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Roman Numerals (page 1 of 2)

Roman numerals are the letters that ancient Romans used as their numbers:




    I (or i)



    V (or v)



    X (or x)



    L (or l)



    C (or c)



    D (or d)



    M (or m)



What is the difference between "numerals" and "numbers"? "Numbers" are values, such as "three"; "numerals" are the actual written characters which stand for the values, such as "3". As you can see above, the ancient Romans used letters as their numerals. They also had particular rules for building written number-names with these numerals.

(Note: Our modern-day rules for Roman numerals are more strict than what the ancient Romans actually used. And some modern-day clocks with Roman-numeral numbering on their dials don't obey our modern-day rules for numbering, especially for the character for "four". But the discussion below will apply in your math class, to movie dates, to outlines in your English class, and other modern-day contexts.)

Roman numerals don't use place value, like our numbers do. For instance, when we write the character (the numeral) "5", this digit stands for "five ones" in the number "215", "five tens" in the number "251", and "five hundreds" in the number "521". In Roman numerals, on the other hand, the digit "V" only and ever means "five ones".

The method for writing numbers in Roman numerals (other than one, five, ten, fifty, etc) is to add symbols for numbers, starting with the largest value smaller than the target value. Then keep adding units, progressively smaller, until we add up to the target value. But we can't have four of the same character in a row; in such a situation, we have to use subtractive notation instead. It's kind of like making change when you're dealing with money. I'll explain as we go.




Starting at the beginning (namely, at "one", because the Romans didn't understand "zero"), we have:

    I = 1
    II = 1 + 1 = 2
    III = 1 + 1 + 1 = 3

The next number is 4, which is 1 + 1 + 1 + 1, but using four I's for "4" isn't allowed (because we can't do four of the same numeral in a row). If we were dealing with money, we could pay four dollars with four singles (which is 1 + 1 + 1 + 1 = 4) or we could pay with a five and get a single in change (which is 5 1 = 4). In Roman numerals, we "subtract" the 1 from the 5 by putting an I in front of a V: IV is "four" in the sense of "one, from five, leaves four".

    IV = (5 1) = 4

In Roman numerals, we can do this subtractive thing with Is, Xs, and Cs (that is, with ones, tens, and hundreds) but not with Vs, Ls, or Ds (that is, not with fives, fifties, or five hundreds). Continuing our counting, we have: Copyright Elizabeth Stapel 2011 All Rights Reserved

    V = 5
    VI = 5 + 1 = 6
    VII = 5 + 1 + 1 = 7
    VIII = 5 + 1 + 1 + 1 = 8

You may be wondering about that expression for "eight" in Roman numerals. Wouldn't we be using fewer characters if we took "ten" and subtracted "two"? Yes, but another rule in Roman numerals is that we can only subtract one character from another, so we aren't allowed to do "IIX = 10  1 1 = 8". We instead have to add up from five, as shown above. But to create the expression for "nine", we can subtract one from ten: IX is "nine" in the sense of "one, from ten, leaves nine".

    IX = (10 1) = 9

Continuing our counting, we have:

    X = 10
    XI = 10 + 1 = 11
    XII = 10 + 1 + 1 = 12
    XIII = 10 + 1 + 1 + 1 = 13

The next number is fourteen, which we get by adding ten and four, where "four" is written as "one from five": XIV is "fourteen" in the sense of "ten, plus the amount of one-from-five".

    XIV = 10 + (5 1) = 10 + 4 = 14

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Cite this article as:

Stapel, Elizabeth. "Roman Numerals." Purplemath. Available from Accessed


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