Roman Numeral Converter

Last updated: 2026-05-17

What are Roman numerals?

Roman numerals are a number system that originated in ancient Rome and remained the dominant notation in Europe through the Middle Ages. While decimal (Arabic) numerals have long replaced them for everyday arithmetic, Roman numerals persist in formal and stylistic contexts: clock faces, book chapter headings, movie sequel titles, Olympic year designations, and legal documents. This converter handles both directions — decimal to Roman and Roman to decimal — for any value in the standard range of 1 to 3999.

The seven symbols

The system is built on seven letters, each representing a fixed value:

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

Symbols are generally written from largest to smallest, left to right, and their values are added together. MCCCII = 1000 + 300 + 2 = 1302.

Subtractive notation

The distinctive feature of Roman numerals is subtractive notation: when a smaller symbol appears immediately before a larger one, it is subtracted rather than added. Six pairs are recognized:

Pair	Value
IV	4 (5 − 1)
IX	9 (10 − 1)
XL	40 (50 − 10)
XC	90 (100 − 10)
CD	400 (500 − 100)
CM	900 (1000 − 100)

The rules governing which subtractions are valid are stricter than they might appear:

• Only I, X, and C can be used subtractively.
• I may precede only V and X (not L, C, D, or M).
• X may precede only L and C (not D or M).
• C may precede only D and M.

This means IIX (8) and IC (99) are not standard — the correct forms are VIII and XCIX.

Reading a Roman numeral

Work left to right. At each position, check whether the current symbol is smaller than the next one. If so, subtract; otherwise, add:

MCMXCIV = M + CM + XC + IV = 1000 + 900 + 90 + 4 = 1994

Step by step:

• M (1000): next symbol is C (100), M > C → add 1000
• C (100): next symbol is M (1000), C < M → part of CM, subtract 100
• M (1000): part of CM → add 1000; net CM = 900
• X (10): next symbol is C (100), X < C → part of XC, subtract 10
• C (100): part of XC → add 100; net XC = 90
• I (1): next symbol is V (5), I < V → part of IV, subtract 1
• V (5): part of IV → add 5; net IV = 4

Writing a Roman numeral

The standard algorithm works greedily — at each step, use the largest symbol (or subtractive pair) that fits into the remaining value:

Convert 1776:

Subtract	Remaining	Symbol added
1000	776	M
500	276	D
100	176	C
100	76	C
50	26	L
10	16	X
10	6	X
5	1	V
1	0	I

Result: MDCCLXXVI — the year of American independence, and famously the design on the base of the US Great Seal.

Why the range is 1–3999

The standard system has no symbol for zero and no way to express fractions as numerals. At the upper end, 3999 (MMMCMXCIX) is the largest number expressible with standard rules — going higher would require four M's in sequence (MMMM for 4000) or a non-standard overline notation where a bar above a letter multiplies it by 1000. Neither is universally recognized, so most converters, including this one, stop at 3999.

Modern uses

Clocks and watches — Analog clock faces frequently use Roman numerals, often with IIII instead of IV for 4 (for visual balance on the face, and because IV was historically an abbreviation for the god Jupiter — IVPITER — and considered inauspicious on timepieces).

Copyright and publication years — Film credits and book copyright pages traditionally use Roman numerals for year attribution, partly as a stylistic convention and partly because the numerals are harder to read quickly (making the age of a film less immediately obvious).

Sequels and series — Movie sequels (Rocky II, The Godfather Part II), sports championships (Super Bowl LVIII), and political dynasties (Henry VIII) use Roman numerals for continuity and gravitas.

Outlines and structured documents — Legal documents, academic papers, and formal outlines use Roman numerals for high-level section numbering (I, II, III) with Arabic numerals for subsections (1.1, 1.2).

Architecture and monuments — Cornerstones, government buildings, and monuments frequently display construction years in Roman numerals. The Lincoln Memorial cornerstone reads MCMXV (1915); the US Capitol dome inscription uses MDCCCLXIII (1863).

Frequently Asked Questions (FAQ)

What are the basic Roman numeral symbols?

There are seven symbols: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Symbols are generally written from largest to smallest, left to right. A symbol placed before a larger one is subtracted: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900.

Why does IV mean 4 instead of IIII?

Roman numerals use subtractive notation as a shorthand. When a smaller symbol precedes a larger one, it is subtracted. So IV = 5 − 1 = 4, and IX = 10 − 1 = 9. Only I, X, and C can be used subtractively, and only before the next two larger symbols (I before V and X, X before L and C, C before D and M).

Why do Roman numerals stop at 3999?

The standard Roman numeral system represents numbers from 1 to 3999 (MMMCMXCIX). Numbers 4000 and above would require four consecutive M symbols (MMMM) or a bar-notation extension not universally supported. In practice, Roman numerals are used today for clocks, book chapters, movie sequels, and year numbers.