibliothèque nationale de France.[47] The Roman numeral for 500 is rendered as VC, instead of D.
  • There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as XVCXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.[48]
  • In some French texts from the 15th century and later, one finds constructions like IIIIXXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).[48] Similarly, in some English documents one finds, for example, 77 written as "iiixxxvii" (which could be read "three-score and seventeen").[49]
  • 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".[50]
  • Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual XLV — 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 a gramogram of "I excel", and is in any case not an unambiguous Roman numeral.[51]

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 number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning "none") was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD.[52][53] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for "nothing") for 0, in a table of epacts, all written in Roman numerals.[54]

The use of N to indicate "none" long survived in the historic apothecaries' system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.[55]

Fractions

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.

The base "Roman fraction" is S, indicating 1⁄2. The use of S (as in VIIS to indicate 71⁄2) is attested in some ancient inscriptions[56] and also in the now rare apothecaries' system (usually in the form SS):[55] but while Roman numerals for whole numbers are essentially decimal S does not correspond to 5⁄10, as one might expect, but 6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 22 × 3) makes it easier to handle the common fractions of 1⁄3 and 1⁄4 than does a system based on ten (10 = 2 × 5). Notation for fractions other than 1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than 1⁄2 are indicated by a dot (·) for each uncia "twelfth", the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is 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.[57] 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.

Each fraction from 1⁄12 to 12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

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"

Other Roman fractional notations included the following:

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

Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus

"1630" on the Westerkerk in Amsterdam. "M" and "D" are given archaic "apostrophus" form.

One of these was the apostrophus,[58] in which 500 was written as IↃ, while 1,000 was written as CIↃ.[31] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage.

Each additional set of C and Ↄ surrounding CIↃ raises the value by a factor of ten: CCIↃↃ represents 10,000 and CCCIↃↃↃ represents 100,000. Similarly, each additional Ↄ to the right of IↃ raises the value by a factor of ten: IↃↃ represents 5,000 and IↃↃↃ represents 50,000. Numerals larger than CCCIↃↃↃ do not occur.[59]

Page from a 16th-century manual, showing a mixture of apostrophus and vinculum numbers (see in particular the ways of writing 10,000).

Sometimes CIↃ was reduced to ↀ for 1,000. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ (ↇ); and CCCIↃↃↃ (ↈ) for 100,000 to ↈ. [60]

IↃ and CIↃ most likely preceded, and subsequently influenced, the adoption of "D" and "M" in Roman numerals.

John Wallis is often credited for introducing the symbol for infinity ⟨∞⟩, and one conjecture is that he based it on ↀ, since 1,000 was hyperbolically used to represent very large numbers.

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a "bar" or "overline", thus:[60]

  • IV = 4,000
  • XXV = 25,000

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).[61] [62] It continued in use in the Middle Ages, though it became known more commonly as titulus,[63] and it appears in modern editions of classical and medieval Latin texts.[64][65]

A three-sided box (now sometimes printed as two vertical lines and a vinculum) was used to multiply by 100,000,[66] thus:

Vinculum notation is distinct from the custom of adding an overline to a numeral simply to indicate that it is a number, and both usages can be seen on Roman inscriptions of the same period and general location, such as on the Antonine Wall.[67][68]

Origin

The system is closely associated with the ancient city-state of 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 the Etruscan 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 since Etruscan was written from right to left.)[69]

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.[69]

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 of Augustus, and soon afterwards became identified with the graphically similar letter ⟨L⟩.[59]

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 letter C) finally winning out. It might have helped that C was the initial letter of CENTUM, Latin for "hundred".

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus, 500 was like a Ɔ superimposed on a ⋌ or ⊢, making it look like Þ. It became 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 a CIↃ, and half of a thousand or "five hundred" is the right half of the symbol, IↃ, and this may have been converted into D.[31]

The notation for 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".[59]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).[70]

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

Classical Roman numerals

The Colosseum was constructed in Rome in CE 72–80,[71] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,[72] 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 - while XL is used for 40, IV is avoided in favour of IIII: in fact, gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western 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 of iiij.

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 a swash variant of "i". Into the early 20th century, the use of a final "j" was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.[73]

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.[74]

Number Medieval
abbreviation 		Notes and etymology
5 A Resembles an upside-down V. Also said to equal 500.
6 ↅ Either from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the στ ligature).[59]
7 S, Z Presumed abbreviation of septem, Latin for 7.
9.5 X̷ Scribal abbreviation, an x with a slash through it. Likewise, IX̷ represented 8.5
11 O Presumed abbreviation of onze, French for 11.
40 F Presumed abbreviation of English forty.
70 S Also could stand for 7, with the same derivation.
80 R
90 N Presumed abbreviation of nonaginta, Latin for 90. (Ambiguous with N for "nothing" (nihil)).
150 Y Possibly derived from the lowercase y's shape.
151 K Unusual, origin unknown; also said to stand for 250.[75]
160 T Possibly derived from Greek tetra, as 4 × 40 = 160.
200 H Could also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I's.
250 E
300 B
400 P, G
500 Q Redundant with D; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000.[76]
800 Ω Borrowed from Gothic.
900 ϡ Borrowed from Gothic.
2000 Z

