How to Read and Write Roman Numerals

The seven symbols

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1,000

There is no symbol for zero, and every other number is built by combining these seven. Case does not matter: xiv and XIV are the same number.

Adding: large to small

When each symbol is equal to or smaller than the one before it, add them all up. VI = 6, XV = 15, LXX = 70, MDC = 1600. Most numerals are nothing more than this.

Subtracting: the six pairs

To avoid four of the same symbol, a smaller symbol written directly before a larger one is subtracted from it. Only six such pairs are used, and only I, X and C ever go first:

Each subtracting symbol reaches only the next two larger ones: I comes before V and X, X before L and C, C before D and M. And only one symbol is subtracted at a time, so 8 is VIII, not IIX.

Repeating: three at most

I, X, C and M can appear up to three times in a row: III is 3, XXX is 30, CCC is 300, MMM is 3000. A fourth would be the next subtractive form instead, so 4 is IV and 40 is XL.

V, L and D never repeat at all, because two of them make a larger symbol that already exists: VV would be X, LL would be C, and DD would be M.

Order: one place at a time

Write the thousands first, then the hundreds, tens and ones, each with its own symbols. For 1994: 1000 = M, 900 = CM, 90 = XC, 4 = IV, which joins into MCMXCIV. Because every place is written separately, you never subtract across places: 99 is XC + IX = XCIX, not IC.

Reading a numeral

1. Start at the left and keep a running total.
2. Look at the next letter. If it is larger than the current one, subtract the current letter; otherwise add it.
3. Move one letter to the right and repeat. The last letter is always added.

For XLIV: X is subtracted (−10), L is added (40), I is subtracted (39), V is added (44), so XLIV is 44. The page for each numeral walks through its own letters the same way.

Times ten: every letter moves up

Multiplying by ten swaps each letter for the one a rank higher: I becomes X, V becomes L, X becomes C, L becomes D and C becomes M. The shape of the numeral stays the same: IV, XL, CD for 4, 40 and 400; VII, LXX, DCC for 7, 70 and 700; IX, XC, CM for 9, 90 and 900. This is why the tens and hundreds follow exactly the same patterns as the ones.

IIII on clock faces

Most clock faces with Roman numerals show four o'clock as IIII rather than IV, a tradition going back to the 14th-century Wells Cathedral clock. Wikipedia Clock faces that use IIII for four still write nine as IX, not VIIII. Wikipedia

Treat IIII as a design tradition for dials, not as a rule: outside clocks, write 4 as IV.

Big numbers: the vinculum

Standard numerals stop at 3999, MMMCMXCIX, because a fourth M is not allowed. For larger values a bar, called a vinculum, is drawn over a symbol to multiply it by 1000:V is 5000, X is 10,000 and M is one million. So 4000 isIV and 12,000 is XII. Turn on the vinculum option in the converter to go up to 3,999,999.

No zero

Roman numerals have no symbol for zero; the system counts things that exist. When medieval scholars needed to write a zero, they used the Latin word nulla, meaning none. The converter answers 0 with the same explanation.

Invalid forms

These are the spellings people type most often that break a rule. The converter flags each one, draws the wrong letters struck, and suggests the standard form.

Some of these can be read more than one way. IIV could be meant as III or as IV, and VX as V or XV, so the converter shows each possible reading instead of guessing silently. IC for 99 appears in some historical texts, yet the standard form is XCIX.

Lowercase and Unicode

Lowercase numerals such as iv and xii are common in page numbers and lists; they follow the same rules. Unicode also has a block of dedicated characters for Roman numerals.Unicode has a dedicated character Ⅳ (ROMAN NUMERAL FOUR, U+2163) in the Number Forms block. Wikipedia Plain letters are usually the better choice, since search and screen readers handle them more reliably.

How to write any number

1. Split the number by place value. Break it into thousands, hundreds, tens and ones: 1994 is 1000 + 900 + 90 + 4.
2. Write each place with its own symbols. Ones use I, V, X; tens use X, L, C; hundreds use C, D, M; thousands use M.
3. Use subtraction for fours and nines. A 4 or 9 in any place is one symbol before a larger one: IV, IX, XL, XC, CD, CM.
4. Join the parts from largest to smallest. M + CM + XC + IV gives MCMXCIV.
5. Check the result. No symbol more than three times in a row, V, L and D never repeated, and values never rising except inside one of the six pairs.

Sources

• Roman numerals, Wikipedia: symbols, subtractive notation, additive forms, vinculum, nulla.
• Number Forms, Wikipedia: Unicode characters U+2160 to U+2188.
• Clock face, Wikipedia: Roman numerals on dials.