Why L Is 50 and C Is 100: Where the Letters Came From

Roman numerals grew out of a family of number systems used by Etruscans and Greeks on the Italian peninsula around 600–500 BC, according to Stephen Chrisomalis's comparative history Numerical Notation (Cambridge University Press, 2010). Those early signs were marks, not letters of a word. Over time they came to look like letters of the Latin alphabet, and that's how we write them now.

The best-known explanation is that C stands for centum, the Latin for 100. Florian Cajori, in A History of Mathematical Notations (1928, § 46), attributes the idea that C and M come from the abbreviations of centum and mille to the historian Gottfried Friedlein. It's a hypothesis, not a settled fact: Cajori sets it beside other views.

L has no Latin word behind it: the Latin for fifty, quinquaginta, doesn't start with L. Cajori (§ 46) reports Theodor Mommsen's view that the signs for 50, 100 and 1,000 were originally Greek aspirate letters, and Moritz Cantor's view that signs which resembled letters were later "transformed by popular etymology" into those letters. Either way, the L shape is the end of a process.

The sign for 1,000 shows the process best. Cajori (§ 53) describes an old form, CIƆ: an I between a C and a reversed C. Writing only the right half, IƆ, gave 500, and Cajori (§ 46) notes that D was taken to be this half of the 1,000 sign. The M of today is one of the later forms of 1,000; the mille abbreviation is one of the proposed explanations.

Whatever their origin, the letters now follow strict rules, and those rules are why 50 and 100 are written the way they are:

• 50 = L. Five tens would be XXXXX, but X can't repeat more than three times, so 50 gets its own letter.
• 100 = C. Two fifties would be LL, but L never repeats.
• 40 = XL (50 − 10) and 90 = XC (100 − 10): X subtracts from L and C.
• 49 = XLIX, never IL: I can only subtract from V and X.
• 99 = XCIX, never IC, for the same reason.

The pattern repeats at every scale: I, V, X for units; X, L, C for tens; C, D, M for hundreds. L plays the same role for tens that V plays for units and D for hundreds.

For the full story of the symbols, from the Etruscans to the arrival of Arabic numerals, see the history of Roman numerals.