Chronograms, messages with dates 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 use

By the 11th century, 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 made using an abacus). 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 using IIII instead of IV as regnal number of Charles IV of Spain.
  • Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced "the second". This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England 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 (see illustration).
  • Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV. These are also usually read as ordinals.
  • In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
  • The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.
The year of construction of the Cambridge Public Library, (USA) 1888, displayed in "standard" Roman numerals on its facade.

Specific disciplines

In astronautics, United States rocket model variants are sometimes designated by Roman numerals, e.g. Titan I, Titan II, Titan III, Saturn I, Saturn V.

In astronomy, the natural satellites or "moons" of the planets are designated by capital Roman numerals appended to the planet's name. For example, Titan's designation is Saturn VI.[78]

In chemistry, Roman numerals are sometimes used to denote the groups of the periodic table, but this has officially been deprecated in favour of Arabic numerals.[79] 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 education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, "grade IX" is sometimes seen for "grade 9".

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

Stylised "IX" represents "9" in unit emblem of 9th Aero Squadron AEF, 1918.

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. 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.

In military unit 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 WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries' system of measurement: including SS to denote "one half" and N to denote "zero".[55][80]

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

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

In sport the team containing the "top" players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the "1st XV", while a lower-ranking cricket or American football team might be the "3rd XI".

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

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being 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 of continental Europe and 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 in Romance languages to denote centuries, e.g. the French XVIIIe siècle[81] and the Spanish siglo XVIII mean "18th century". Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes "18." (with a period) before the local word for "century".

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). The month is 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 in Vilnius, Lithuania.

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,[82] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. 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 is closed on Sundays. Note that the listing uses 24-hour time.

Sign at 17.9 km on route SS4 Salaria, north of Rome, Italy.

Roman numerals may also be used for floor numbering.[83][84] For instance, 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 Italy, where roads outside built-up areas have kilometre 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 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Italian Parliament from 2018 to 2022 (elected in the 2018 Italian general election) is called the XVIII 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, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The "Number Forms" block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.[85] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). 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".[86] The block also includes some apostrophus symbols for large numbers, an old variant of "L" (50) similar to the Etruscan character, the Claudian letter "reversed C", etc.

Symbol ↀ ↁ ↂ ↅ ↆ ↇ ↈ
Value 1,000 5,000 10,000 6 50 50,000 100,000

See also

References

Notes

  1. ^ Without theorising about causation, it may be noted that IV and IX not only have fewer characters than IIII and VIIII, but are less likely to be confused (especially at a quick glance) with III and VIII.
  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. ^ Presumably to enable the more "flexible" rendering of numbers in spreadsheet cells.
  4. ^ XIII = 13 x 100,000 = 1,300,000 and XXXII = 32 x 1000 = 32,000, so 'XIII XXXII = 1,332,000. p. is a common abbreviation for passus, 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 from the original on 15 November 2020. Retrieved 13 August 2019. 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. ^ a b Hayes, 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. ISBN 978-0-203-49534-6. Table 1-1 Roman and Arabic numerals (table very similar to the table here, apart from inclusion of Vinculum notation.
  5. ^ Stanislas Dehaene (1997): The Number Sense : How the Mind Creates Mathematics. Oxford University Press; 288 pages. ISBN 9780199723096
  6. ^ Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990): Encyclopaedia of Mathematics, Volume 10, page 502. Springer; 546 pages. ISBN 9781556080050
  7. ^ Dela Cruz, M. L. P.; Torres, H. D. (2009). Number Smart Quest for Mastery: Teacher's Edition. Rex Bookstore, Inc. ISBN 9789712352164.
  8. ^ Martelli, Alex; Ascher, David (2002). Python Cookbook. O'Reilly Media Inc. ISBN 978-0-596-00167-4.
  9. ^ Seitz, Lee K. (8 December 1999). "LURNC: How Roman Numerals Work". home.hiwaay.net. Retrieved 24 May 2020.
  10. ^ Shaw, Allen A. (December 1938). "Note on Roman Numerals". National Mathematics Magazine. 13 (3). Taylor & Francis, Ltd. on behalf of the Mathematical Association of America: 127–128. doi:10.2307/3028752. Retrieved 27 November 2018.
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  37. ^ Raphael Sulpicius à Munscrod (1621): Vera Ac Germana Detecto Clandestinarvm Deliberationvm. 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".
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Sources

Further reading

  • 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 medievalia 26: 147–60.

External links

Library resources about
Roman numerals
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