Roman numerals#Zero

File:CuttySarkRomNum.jpg in feet. The numbers range from 13 to 22, from bottom to top.]]

Roman numerals use different symbols for each power of ten, and there is 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. 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".{{Cite web |last=Adams |first=Cecil |date=23 February 1990 |title=What is the proper way to style Roman numerals for the 1990s? |url=http://www.straightdope.com/columns/read/1371/what-is-the-proper-way-to-style-roman-numerals-for-the-1990s |website=The Straight Dope}} Roman numerals may be considered legally binding expressions 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).{{Cite web |last=Hayes |first=David P. |title=Guide to Roman Numerals |url=https://chart.copyrightdata.com/ch02.html#Roman |website=Copyright Registration and Renewal Information Chart and Web Site}}

The following table displays how Roman numerals are usually written in modern times:{{Cite book |last1=Reddy |first1=Indra K. |url=https://books.google.com/books?id=U3QY7gz0C2cC |title=Essential Math and Calculations for Pharmacy Technicians |last2=Khan |first2=Mansoor A. |date=2003 |publisher=CRC Press |isbn=978-0-203-49534-6 |page=3 |chapter=1 (Working with Arabic and Roman numerals) |quote="Table 1-1 Roman and Arabic numerals (table very similar to the table here, apart from inclusion of Vinculum notation."}}

{{anchor|Subtractive notation}} The numerals for 4 ({{rn|IV}}) and 9 ({{rn|IX}}) are written using subtractive notation,{{Cite book |last=Dehaene |first=Stanislas |title=The Number Sense : How the Mind Creates Mathematics |date=1997 |publisher=Oxford University Press |isbn=9780199723096}} 288 pages. where the smaller symbol ({{rn|I}}) is subtracted from the larger one ({{rn|V}}, or {{rn|X}}), thus avoiding the clumsier {{rn|IIII}} and {{rn|VIIII}}.{{efn|Without theorising about causation, it may be noted that {{rn|IV}} and {{rn|IX}} not only have fewer characters than {{rn|IIII}} and {{rn|VIIII}}, but are less likely to be confused (especially at a quick glance) with {{rn|III}} and {{rn|VIII}}.}} Subtractive notation is also used for 40 ({{rn|XL}}), 90 ({{rn|XC}}), 400 ({{rn|CD}}) and 900 ({{rn|CM}}).{{Cite encyclopedia |title=Numbers, Representations of |encyclopedia=Encyclopaedia of Mathematics |publisher=Springer |url=https://books.google.com/books?id=kwMdtnhtUMMC&dq=%22Roman+numerals%22+additive&pg=PA502 |date=1990 |editor-last=Hazewinkel |editor-first=Michiel |volume=6 |page=502 |isbn=9781556080050}} 546 pages. 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 = {{rn|XXX}} + {{rn|IX}} = {{rn|XXXIX}}.
•   246 = {{rn|CC}} + {{rn|XL}} + {{rn|VI}} = {{rn|CCXLVI}}.
•   789 = {{rn|DCC}} + {{rn|LXXX}} + {{rn|IX}} = {{rn|DCCLXXXIX}}.
• 2,421 = {{rn|MM}} + {{rn|CD}} + {{rn|XX}} + {{rn|I}} = {{rn|MMCDXXI}}.

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

•   160 = {{rn|C}} + {{rn|LX}} = {{rn|CLX}}
•   207 = {{rn|CC}} + {{rn|VII}} = {{rn|CCVII}}
• 1,009 = {{rn|M}} + {{rn|IX}} = {{rn|MIX}}
• 1,066 = {{rn|M}} + {{rn|LX}} + {{rn|VI}} = {{rn|MLXVI}}{{Cite book |last1=Dela Cruz |first1=M. L. P. |url=https://books.google.com/books?id=PVK6lt2xXz4C |title=Number Smart Quest for Mastery: Teacher's Edition |last2=Torres |first2=H. D. |date=2009 |publisher=Rex Bookstore, Inc. |isbn=9789712352164}}{{Cite book |last1=Martelli |first1=Alex |url=https://archive.org/details/pythoncookbook00mart |title=Python Cookbook |last2=Ascher |first2=David |date=2002 |publisher=O'Reilly Media Inc. |isbn=978-0-596-00167-4 |url-access=registration}}

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

• 1776 = {{rn|M}} + {{rn|DCC}} + {{rn|LXX}} + {{rn|VI}} = {{rn|MDCCLXXVI}} (the date written on the book held by the Statue of Liberty).
• 1918 = {{rn|M}} + {{rn|CM}} + {{rn|X}} + {{rn|VIII}} = {{rn|MCMXVIII}} (the first year of the Spanish flu pandemic)
• 1944 = {{rn|M}} + {{rn|CM}} + {{rn|XL}} + {{rn|IV}} = {{rn|MCMXLIV}} (erroneous copyright notice of the 1954 movie The Last Time I Saw Paris)
• {{#time:Y}} = {{rn|{{#time:xrY}}}} (this year){{efn|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.}}

Prior to the introduction of Arabic numerals in the West, ancient and medieval users of Roman numerals used various means to write larger numbers {{xref|(see {{slink||Large numbers}} below)}}.

