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 with a fixed integer value. The modern style uses only these seven:
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 persisted in various places, including on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:
The notations Template:Rn and Template:Rn can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring the representation of "4" as "Template:Rn" on Roman numeral clocks.<ref>Template:Cite news</ref>
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of films and television programmes. Template:Rn, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written Template:Rn. For the years of the current (21st) century, Template:Rn indicates 2000; this year is Template:Rn (2025).
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".<ref name="adams">Template:Cite web</ref> 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).<ref name="Hayes">Template:Cite web</ref>
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:
The largest number that can be represented in this manner is 3,999 (Template:Rn), but this is sufficient for the values for which Roman numerals are commonly used today, such as year numbers:
Prior to the introduction of Arabic numerals in the West, ancient and medieval users of Roman numerals used various means to write larger numbers Template:Xref.
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, Template:Rn is systematically used instead of Template:Rn, but subtractive notation is used for Template:Rn; consequently, gate 44 is labelled Template:Rn.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>
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.
Template:Rn 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 Template:Lang (literally "two and twentieth") rather than the "regular" Template:Lang (twenty second).<ref name="malo2005">Template:Cite thesis 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 Template:Lang 'twenty-second': cf. X5398, Template:Lang; VI 1551, Template:Lang; III 14207.7, Template:Lang; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' – surely here the stonecutter's hypercorrection for IIXX PR.</ref> Apparently, at least one ancient stonecutter mistakenly thought that the Template:Rn of "22nd Legion" stood for 18, and "corrected" it to Template:Rn.<ref name=malo2005/>
Other numerals that do not fit the usual patterns – such as Template:Rn for 45, instead of the usual Template:Rn — 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.<ref name="ixl-story">Template:Cite web</ref>
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 Template:Wikt-lang (the Latin word meaning "none") was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used Template:Lang alongside Roman numerals in a manuscript from 525 AD.<ref>Template:Cite book</ref><ref>Template:Cite book</ref> About 725, Bede or one of his colleagues used the letter Template:Rn, the initial of Template:Lang or of Template:Wikt-lang (the Latin word for "nothing") for 0, in a table of epacts, all written in Roman numerals.<ref name="zero">Template:Cite book</ref>
The use of Template:Rn to indicate "none" long survived in the historic apothecaries' system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.<ref name="Bachenheimer">Template:Cite book</ref>
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.
The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve Template:Nowrap makes it easier to handle the common fractions of Template:Frac and Template:Frac than does a system based on ten Template:Nowrap. Notation for fractions other than Template:Frac is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit Template:Lang. Fractions less than Template:Frac are indicated by a dot (·) for each Template:Lang "twelfth", the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is Template:Rn for Template:Lang "half". Uncia dots were added to Template:Rn for fractions from seven to eleven twelfths, just as tallies were added to Template:Rn for whole numbers from six to nine.<ref>Template:Cite journal</ref> 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 Template:Lang and Template:Lang are the source of the English words sextant and quadrant.
Each fraction from Template:Frac to Template:Frac had a name in Roman times; these corresponded to the names of the related coins:
Fractions could also be indicated with a slash through the last letter in a numeral (e.g. Template:Rn), which subtracted the number by an amount less than one (usually Template:Frac).<ref name=cappelli/>
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.
Using the Template:Lang method,<ref name="merriam-webster">Template:Cite web</ref> 500 is written as Template:Rn, while 1,000 is written as Template:Rn.<ref name="asimov on numbers 12" /> This system of encasing numbers to denote thousands (imagine the Template:Rns and Template:Rns as parentheses) had its origins in Etruscan numeral usage.
