Roman Numeral Converter — Number ↔ Roman

How Roman numerals work

Roman numerals use seven letters, combined additively with a subtractive shortcut for six specific cases. Values are written largest to smallest and added together, except where a smaller symbol precedes a larger one, in which case it is subtracted.

Symbol	I	V	X	L	C	D	M
Value	1	5	10	50	100	500	1,000

A mnemonic for the order: I Value Xylophones Like Cows Dig Milk.

The six subtractive pairs

Only these combinations are valid. Any other subtraction is incorrect in standard notation.

Pair	Value	Pair	Value
IV	4	CD	400
IX	9	CM	900
XL	40
XC	90

The governing rules are that only I, X and C may be subtracted; each may only precede the next two larger symbols (I before V and X, X before L and C, C before D and M); and only one symbol may be subtracted at a time. So 99 is XCIX — ninety plus nine — not IC. Similarly 45 is XLV, not VL.

A worked example

Converting 1994:

1000 = M
900 = CM
90 = XC
4 = IV
Result: MCMXCIV

Reading back the other way, work left to right and subtract whenever a symbol is smaller than the one following it: M(1000) + CM(900) + XC(90) + IV(4) = 1994.

Common numbers

Number	Roman	Number	Roman
4	IV	50	L
9	IX	90	XC
14	XIV	100	C
19	XIX	400	CD
40	XL	500	D
44	XLIV	900	CM
49	XLIX	1000	M
2024	MMXXIV	2026	MMXXVI

Limits of the system

Standard Roman numerals run from 1 to 3,999. There is no zero, no way to write a negative number, and no fractional notation in the standard set. The upper limit exists because M is the largest symbol and no more than three may repeat, capping the thousands at MMM.

Larger values were written with a vinculum, an overbar multiplying the symbol by a thousand, so V-bar is 5,000 and X-bar is 10,000. The Romans themselves used several other notations and were far less consistent than the tidy rules taught today — IIII appears on monuments and, famously, on most clock faces, where it balances the VIII opposite it visually.

The absence of zero is not an oversight so much as a consequence of the system being positional-free: each symbol carries its own value regardless of where it sits, so there is no empty column that needs marking. That same property makes the numerals fine for recording quantities and hopeless for arithmetic, which is why they were superseded by Hindu-Arabic numerals for calculation.

Where they are still used

Clock and watch faces, usually with IIII rather than IV.
Book front matter, where prefaces are numbered in lowercase roman.
Monarchs and popes — Elizabeth II, Louis XIV.
Film copyright dates and building cornerstones.
Super Bowls, and sequels of various kinds.
Outlines and legal documents, as section numbering.

Frequently asked questions

Why is 99 written XCIX and not IC?

Because only I, X and C may be subtracted, and each only from the next two larger symbols. I can precede V and X but not C. So 99 must be built as 90 (XC) plus 9 (IX).

Is there a Roman numeral for zero?

No. The system has no zero and no negative numbers. Roman writers used the word nulla when they needed to express nothing, but there is no symbol for it.

What is the largest Roman numeral?

MMMCMXCIX, which is 3,999, in the standard system. Beyond that a vinculum — an overbar multiplying by 1,000 — was used, so V-bar means 5,000.

Why do clocks show IIII instead of IV?

Tradition, and visual balance against the VIII directly opposite. It also keeps the first four hours using only I, which some historians argue made dials easier to read. Both forms are valid.

How do I read a long numeral like MCMXLIV?

Work left to right, subtracting whenever a symbol is smaller than the one after it: M is 1000, CM is 900, XL is 40, IV is 4. Total 1944.