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

File:BadSalzdetfurthBadenburgerStr060529.jpg with the Roman numerals typical for clocks, in Bad Salzdetfurth, Germany]]

While subtractive notation for 4, 40, and 400 ({{rn|IV}}, {{rn|XL}}, and {{rn|CD}}) has been the usual form since Roman times {{Citation needed|reason=From what I've seen it seems that the additive notation was by far the normal until somewhere around the 18th century, at least for 4.|date=January 2024}}, additive notation to represent these numbers ({{rn|IIII}}, {{rn|XXXX}}, and {{rn|CCCC}}){{Cite Wikisource |author=Gaius Iulius Caesar |title=Commentarii de bello Gallico, Book II, Section 4 |wslink=Commentarii de bello Gallico/Liber II |anchor=4 |wslanguage=la}}
Book II, Section 4: "{{lang|la|... 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: "{{lang|la|... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit...}}"
Book IV, Section 15: "{{lang|la|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: "{{lang|la|...in hiberna remissis ipse se recipit die XXXX Bibracte.}}" very frequently continued to be used, including in compound numbers like 24 ({{rn|XXIIII}}),{{Cite book |last=Rocca |first=Angelo |title=De campanis commentarius |date=1612 |publisher=Guillelmo Faciotti |location=Rome}} Title of a Plate: "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men"). 74 ({{rn|LXXIIII}}),Gerard Ter Borch (1673): Portrait of Cornelis de Graef. Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII". and 490 ({{rn|CCCCLXXXX}}).{{Cite Wikisource |author=Gaius Plinius Secundus |title=Naturalis Historia, Book III |wslink=Naturalis Historia/Liber III |anchor=IV |wslanguage=la}} Book III: "{{lang|la|Saturni vocatur, Caesaream Mauretaniae urbem {{overline|CCLXXXXVII}} p[assum]. traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per {{overline|CCCCL}} p. fluens ...}}"
Book IV: "{{lang|la|Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII.}}"
Book VI: "{{lang|la|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.}}" The additive forms for 9, 90, and 900 ({{rn|VIIII}}, {{rn|LXXXX}},{{Cite book |last=Bennet |first=Thomas |title=Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia |date=1731 |publisher=T. Astley |page=24}} Copy in the British Library; 149 pages.
Page 24: "{{lang|la|PRÆFIXA duo sunt}} viz. He {{lang|la|emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) &}} Shin {{lang|la|cum}} Segal {{lang|la|sequente}} Dagesh, {{lang|la|quod denotat pronomen relativum...}}" and {{rn|DCCCC}}{{Cite book |last=Della Mirandola |first=Pico |url=http://www.esotericarchives.com/pico/conclus.htm |title=Conclusiones sive Theses DCCCC |date=1486 |language=la |trans-title=Conclusions, or 900 Theses}}) 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, {{rn|IIII}} is systematically used instead of {{rn|IV}}, but subtractive notation is used for {{rn|XL}}; consequently, gate 44 is labelled {{rn|XLIIII}}.{{Cite web |date=2 January 2011 |title=360:12 tables, 24 chairs, and plenty of chalk |url=https://threesixty360.wordpress.com/2011/01/01/roman-numerals-not-quite-so-simple/ |website=Roman Numerals...not quite so simple}}{{Cite web |date=13 November 2021 |title=Paul Lewis |url=http://www.web40571.clarahost.co.uk/roman/howtheywork.htm |website=Roman Numerals...How they work}}

Especially on tombstones and other funerary inscriptions, 5 and 50 have been occasionally written {{rn|IIIII}} and {{rn|XXXXX}} instead of {{rn|V}} and {{rn|L}}, and there are instances such as {{rn|IIIIII}} and {{rn|XXXXXX}} rather than {{rn|VI}} or {{rn|LX}}.{{Cite encyclopedia |title=numbers, Roman |encyclopedia=Oxford Classical Dictionary |publisher=Oxford University Press |url=https://archive.org/details/isbn_9780198661726 |date=1996 |editor-last=Hornblower |editor-first=Simon |edition=3rd |isbn=0-19-866172-X |last2=Spawforth |first2=Anthony J. S. |first1=Joyce Maire |last1=Reynolds |editor2-first=Anthony |editor2-last=Spawforth |url-access=registration}}{{Cite book |last=Kennedy |first=Benjamin Hall |title=The Revised Latin Primer |date=1923 |publisher=Longmans, Green & Co. |location=London}}

Modern clock faces that use Roman numerals still very often use {{rn|IIII}} for four o'clock but {{rn|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.{{Cite book |last=Milham |first=W.I. |title=Time & Timekeepers |date=1947 |publisher=Macmillan |location=New York |page=196}}{{Cite book |last=Pickover |first=Clifford A. |url={{google books|id = 52N0JJBspM0C|page = 282|plainurl = yes }} |title=Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning |date=2003 |publisher=Oxford University Press |isbn=978-0-19-534800-2 |page=282 |author-link=Clifford A. Pickover}}{{Cite book |last1=Adams |first1=Cecil |url=https://archive.org/details/moreofstraightdo00adam/page/154 |title=More of the straight dope |last2=Zotti |first2=Ed |date=1988 |publisher=Ballantine Books |isbn=978-0-345-35145-6 |page=[https://archive.org/details/moreofstraightdo00adam/page/154 154]}} However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive {{rn|IV}} for 4 o'clock.{{efn|Isaac Asimov once mentioned an "interesting theory" that Romans avoided using {{rn|IV}} because it was the initial letters of {{lang|la|IVPITER}}, the Latin spelling of Jupiter, and might have seemed impious.{{Cite book |last=Asimov |first=Isaac |url=http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf |title=Asimov on Numbers |date=1966 |publisher=Pocket Books, a division of Simon & Schuster, Inc |page=12}} He did not say whose theory it was.}}

File:AdmiraltyArchLondonCloseup.jpg, London. The year 1910 is rendered as {{rn|MDCCCCX}}, rather than the more usual {{rn|MCMX}}|alt=]]

Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written {{rn|MCM}}). These vary from {{rn|MDCCCCX}} for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique {{rn|MDCDIII}} for 1903, on the north entrance to the Saint Louis Art Museum.{{Cite web |title=Gallery: Museum's North Entrance (1910) |url=http://www.slam.org/century_of_free/gallery.php |url-status=dead |archive-url=https://web.archive.org/web/20101204081437/http://slam.org:80/century_of_free/gallery.php |archive-date=4 December 2010 |access-date=10 January 2014 |publisher=Saint Louis Art Museum |quote=The inscription over the North Entrance to the Museum reads: "Dedicated to Art and Free to All MDCDIII." These roman numerals translate to 1903, indicating that the engraving was part of the original building designed for the 1904 World's Fair.}}