The vinculum came into use in the late Republic,<ref name=Dilke>Template:Cite book</ref> 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).<ref name="Chrisomalis01">Template:Cite book</ref><ref name="gordon01">Template:Cite book</ref> It continued in use in the Middle Ages, though it became known more commonly as Template:Lang,<ref name="Chrisomalis02">Template:Cite book</ref> and it appears in modern editions of classical and medieval Latin texts.<ref>Template:Cite book</ref><ref name="PlinyNH" />
In an extension of the Template:Lang, a three-sided box (now sometimes printed as two vertical lines and a Template:Lang) is used to multiply by 100,000,<ref name="Chrisomalis03">Template:Cite book</ref><ref name=Dilke /> thus:
Template:Lang 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.<ref>Template:Cite web</ref><ref>Template:Cite web</ref>
There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as Template:Rn, corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as Template:Rn as in Frenchquinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.<ref name="gach1862">Template:Cite journal Page 347: Template:Lang" Page 356: Template:Lang" Page 374: Template:Lang: "Template:Lang ['fifteen hundred thirty-two'] Template:Lang" Page 419: Template:Lang".</ref>
In some French texts from the 15th century and later, one finds constructions like Template:Rn for 99, reflecting the French reading of that number as Template:Lang (four-score and nineteen).<ref name=gach1862/> Similarly, in some English documents one finds, for example, 77 written as "Template:Rn" (which could be read "three-score and seventeen").<ref name=salt1923>Template:Cite book 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iiixxxvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.</ref>
A medieval accounting text from 1301 renders numbers like 13,573 as "Template:Rn", that is, "13×1000 + 5×100 + 3×20 + 13".<ref name="wade1865">Template:Cite encyclopedia</ref>
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.
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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: Template:Angbr, Template:Angbr, Template:Angbr, Template:Angbr, and Template:Angbr 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.)<ref name="heem2009">Template:Cite journal</ref>
The symbols Template:Angbr and Template:Angbr resembled letters of the Etruscan alphabet, but Template:Angbr, Template:Angbr, and Template:Angbr 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.<ref name=heem2009/>
The numbers 500 and 1000 were denoted by Template:Rn or Template:Rn overlaid with a box or circle. Thus, 500 was like a Template:Rn superimposed on a Template:Rn or Template:Rn, making it look like Template:Rn. It became Template:Rn or Template:Rn by the time of Augustus, under the graphic influence of the letter Template:Rn. It was later identified as the letter Template:Rn; an alternative symbol for "thousand" was a Template:Rn, and half of a thousand or "five hundred" is the right half of the symbol, Template:Rn, and this may have been converted into Template:Rn.<ref name="asimov on numbers 12" />
The notation for 1000 was a circled or boxed Template:Rn: Ⓧ, Template:Rn, Template:Rn, and by Augustan times was partially identified with the Greek letter Template:Rnphi. Over time, the symbol changed to Template:Rn and Template:Rn. The latter symbol further evolved into Template:Rn, then Template:Rn, and eventually changed to Template:Rn under the influence of the Latin word mille "thousand".<ref name=PropN3218/>
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 "Template:Rn" for "Template:Rn", or "Template:Rn" for "Template:Rn"), while others serve as abbreviations for compound numerals ("Template:Rn" for "Template:Rn", or "Template:Rn" for "Template:Rn"). Although they are still listed today in some dictionaries, they are long out of use.<ref name=cappelli>Template:Cite book</ref>
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|thumb|upright=1.1|Spanish Real using Template:Rn instead of Template:Rn as regnal number of [[Charles IV of Spain|Charles Template:Rn of Spain]].|alt=]]
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.
File:Cambridge Main Public Library 1888.jpgThe year of construction of the Cambridge Public Library (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.
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 Template:Rn" is sometimes seen for "grade 9".
In mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using Template:Rn, Template:Rn, Template:Rn, and Template:Rn.<ref>Template:Cite web</ref> 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 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 Template:Rn", while a lower-ranking cricket or American football team might be the "3rd Template:Rn".
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.
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:
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 Template:Strong is written in Roman numerals, while the day is in Arabic numerals: "4.Template:Rn.1789" and "Template:Rn.4.1789" both refer unambiguously to 4 June 1789.
Roman numerals are sometimes used to represent the Template:Strong in hours-of-operation signs displayed in windows or on doors of businesses,<ref>Template:Cite web</ref> and sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by Template:Rn. Sunday is represented by Template:Rn. 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.
Roman numerals may also be used for floor numbering.<ref>Template:Cite web</ref><ref>Template:Cite web</ref> For instance, apartments in central Amsterdam are indicated as 138-Template:Rn, 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 Template:Lang.
In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from Template:Rn to Template:Rn for the smaller intervals. The sign Template:Sfrac thus marks 17.9 km.
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.<ref name="UnicodeChartU2150">Template:Cite web</ref> This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or Template:Rn). 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".<ref>Template:Cite web</ref> The block also includes some Template:Lang symbols for large numbers, an old variant of "Template:Rn" (50) similar to the Etruscan character, the Claudian letter "reversed C", etc.<ref>Template:Cite web</ref>
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.
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