History of Roman Numerals

The dates and the Italic setting come from Chrisomalis's chapter on "Italic systems" in Numerical Notation (Cambridge University Press, 2010), the standard comparative history of number writing. Beyond that, the origin of each sign is debated, and the explanations below are hypotheses, each with the scholar who proposed it.

• Signs that became letters. Moritz Cantor argued that the original signs resembled letters and were later "transformed by popular etymology" into those letters, as Florian Cajori summarizes in A History of Mathematical Notations (1928, § 46).
• C and M as abbreviations. Gottfried Friedlein suggested that C and M could come from the abbreviations of centum (100) and mille (1,000) (Cajori, § 46). This is the explanation most people know, but it is one hypothesis among several.
• Greek letters for 50, 100 and 1,000. Theodor Mommsen proposed that the signs for 50, 100 and 1,000 were originally three Greek aspirate letters (Cajori, § 46).
• V as a hand. The popular idea that V shows an open hand and X two hands joined is called "highly dubious" by Chrisomalis in his 2003 thesis.

What these accounts share is that the modern letters are the end of a process, not the starting point.

The clearest evidence of that process is the old sign for 1,000. Cajori (§ 53) describes it as CIƆ: an I enclosed between a C and a reversed C, like a stroke in parentheses. Writing only the right half, IƆ, gave 500, and Cajori (§ 46) notes that D was taken to be this half of the sign for 1,000. How 1,000 itself ended up as M is less certain; Friedlein's mille abbreviation is one of the proposals.

You can still see the logic in the values: 500 is half of 1,000, and 5 and 50 work the same way for 10 and 100. Chrisomalis describes Roman numerals as a decimal system with a sub-base of 5.

Roman numerals are good for recording a number and poor for doing arithmetic on paper. Herbert Bruderer, a historian of computing writing for Communications of the ACM, argues that the Romans calculated on the abacus and used the numerals only to record results, and notes that no surviving document describes how written Roman numerals would be used for calculation. The system also has no sign for zero.

That is a practical reason the system later lost ground: written column arithmetic needs place value and zero, which Roman numerals lack.

Today 4 is IV and 9 is IX. In antiquity the additive forms IIII and VIIII were common, especially on official inscriptions. Keith Houston, citing the Oxford Classical Dictionary, writes that "the additive notation was preferred for inscriptions", and gives the example of a Roman altar where a cohort number is written "coh(ortis) IIII".

The habit lasted. Cajori (§ 48) quotes the palaeographer Adriano Cappelli, who found that subtraction "was seldom applied by the old Romans and during the entire Middle Ages one finds only a few instances of it". The strict modern rules (only six subtractive pairs, no symbol more than three times in a row) are a later standardization.

For numbers far above 1,000, Roman and medieval writers added marks to the letters. Cajori (§ 51) describes a horizontal line above a numeral to multiply it by 1,000, and strokes on the sides and top to indicate hundreds of thousands, giving the example |X|CLXXXDC for 1,180,600. The full system, and how it is written today, is in the guide to large Roman numerals.

Roman numerals did not disappear with the Western Roman Empire. Chrisomalis notes that the collapse of the empire brought the greatest expansion of the system, which spread through medieval Europe.

The change came through trade. Leonardo of Pisa (Fibonacci) published Liber abaci in 1202, and the MacTutor biography describes it as the book that "introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe"; it was widely copied and imitated. The economic historian Raffaele Danna shows that thirteenth-century merchant-bankers were among the first Europeans to use the new numerals, with Italy as the early adopter and England following later.

Roman numerals stopped being used for calculation but kept the jobs where tradition and order matter more than arithmetic:

• Names of monarchs and popes. Leo XIV was elected pope on 8 May 2025 (USCCB).
• Clocks. Many dials use Roman numerals; the Great Clock of Westminster uses IV for four (UK Parliament), while many other clocks use IIII. See why clocks use IIII.
• Numbered events and editions, chapters, volumes and the front pages of books, explained in how Roman numerals work.