File:Epitaph des Marcus Caelius.JPG Marcus Caelius, showing "{{rn|XIIX}}"]]

There are numerous historical examples of {{rn|IIX}} being used for 8; for example, {{rn|XIIX}} was used by officers of the XVIII Roman Legion to write their number.{{Cite book |last1=Adkins |first1=Lesley |title=Handbook to life in ancient Rome |last2=Adkins |first2=Roy A |date=2004 |isbn=0-8160-5026-0 |edition=2 |page=270|publisher=Facts On File }}{{Cite book |last=Boyne |first=William |title=A manual of Roman coins |date=1968 |page=13}} The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius ({{circa|45 BC|lk=no}} – 9 AD). On the publicly displayed official Roman calendars known as Fasti, {{rn|XIIX}} is used for the 18 days to the next Kalends, and {{rn|XXIIX}} for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.{{Cite book |title=Inscriptiones Italiae |date=1963 |publisher=Istituto Poligrafico dello Stato |editor-last=Degrassi |editor-first=Atilius |editor-link=Attilio Degrassi |volume=13: Fasti et Elogia |location=Rome |at=Fasciculus 2: Fasti anni Numani et Iuliani}}

There are historical examples of other subtractive forms: {{rn|IIIXX}} for 17,{{Cite book |last=Lundorphio |first=Michaele Gaspar |url=https://books.google.com/books?id=C41mAAAAcAAJ&pg=PA123 |title=Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores... |date=1621 |publisher=Ian-Friderici Weissii |page=123 |language=la}}
Page 123: "{{lang|la|Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX}}".
Page 126, end of the same document: "{{lang|la|Dabantur Pragæ 17 Decemb. M. DC. IIXX}}". {{rn|IIXX}} for 18,{{Cite book |last=Sulpicius à Munscrod |first=Raphael |url=https://archive.org/details/bub_gb_N43WFqB1wtoC/page/n69 |title=Vera Ac Germana Detecto Clandestinarvm Deliberationvm |date=1621 |page=16 |language=la}}
Page 16, line 1: "{{lang|la|repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX}}".
Page 41, upper right corner: "{{lang|la|Decemb. A. C. MDC.IIXX}}". Page 42, upper left corner: "{{lang|la|Febr. A. C. MDC.XIX}}". Page 70: "{{lang|la|IIXX. die Maij sequentia in consilio noua ex Bohemia allata....}}".
Page 71: "{{lang|la|XIX. Maij}}. {{rn|IIIC}} for 97,{{Cite book |last=Tentzel |first=Wilhelm Ernst |url=https://books.google.com/books?id=VN9lAAAAcAAJ&pg=PA39 |title=Als Ihre Königl. Majestät in Pohlen und ... |date=1699 |page=39 |language=de}}
Page 39: "{{lang|de|... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC [1699].}}" {{rn|IIC}} for 98,{{Cite book |last=Posner |first=Johann Caspar |url=https://books.google.com/books?id=bmtOAAAAcAAJ&pg=PP9 |title=Mvndvs ante mvndvm sive De Chao Orbis Primordio |date=1698 |language=la}}
Title page: "{{lang|la|Ad diem jvlii A. O. R. M DC IIC}}".{{Cite book |last=Tentzel |first=Wilhelm Ernst |url=https://books.google.com/books?id=qFVPAAAAcAAJ&pg=PA93 |title=Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten... |date=1700 |page=26 |language=de}}
Page 26: "{{lang|de|Die Revers hat eine feine Inscription}}: {{lang|la|SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT [year 1698 day 18 oct].}}" and {{rn|IC}} for 99.{{Cite book |last=Piccolomini |first=Enea Silvio |url=https://books.google.com/books?id=0RNXAAAAcAAJ&pg=PA1 |title=Opera Geographica et Historica |date=1698 |publisher=J. M. Sustermann |edition=1st |location=Helmstadt |language=la |author-link=Pope Pius II}} Title page of first edition: "{{lang|la|Bibliopolæ ibid. M DC IC}}". A possible explanation is that the word for 18 in Latin is {{lang|la|duodeviginti}}{{px2}}{{mdash}}{{tsp}}literally "two from twenty"⁠{{mdash}}{{tsp}}while 98 is {{lang|la|duodecentum}} (two from hundred) and 99 is {{lang|la|undecentum}} (one from hundred).{{Cite book |last=Kennedy |first=Benjamin H. |url=https://archive.org/details/publiclatin00kennrich |title=Latin grammar |date=1879 |publisher=Longmans, Green, and Co. |isbn=9781177808293 |location=London |page=[https://archive.org/details/publiclatin00kennrich/page/150 150]}} However, the explanation does not seem to apply to {{rn|IIIXX}} and {{rn|IIIC}}, since the Latin words for 17 and 97 were {{lang|la|septendecim}} (seven ten) and {{lang|la|nonaginta septem}} (ninety seven), respectively.

The {{code|ROMAN()}} function in Microsoft Excel supports multiple subtraction modes depending on the "{{tt|Form}}" setting. For example, the number "499" (usually {{rn|CDXCIX}}) can be rendered as {{rn|LDVLIV}}, {{rn|XDIX}}, {{rn|VDIV}} or {{rn|ID}}. The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".{{Cite web |title=ROMAN function |url=https://support.microsoft.com/en-us/office/roman-function-d6b0b99e-de46-4704-a518-b45a0f8b56f5 |website=Microsoft Support}}

File:Padlock,_Athlone.jpg of the Irish town of Athlone. "1613" in the date is rendered {{rn|XVIXIII}}, (literally "16, 13") instead of {{rn|MDCXIII}}.]]

