Roman Numerals Calculator — Roman and Decimal

Background.

MCMLXXXIV at the end of a film's credits is the year 1984, and you can read it in four bites: M is 1,000, CM is 900, LXXX is 80 and IV is 4. Two rules are all you need. Letters normally add, largest first, so LXXX is 50 + 10 + 10 + 10. A smaller letter placed directly in front of a larger one is taken away instead, so CM is 1,000 − 100 and IV is 5 − 1.

Roman numerals stopped being anyone's working number system centuries ago, yet they turn up constantly: hour marks on clock faces, the II in Elizabeth II and the XIV in Louis XIV, the Super Bowl's LX, chapter and volume numbers, the act and scene of a play, the i, ii, iii of a book's preface pages, the I, II, III of an outline, and the founding year carved over a doorway. Most of the time the job is either to write a number that way for a design, a tattoo or a document heading, or to read one you have come across.

The converter does both, for whole numbers from 1 to 3,999. Give it a number and it builds the standard modern form; give it letters and it returns the value, provided the letters are written the standard way. That last condition is deliberate. A lenient reader would happily total IC as 99, but anyone checking a numeral for an engraving wants to be told that 99 is written XCIX, so non-standard strings are refused rather than guessed at.

The ceiling is 3,999, MMMCMXCIX, because the standard form allows a letter to repeat at most three times and has no letter above M. Larger values were written with extra marks, such as a bar over a numeral to multiply it by a thousand, which ordinary keyboards and fonts don't handle consistently.

What is roman numerals calculator?

Roman numerals write whole numbers with seven letters: I (1), V (5), X (10), L (50), C (100), D (500) and M (1,000). The system is not positional. There is no zero and no columns; a letter's value never changes, only whether it is added or subtracted. In the standard modern form, letters run from largest to smallest and add up, except for six subtractive pairs: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). Only I, X and C ever subtract, and each only from the next two letters up. V, L and D never repeat and never subtract, and I, X, C and M appear at most three times in a row. In practice this means a letter that is larger than the one before it always marks a pair, which is the cue to subtract when reading. Those rules give every number from 1 to 3,999 exactly one correct spelling, which is the spelling this converter produces and accepts.

How to use this calculator.

1. 01Choose the direction under Conversion: decimal to Roman numeral, or Roman numeral to decimal.
2. 02To write a number in Roman numerals, type a whole number from 1 to 3,999 in the Decimal integer field. Fractions, zero and negative numbers have no standard Roman form and are not accepted.
3. 03To read a numeral, type it in the Roman numeral field using the letters I, V, X, L, C, D and M. Lowercase is fine and spaces at either end are ignored, but spaces between letters, the special Unicode numeral characters (such as Ⅳ) and overlines are not.
4. 04Leave something in the field you are not using. It is ignored for the conversion, but it can't be blank, and the decimal field must hold a whole number from 1 to 3,999 even when you are decoding letters.
5. 05Use the character count when sizing letters for an engraving, a plaque or a tattoo: MMXXVI needs six letter spaces, MCMLXXXIV nine, and a year from the 1880s can need thirteen.
6. 06If a numeral is refused, rewrite it with the standard subtractive pairs: IIII becomes IV, IC becomes XCIX, MIM becomes MCMXCIX. When you are transcribing an old inscription or a clock face, record the original spelling as it is and use the converter only to check the value.

The formula.

Writing a number in Roman numerals works from a list of thirteen building blocks in descending order: M (1,000), CM (900), D (500), CD (400), C (100), XC (90), L (50), XL (40), X (10), IX (9), V (5), IV (4) and I (1). Starting from the top, take the largest block that still fits into what remains, write it down, subtract its value, and repeat until nothing is left. Because the subtractive pairs sit in the list between the letters they are made from, 900 comes out as CM rather than DCCCC, and 4 as IV rather than IIII.

An equivalent way to see it is digit by digit. Each decimal digit converts on its own, using the letters for its place: units use I, V and X; tens use X, L and C; hundreds use C, D and M; thousands use M alone. The nine patterns are the same at every level, so 3 is III, 30 is XXX and 300 is CCC, while 9 is IX, 90 is XC and 900 is CM. Writing "one", "five" and "ten" for the three letters of a place, the patterns for 1 to 9 are: one; one one; one one one; one five; five; five one; five one one; five one one one; one ten. Fill in I, V, X for units and the same shapes give the tens as X, L, C and the hundreds as C, D, M. That is why 3,449 is simply MMM + CD + XL + IX, MMMCDXLIX, with no carrying between places.

Reading a numeral runs left to right. Each letter is added unless the letter after it is larger, in which case it is subtracted. That arithmetic on its own would give a total to strings no careful writer would use: IC comes to 99, IIII to 4 and VX to 5. So the decoded total is converted back into Roman form, and the input is accepted only if it matches that standard spelling letter for letter. The character count is simply the number of letters in the result. Across the whole range it runs from 1, for the seven numbers that are a single letter, to 15 for 3,888.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Unicode Standard Chapter 22 documents Roman numeral characters and recommends ordinary letter sequences for general representation.
2. [2]Encyclopaedia Britannica lists the seven symbol values and explains the additive/subtractive convention.
3. [3]Wolfram MathWorld supplies an independent mathematical account of modern Roman numeral forms.
4. [4]Chicago Manual of Style Numbers Q&A provides independent editorial context for Roman-numeral usage.
5. [5]Library of Congress Romanization resources provide independent cataloguing context for Roman-number notation.