Roman Numeral Converter
Type a number to get its Roman numeral, or switch direction and type a numeral to read it back. It shows the pieces the answer was built from.
Roman numeral
MCMLXXXVII
- Number
- 1,987
- In words
- One thousand nine hundred and eighty-seven
- Letters used
- 9
- Built from the largest pieces down: M + CM + L + X + X + X + V + I + I, which is 1,000 + 900 + 50 + 10 + 10 + 10 + 5 + 1 + 1 = 1,987.
- Six pairs are written by subtraction rather than repetition — CM, CD, XC, XL, IX and IV. Without them 900 would be DCCCC, and the Romans preferred CM.
- No letter repeats more than three times in a row, which is why four is IV and not IIII.
About Roman numerals
Seven letters do all the work: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1,000. A numeral is written from the largest piece down, and the pieces are added together.
The exception is the one that makes the system awkward. Six pairs are written by subtraction instead — IV, IX, XL, XC, CD and CM — where a smaller letter placed before a larger one means take it away. So IV is four and VI is six, and reading left to right, any letter smaller than the one after it is being subtracted.
The reason for it is that no letter repeats more than three times in a row. Without the subtractive pairs four would be IIII and nine hundred would be DCCCC, which are both legal-looking and both wrong by the usual convention. Clock faces are the famous exception, where IIII is still common.
There is no zero and no way of writing a negative number, because the system was built for counting things rather than for arithmetic. That is also why it eventually lost to the digits we use now: you cannot easily do long multiplication in Roman numerals, and everyone who tried agreed.
What it works out
- Numbers from 1 to 3,999 into Roman numerals
- Roman numerals back into numbers
- The pieces the numeral was built from
- The number written out in words
The formula
M=1000 D=500 C=100 L=50 X=10 V=5 I=1 A smaller letter before a larger one is subtracted
Take the largest piece that fits, write it down, subtract it, and repeat with what is left.
For 1987: the largest is M, worth 1,000, leaving 987. The largest that fits into 987 is CM, worth 900, leaving 87. Then L for 50, leaving 37. Then X three times, leaving 7. Then V, leaving 2. Then I twice.
That gives MCMLXXXVII, and adding the pieces back up — 1,000 + 900 + 50 + 10 + 10 + 10 + 5 + 1 + 1 — returns 1,987.
Reading one is the same rule backwards. Go left to right and compare each letter with the one after it. If it is smaller, subtract it; otherwise add it. In MCMLXXXVII the C sits before an M, so it is minus 100 followed by plus 1,000 — which is the 900.
- I, V, X
- One, five and ten. Between them they cover everything below forty.
- L, C
- Fifty and a hundred.
- D, M
- Five hundred and a thousand. M is as large as the standard system goes.
A worked example
The year 1987 written as a Roman numeral.
That works out to MCMLXXXVII .
- Number
- 1,987
- In words
- One thousand nine hundred and eighty-seven
- Letters used
- 9
Questions
How do you write 1987 in Roman numerals?
MCMLXXXVII. That is M for 1,000, CM for 900, L for 50, XXX for 30, V for 5 and II for 2.
Why is four written IV and not IIII?
Because no letter is meant to repeat more than three times in a row, so four is written as one less than five. Clock faces often use IIII anyway, which is a genuine and very old exception.
Which pairs are subtracted?
Six of them: IV is 4, IX is 9, XL is 40, XC is 90, CD is 400 and CM is 900. Only I, X and C are ever used this way, and only before the next two letters up.
Is there a Roman numeral for zero?
No. The system was built for counting and had no need for a symbol meaning nothing. Medieval scholars who wanted one wrote the letter N, for nulla, but it was never part of the standard set.
What is the largest Roman numeral?
In the standard system, MMMCMXCIX — 3,999. Beyond that the Romans drew a bar over a letter to multiply it by a thousand, so V with a bar meant five thousand, but that notation is not part of ordinary use.
How do you read a long Roman numeral?
Left to right, comparing each letter with the one after it. If it is smaller than the next, subtract it; otherwise add it. Then total everything up.
Why are Roman numerals still used?
For things where the look matters more than the arithmetic: clock faces, book chapters, film copyright dates, monarchs and popes, and the Super Bowl. Nobody calculates with them.
What is my birth year in Roman numerals?
Switch the tool to "number to Roman numeral" and type it in. Anything from 1 to 3,999 works, so every year anyone has been born in is covered.