File:Excerpt from BnF ms. 1433 fr., fol. 24r.png.{{Cite book |url=https://gallica.bnf.fr/ark:/12148/btv1b105096493 |via=Gallica |title=L' Atre périlleux et Yvain, le chevalier au lion . |date=1301–1350 |language=EN}} The Roman numeral for 500 is rendered as {{Rn|{{Overset|C|V}}}}, instead of {{Rn|D}}.]]

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.

• {{rn|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 {{lang|la|duo et vice(n)sima}} (literally "two and twentieth") rather than the "regular" {{lang|la|vice(n)sima secunda}} (twenty second).{{Cite thesis |last=Malone |first=Stephen James |title=Legio XX Valeria Victrix: A Prosographical and Historical Study |date=Aug 2005 |publisher=University of Nottingham |url=http://eprints.nottingham.ac.uk/13316/2/423645_vol2.pdf |volume=2}}
  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 Latin {{lang|la|duo et vicensima}} 'twenty-second': cf. X5398, {{lang|la|legatus I[eg II] I et vicensim(ae) Pri[mi]g}}; VI 1551, {{lang|la|legatus leg] IIXX Prj}}; III 14207.7, {{lang|la|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. Apparently, at least one ancient stonecutter mistakenly thought that the {{rn|IIXX}} of "22nd Legion" stood for 18, and "corrected" it to {{rn|XVIII}}.

• Other numerals that do not fit the usual patterns – such as {{rn|VXL}} for 45, instead of the usual {{rn|XLV}} — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.

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.{{Cite web |title=Our Brand Story |url=http://spcardmona.com.au/healthy-brands/ixl/our-brand-story |access-date=2014-03-11 |publisher=SPC Ardmona}}

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 {{wikt-lang|la|nulla}} (the Latin word meaning "none") was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used {{lang|la|nulla}} alongside Roman numerals in a manuscript from 525 AD.{{Cite book |title=Bede: The Reckoning of Time |date=2004 |publisher=Liverpool University Press |isbn=0-85323-693-3 |location=Liverpool |translator-last=Wallis |translator-first=Faith |orig-date=725}}{{Cite book |title=Byrhtferth's Enchiridion |date=1995 |publisher=Early English Text Society |isbn=978-0-19-722416-8 |editor-last=Baker |editor-first=Peter S. |orig-date=1016 |editor-last2=Lapidge |editor-first2=Michael}} About 725, Bede or one of his colleagues used the letter {{rn|N}}, the initial of {{lang|la|nulla}} or of {{wikt-lang|la|nihil}} (the Latin word for "nothing") for 0, in a table of epacts, all written in Roman numerals.{{Cite book |title=Opera Didascalica |editor-last=Jones |editor-first=C. W. |series=Corpus Christianorum, Series Latina |volume=123C}}

The use of {{rn|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.{{Cite book |last=Bachenheimer |first=Bonnie S. |title=Manual for Pharmacy Technicians |date=2010 |isbn=978-1-58528-307-1}}

In later times, the Arabic numeral "0" has been used as a zero to open enumerations with Roman numbers. Examples include the 24-hour Shepherd Gate Clock from 1852 and tarot packs such as the 15th-century Sola Busca and the 20th century Rider–Waite packs.

File:Vecchi 003.jpg}} coin ({{frac|1|3}} or {{frac|4|12}} of an {{lang|la|as}}). Note the four dots (····) indicating its value.]]

File:Semisse.jpg}} coin ({{frac|1|2}} or {{frac|6|12}} of an {{lang|la|as}}). Note the {{rn|S}} indicating its value.]]

The base "Roman fraction" is {{rn|S}}, indicating {{frac|1|2}}. The use of {{rn|S}} (as in {{rn|VIIS}} to indicate 7{{frac|1|2}}) is attested in some ancient inscriptions{{Cite web |title=RIB 2208. Distance Slab of the Sixth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2196 |access-date=11 November 2020 |website=Roman Inscriptions in Britain}} and in the now rare apothecaries' system (usually in the form {{rn|SS}}): but while Roman numerals for whole numbers are essentially decimal, {{rn|S}} does not correspond to {{frac|5|10}}, as one might expect, but {{frac|6|12}}.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve {{nowrap|1= (12 = 2² × 3)}} makes it easier to handle the common fractions of {{frac|1|3}} and {{frac|1|4}} than does a system based on ten {{nowrap|1= (10 = 2 × 5)}}. Notation for fractions other than {{frac|1|2}} is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit {{lang|la|as}}. Fractions less than {{frac|1|2}} are indicated by a dot (·) for each {{lang|la|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 {{rn|S}} for {{lang|la|semis}} "half". Uncia dots were added to {{rn|S}} for fractions from seven to eleven twelfths, just as tallies were added to {{rn|V}} for whole numbers from six to nine.{{Cite journal |last1=Maher |first1=David W. |last2=Makowski |first2=John F. |date=2011 |title=Literary Evidence for Roman Arithmetic with Fractions |url=http://dmaher.org/Publications/romanarithmetic.pdf |journal=Classical Philology |volume=96 |issue=4 |pages=376–399 |doi=10.1086/449557 |s2cid=15162149 |archive-url=https://web.archive.org/web/20130827220707/http://dmaher.org/Publications/romanarithmetic.pdf |archive-date=27 August 2013}} 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 {{lang|la|sextans}} and {{lang|la|quadrans}} are the source of the English words sextant and quadrant.

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

Other Roman fractional notations included the following:

Fractions could also be indicated with a slash through the last letter in a numeral (e.g. {{rn|Ɨ}}), which subtracted the number by an amount less than one (usually {{frac|1|2}}).

The modern form can only write numbers up to 3999, and without M in early Roman times only numbers up to 899 could be written. Various schemes have been used over time to write larger numbers.

File:Westerkerk MDCXXX.jpg in Amsterdam. "{{rn|M}}" and "{{rn|D}}" are given archaic {{lang|la|apostrophus}} form.]]

Using the {{lang|la|apostrophus}} method,{{Cite web |url=https://www.merriam-webster.com/dictionary/apostrophus |title=Definition of Apostrophus |website=www.merriam-webster.com}} 500 is written as {{rn|IↃ}}, while 1,000 is written as {{rn|CIↃ}}. This system of encasing numbers to denote thousands (imagine the {{rn|C}}s and {{rn|Ↄ}}s as parentheses) had its origins in Etruscan numeral usage.

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

File:Roman numerals Bungus 1584-1585.png

• {{rn|IↃ}} = 500               {{rn|CIↃ}} = 1,000
• {{rn|IↃↃ}} = 5,000         {{rn|CCIↃↃ}} = 10,000
• {{rn|IↃↃↃ}} = 50,000    {{rn|CCCIↃↃↃ}} = 100,000

Sometimes {{rn|CIↃ}} (1000) is reduced to {{rn|ↀ}}, {{rn|IↃↃ}} (5,000) to {{rn|ↁ}}; {{rn|CCIↃↃ}} (10,000) to {{rn|ↂ}}; {{rn|IↃↃↃ}} (50,000) to {{rn|ↇ}}; and {{rn|CCCIↃↃↃ}} (100,000) to {{rn|ↈ}}.{{Cite book |last=Ifrah |first=Georges |title=The Universal History of Numbers: From Prehistory to the Invention of the Computer |date=2000 |publisher=John Wiley & Sons |others=Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk}} It is likely {{rn|IↃ}} (500) reduced to {{rn|D}} and {{rn|CIↃ}} (1000) influenced the later {{rn|M}}.

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

Using the {{lang|la|vinculum}}, conventional Roman numerals are multiplied by 1,000 by adding a "bar" or "overline", thus:

• {{rn|IV|border=t}} = 4,000
• {{rn|XXV|border=t}} = 25,000

The vinculum came into use in the late Republic,{{Cite book |last=Dilke |first=Oswald Ashton Wentworth |title=Mathematics and measurement |date=1987 |publisher=British Museum Publications |isbn=978-0-7141-8067-0 |series=Reading the past |location=London|page=15}} 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).{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=102–109}}{{Cite book |last=Gordon |first=Arthur E. |title=Illustrated Introduction to Latin Epigraphy |date=1982 |publisher=University of California Press |isbn=0-520-05079-7 |location=Berkeley |pages=122–123}} It continued in use in the Middle Ages, though it became known more commonly as {{lang|la|titulus}},{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=119}} and it appears in modern editions of classical and medieval Latin texts.{{Cite book |last=Boethius |url=https://archive.org/download/aniciimanliitor00friegoog/aniciimanliitor00friegoog.pdf |title=De Institutione Arithmetica, libri duo |date=1867 |publisher=B.G.Teubner |pages=42 |author-link=Boethius |access-date=18 January 2023 |orig-date=6th century AD}}

In an extension of the {{lang|la|vinculum}}, a three-sided box (now sometimes printed as two vertical lines and a {{lang|la|vinculum}}) is used to multiply by 100,000,{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=402–403}} thus:

• {{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} p. = 1,332,000 paces (1,332 Roman miles).{{efn|1={{rn|XIII|border=vt}} = 13 × 100,000 = 1,300,000 and {{rn|XXXII|border=t}} = 32 × 1000 = 32,000, so '{{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} = 1,332,000. p. is a common abbreviation for {{lang|la|passus}}, paces, the Romans counting a pace as two steps.}}{{Cite book |last=Pliny |url=https://archive.org/details/L352PlinyNaturalHistoryII37/page/n429/mode/2up |title=Natural History |date=1961 |publisher=Harvard University Press |series=Loeb Classical Library |volume=L352 |at=Book VI, XXVI, 100 (pp 414-415) |orig-date=1st century AD}}

{{lang|la|Vinculum}} notation 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 the Antonine Wall.{{Cite web |title=RIB 2208. Distance Slab of the Twentieth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2208 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}{{Cite web |title=RIB 2171. Building Inscription of the Second and Twentieth Legions |url=https://romaninscriptionsofbritain.org/inscriptions/2171 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}

• There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as {{rn|XVIXIII}}, corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as {{rn|X{{Overset|C|V}}XIX}} as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.{{Cite journal |last=Gachard |first=M. |date=1862 |title=II. Analectes historiques, neuvième série (n^os CCLXI-CCLXXXIV) |url=https://www.persee.fr/doc/bcrh_0770-6707_1862_num_31_3_3033 |journal=Bulletin de la Commission royale d'Historie |volume=31 |issue=3 |pages=345–554 |doi=10.3406/bcrh.1862.3033}}
  Page 347: {{lang|fr|Lettre de Philippe le Beau aux échevins..., quote: "Escript en nostre ville de Gand, le XXIIII^me de febvrier, l'an IIII^XXXIX [quatre-vingt-dix-neuf {{=}} 99].}}"
  Page 356: {{lang|fr|Lettre de l'achiduchesse Marguerite au conseil de Brabant..., quote: "... Escript à Bruxelles, le dernier jour de juing anno XV^cXIX [1519].}}"
  Page 374: {{lang|fr|Letters patentes de la rémission ... de la ville de Bruxelles, quote}}: "{{lang|nl|... Op heden, tweentwintich ['twenty-two'] daegen in decembri, anno vyfthien hondert tweendertich}} ['fifteen hundred thirty-two'] {{lang|nl|... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich [1532] vorschreven.}}"
  Page 419: {{lang|fr|Acte du duc de Parme portant approbation..., quote: "Faiet le XV^me de juillet XV^c huytante-six [1586].}}".

• In some French texts from the 15th century and later, one finds constructions like {{rn|IIII^XXXIX}} for 99, reflecting the French reading of that number as {{lang|fr|quatre-vingt-dix-neuf}} (four-score and nineteen). Similarly, in some English documents one finds, for example, 77 written as "{{rn|iii^xxxvii}}" (which could be read "three-score and seventeen").{{Cite book |last=Salter |first=Herbert Edward |url=https://books.google.com/books?id=dfNAAAAAYAAJ&q=iiixx |title=Registrum Annalium Collegii Mertonensis 1483–1521 |date=1923 |publisher=Oxford Historical Society |volume=76}} 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iii^xxxvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.

• A medieval accounting text from 1301 renders numbers like 13,573 as "{{rn|{{sc|XIII. M. V. C. III. XX. XIII}}}}", that is, "13×1000 + 5×100 + 3×20 + 13".{{Cite encyclopedia |chapter=E Duo Codicibus Ceratis Johannis de Sancto Justo |url=https://books.google.com/books?id=NrxuEwPNWD4C&pg=PA530 |date=1865 |orig-date=1301 |last1=de Wailly |last2=Delisle | title=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 |trans-chapter=From Two Texts in Wax by John of St Just |encyclopedia=Recueil des Historiens des Gaules et de la France |lang=la |volume=22 |quote-page=530 |quote= SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. |trans-quote=Sum total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers.}}

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.

{{Main|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: {{angbr|𐌠}}, {{angbr|𐌡}}, {{angbr|𐌢}}, {{angbr|𐌣}}, and {{angbr|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.){{Cite journal |last=Van Heems |first=Gilles |date=2009 |title=Nombre, chiffre, lettre: Formes et réformes. Des notations chiffrées de l'étrusque |trans-title=Between Numbers and Letters: About Etruscan Notations of Numeral Sequences |url=https://www.cairn.info/revue-de-philologie-litterature-et-histoire-anciennes-2009-1-page-103.htm |journal=Revue de philologie, de littérature et d'histoire anciennes |language=fr |volume=83 |issue=1 |pages=103–130 |issn=0035-1652}}

The symbols {{angbr|𐌠}} and {{angbr|𐌡}} resembled letters of the Etruscan alphabet, but {{angbr|𐌢}}, {{angbr|𐌣}}, and {{angbr|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.

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

The symbol for 100 was written variously as {{angbr|𐌟}} or {{angbr|ↃIC}}, and was then abbreviated to {{angbr|{{rn|Ↄ}}}} or {{angbr|{{rn|C}}}}, with {{angbr|{{rn|C}}}} (which matched the Latin letter C) finally winning out. It might have helped that C was the initial letter of {{lang|la|CENTUM}}, Latin for "hundred".

The numbers 500 and 1000 were denoted by {{rn|V}} or {{rn|X}} overlaid with a box or circle. Thus, 500 was like a {{rn|Ɔ}} superimposed on a {{rn|⋌}} or {{rn|⊢}}, making it look like {{rn|Þ}}. It became {{rn|D}} or {{rn|Ð}} by the time of Augustus, under the graphic influence of the letter {{rn|D}}. It was later identified as the letter {{rn|D}}; an alternative symbol for "thousand" was a {{rn|CIↃ}}, and half of a thousand or "five hundred" is the right half of the symbol, {{rn|IↃ}}, and this may have been converted into {{rn|D}}.

The notation for 1000 was a circled or boxed {{rn|X}}: Ⓧ, {{rn|⊗}}, {{rn|⊕}}, and by Augustan times was partially identified with the Greek letter {{rn|Φ}} phi. Over time, the symbol changed to {{rn|Ψ}} and {{rn|ↀ}}. The latter symbol further evolved into {{rn|∞}}, then {{rn|⋈}}, and eventually changed to {{rn|M}} under the influence of the Latin word mille "thousand".

According to Paul Kayser, the basic numerical symbols were {{rn|I}}, {{rn|X}}, {{rn|𐌟}} and {{rn|Φ}} (or {{rn|⊕}}) and the intermediate ones were derived by taking half of those (half an {{rn|X}} is {{rn|V}}, half a {{rn|𐌟}} is {{rn|ↆ}} and half a {{rn|Φ/⊕}} is {{rn|D}}). Then 𐌟 and ↆ developed as mentioned above.{{Cite journal |last=Keyser |first=Paul |date=1988 |title=The Origin of the Latin Numerals 1 to 1000 |journal=American Journal of Archaeology |volume=92 |issue=4 |pages=529–546 |doi=10.2307/505248 |jstor=505248 |s2cid=193086234}}

File:Colosseum-Entrance LII.jpg, with numerals still visible]]

The Colosseum was constructed in Rome in CE 72–80,{{Cite book |last=Hopkins |first=Keith |title=The Colosseum |date=2005 |publisher=Harvard University Press |isbn=978-0-674-01895-2 |location=Cambridge, MA}} and while the original perimeter wall has largely disappeared, the numbered entrances from {{rn|XXIII}} (23) to {{rn|LIIII}} (54) survive,{{Cite book |last=Claridge |first=Amanda |title=Rome: An Oxford Archaeological Guide (First ed.) |date=1998 |publisher=Oxford University Press |isbn=978-0-19-288003-1 |location=Oxford}} 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 {{rn|XL}} is used for 40, {{rn|IV}} is avoided in favour of {{rn|IIII}}: in fact, gate 44 is labelled {{rn|XLIIII}}.

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: {{rn|i}}, {{rn|ii}}, {{rn|iii}}, {{rn|iv}}, and so on.

File:Excerpt from BnF ms. 23112 fr., fol. 343v.png

Since the Middle Ages, a "{{rn|j}}" has sometimes been substituted for the final "{{rn|i}}" of a "lower-case" Roman numeral, such as "{{rn|iij}}" for 3 or "{{rn|vij}}" for 7. This "{{rn|j}}" can be considered a swash variant of "{{rn|i}}". Into the early 20th century, the use of a final "{{rn|j}}" was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.Bastedo, Walter A. [https://archive.org/details/materiamedica00bastgoog/page/n604 Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582]. Retrieved 15 March 2010.

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 "{{rn|A}}" for "{{rn|V}}", or "{{rn|Q}}" for "{{rn|D}}"), while others serve as abbreviations for compound numerals ("{{rn|O}}" for "{{rn|XI}}", or "{{rn|F}}" for "{{rn|XL}}"). Although they are still listed today in some dictionaries, they are long out of use.{{Cite book |last=Capelli |first=Adriano |title=Lexicon abbreviaturarum : dizionario di abbreviature Latine ed Italiane |date=1912|chapter-url=https://archive.org/details/pbc.gda.pl.Lexicon_abbreviaturarum_Cappelli_A_90447/page/413/mode/1up|access-date=2025-03-21|pages=413–421|chapter=Numerazione romana|publisher=Ulrico Hoepli |lang=it}}

A superscript "o" (sometimes written directly above the symbol) was sometimes used as an ordinal indicator.{{Cite web |url=http://agad.archiwa.gov.pl/prezentacje/foto08m.jpg |title=Example of superscript 'o' used as an ordinal indicator |access-date=2014-01-25 |archive-date=2016-03-04 |archive-url=https://web.archive.org/web/20160304055339/http://agad.archiwa.gov.pl/prezentacje/foto08m.jpg |url-status=dead}}

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

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:

File:Carlos IV Coin.jpg using {{rn|IIII}} instead of {{rn|IV}} as regnal number of Charles IV of Spain.|alt=]]

• Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Leo XIV. These are referred to as regnal numbers and are usually read as ordinals; e.g. {{rn|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, Louis XIV of France and William IV of Great Britain) seem to have preferred the use of {{rn|IIII}} instead of {{rn|IV}} on their coinage (see illustration).
• Generational suffixes, particularly in the U.S., for people sharing the same name across generations, such as 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 {{rn|I}} (1792) when this calendar was introduced to the year {{rn|XIV}} (1805) when it was abandoned.
• File:Cambridge Main Public Library 1888.jpg (Massachusetts, U.S.), 1888, displayed in "standard" Roman numerals on its facade.]] 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.
  • Hour marks on timepieces. In this context, 4 is often written {{rn|IIII}}.
  • The year of construction on building façades and cornerstones.
  • Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
  • Book volume and chapter numbers, as well as the several acts within a play (e.g. Act {{Rn|iii}}, Scene 2).
  • Sequels to some films, video games, and other works (as in Rocky II, Grand Theft Auto V, Myst III: Exile).
  • Outlines that 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 XLII; Super Bowl 50 was a one-time exception{{Cite web |last=Rosenthal |first=Gregg |date=June 4, 2014 |title=NFL won't use Roman numerals for Super Bowl 50 |url=https://www.nfl.com/news/nfl-won-t-use-roman-numerals-for-super-bowl-50-0ap2000000355943 |url-status=live |archive-url=https://web.archive.org/web/20151201194151/http://www.nfl.com/news/story/0ap2000000355943/article/nfl-wont-use-roman-numerals-for-super-bowl-50 |archive-date=1 December 2015 |access-date=5 November 2014 |publisher=National Football League}}).
  • WrestleMania, the annual professional wrestling event for WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.

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 {{rn|VI}}.{{Cite web |date=15 November 2021 |title=Planetary Satellite Discovery Circumstances |url=https://ssd.jpl.nasa.gov/sats/discovery.html |access-date=7 January 2022 |website=JPL Solar System Dynamics |publisher=NASA}}

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.{{Cite journal |last=Fluck |first=E. |date=1988 |title=New Notations in the Periodic Table |url=http://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf |journal=Pure Appl. Chem. |publisher=IUPAC |volume=60 |issue=3 |pages=431–436 |doi=10.1351/pac198860030431 |s2cid=96704008 |access-date=24 March 2012}} 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 {{rn|IX}}" is sometimes seen for "grade 9".

File:9th Aero Squadron AEF.jpg AEF, 1918.]]

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

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 numbering UK Acts of Parliament within a given year (a given session until 1963), local acts have lowercase Roman numerals, whereas public acts have plain Arabic numerals and personal acts have italic Arabic numerals.{{cite web |title=Introduction to Private and Personal Acts |url=https://www.legislation.gov.uk/changes/chron-tables/private/intro#6ListingNumberingandAnnotationsofActs |website=legislation.gov.uk |access-date=22 July 2024 |page=6. Listing, Numbering and Annotations of Acts}}

In mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using {{rn|I}}, {{rn|II}}, {{rn|III}}, and {{rn|IV}}.{{Cite web |date=2020-08-04 |title=2.1: Definition and Label Quadrants |url=https://math.libretexts.org/Bookshelves/Applied_Mathematics/Calculus_for_Business_and_Social_Sciences_Corequisite_Workbook_(Dominguez_Martinez_and_Saykali)/02:_Cartesian_Coordinate_System/2.01:_Definition__and_Label_Quadrants |access-date=2025-01-31 |website=Mathematics LibreTexts |language=en}} 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 Nazi III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

• Movements are often numbered using Roman numerals.
• In Roman numeral analysis, harmonic function is identified using Roman numerals.
• Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries' system of measurement: including {{rn|SS}} to denote "one half" and {{rn|N}} to denote "zero".{{Cite book |last1=Reddy |first1=Indra K. |url=https://books.google.com/books?id=U3QY7gz0C2cC |title=Essential Math and Calculations for Pharmacy Technicians |last2=Khan |first2=Mansoor A. |date=2003 |publisher=CRC Press |isbn=978-0-203-49534-6}}

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.

File:Eire Frankng I-IV-1986.jpg

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 {{rn|XV}}", while a lower-ranking cricket or American football team might be the "3rd {{rn|XI}}".

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

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

In theology and biblical scholarship, the Septuagint is often referred to as {{rn|LXX}}, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for "seventy").

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 {{strong|centuries}}, e.g. the French {{lang|fr|{{Smallcaps|xviii}}^e siècle}}{{Cite book |title=Lexique des règles typographiques en usage à l'imprimerie nationale |date=March 2011 |publisher=Imprimerie nationale |isbn=978-2-7433-0482-9 |edition=6th |location=Paris |pages=126 |language=fr}} On composera en chiffres romains petites capitales les nombres concernant : ↲ 1. Les siècles. and the Spanish {{lang|es|siglo {{Smallcaps|xviii}}}} (not {{lang|es|{{Smallcaps|xviii}} siglo}}) for "18th century". Some Slavic and Turkic languages (especially in and adjacent to Russia) similarly favour Roman numerals (e.g. Russian {{lang|ru|XVIII век}}, Azeri {{lang|az|XVIII əsr}} or Polish {{lang|pl|wiek XVIII}}{{Cite web |title=cyfry arabskie a zapis wieku |url=https://poradnia-jezykowa.uni.lodz.pl/faq/cyfry-arabskie-a-zapis-wieku/ |first=Katarzyna |last=Burska |website=Poradnia językowa Uniwersytetu Łódzkiego |publisher=University of Łódź |language=pl |trans-title=Arabic digits when formatting centuries}}). On the other hand, in Turkish and some Central European Slavic languages, like most Germanic languages, one writes "18." (with a period) before the local word for "century" (e.g. Turkish {{lang|tr|18. yüzyıl}}, Czech {{lang|cs|18. století}}).

File:Yeltsin-authograph-1988.gif's signature, dated 10 November 1988, rendered as 10.{{rn|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 {{strong|month}} is written in Roman numerals, while the day is in Arabic numerals: "4.{{rn|VI}}.1789" and "{{rn|VI}}.4.1789" both refer unambiguously to 4 June 1789.

File:DarboLaikas.jpg, Lithuania.]]

Roman numerals are sometimes used to represent the {{strong|days of the week}} in hours-of-operation signs displayed in windows or on doors of businesses,{{Cite web |title=Beginners latin |url=http://www.nationalarchives.gov.uk/latin/beginners/dating/default.htm |archive-url=https://web.archive.org/web/20131203092331/http://www.nationalarchives.gov.uk/latin/beginners/dating/default.htm |archive-date=3 December 2013 |access-date=1 December 2013 |website=nationalarchives.gov.uk}} and sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by {{rn|I}}. Sunday is represented by {{rn|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.

File:S6002447 cropped.jpg, north of Rome, Italy.]]

Roman numerals may also be used for floor numbering.{{Cite web |title=Roman Arithmetic |url=http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/ |archive-url=https://web.archive.org/web/20131122162120/http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/ |archive-date=22 November 2013 |access-date=1 December 2013 |publisher=Southwestern Adventist University}}{{Cite web |title=Roman Numerals History |url=http://romannumerals.info/roman-numerals-history/ |archive-url=https://web.archive.org/web/20131203091427/http://romannumerals.info/roman-numerals-history/ |archive-date=3 December 2013 |url-status=usurped |access-date=1 December 2013}} For instance, apartments in central Amsterdam are indicated as 138-{{rn|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 {{lang|nl|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 {{rn|I}} to {{rn|IX}} for the smaller intervals. The sign {{sfrac|{{rn|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.

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.{{Cite web |url=https://www.unicode.org/charts/PDF/U2150.pdf |title=Unicode Number Forms}} This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or {{rn|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".{{Cite web |date=2011 |title=The Unicode Standard, Version 6.0 – Electronic edition |url=https://www.unicode.org/versions/Unicode6.0.0/ch15.pdf |publisher=Unicode, Inc. |pages=486}} The block also includes some {{lang|la|apostrophus}} symbols for large numbers, an old variant of "{{rn|L}}" (50) similar to the Etruscan character, the Claudian letter "reversed C", etc.{{Cite web |title=Roman symbol |url=https://symbolonly.com/roman-symbols.html |website=symbolonly.com}}

{{Columnslist|colwidth=23em|

• Biquinary
• Egyptian numerals
• Etruscan numerals
• Greek numerals
• Hebrew numerals
• Kharosthi numerals
• Maya numerals
• Chinese numerals
• Roman abacus
• Proto-writing
• Roman numerals in Unicode

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{{Notelist}}

{{Reflist}}

• {{Cite book |last=Menninger |first=Karl |title=Number Words and Number Symbols: A Cultural History of Numbers |date=1992 |publisher=Dover Publications |isbn=978-0-486-27096-8}}

{{Library resources box |by=no |onlinebooks=yes |others=yes |about=yes |label=Roman numerals

|viaf= |lcheading= |wikititle= }}

• 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.

• {{Cite web |title=Roman Numerals (Totally Epic Guide) |url=https://www.knowtheromans.co.uk/Categories/SubCatagories/RomanNumerals/ |website=Know The Romans}}

{{Latin alphabet}}

{{Ancient Rome topics}}

{{List of writing systems}}

{{Sister bar|auto=yes|wikt=Appendix:Roman numerals}}

Category:Numerals

Category:Numeral systems

Category:Ancient Roman mathematics

Category:Latin script

Category:Legacy of the Roman Empire