Roman Numeral Converter

Symbol	Value	Origin / Note
M	1,000	Mille (Latin: thousand)
CM	900	Subtractive: C before M
D	500	Dimidium (half of M)
CD	400	Subtractive: C before D
C	100	Centum (Latin: hundred)
XC	90	Subtractive: X before C
L	50	Quinquaginta (fifty)
XL	40	Subtractive: X before L
X	10	Decem (Latin: ten)
IX	9	Subtractive: I before X
V	5	Quinque (Latin: five)
IV	4	Subtractive: I before V
I	1	Unus (Latin: one)

Year	Roman	Event
753	DCCLIII	Founding of Rome (traditional)
44	XLIV	Assassination of Julius Caesar
476	CDLXXVI	Fall of the Western Roman Empire
1066	MLXVI	Norman Conquest of England
1492	MCDXCII	Columbus reaches the Americas
1776	MDCCLXXVI	American Declaration of Independence
1969	MCMLXIX	Moon landing (Apollo 11)
2024	MMXXIV	Paris Olympics

1

Choose a conversion direction

Select <strong>Decimal → Roman</strong> to convert a regular number into Roman numerals, or <strong>Roman → Decimal</strong> to decode a Roman numeral. The input field updates to match your choice.

2

Enter your value

For Decimal → Roman: type any whole number from 1 to 3,999. For Roman → Decimal: type a valid Roman numeral using I, V, X, L, C, D, and M. The result appears instantly.

3

Read the result and breakdown

The result card shows the converted value. Below it, the step-by-step breakdown lists every symbol used and a running total — so you can see exactly how the conversion works, not just the answer.

Decimal → Roman (greedy subtraction)

repeat: subtract largest possible value, append its symbol

Work through the value table from M (1,000) down to I (1). Each time the remaining amount is ≥ a symbol's value, subtract that value and append the symbol. Repeat until the remainder is zero. Example: 1776 → M (776 left) → D (276) → CC (76) → L (26) → XX (6) → V (1) → I = MDCCLXXVI.

Roman → Decimal (left-to-right scan)

if value[i] < value[i+1]: subtract value[i]; else: add value[i]

Read each symbol left to right. If a symbol's value is less than the next symbol's value (subtractive pair like IV or CM), subtract it from the total. Otherwise, add it. Example: IX → I (1) < X (10) → subtract 1, add 10 = 9.

Roman numeral A numeral in a system originating in ancient Rome that uses combinations of letters (I, V, X, L, C, D, M) to represent numbers. Still used today on clock faces, movie titles, monarchs, and architectural inscriptions.

Subtractive notation When a smaller value symbol is placed before a larger one, it is subtracted rather than added. The six valid subtractive pairs are IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900).

Additive notation The default rule: symbols are added left to right. III = 3, VIII = 8, LXX = 70. Subtractive notation is the exception, not the rule.

Vinculum An overline drawn above a Roman numeral that multiplies its value by 1,000. Used in medieval manuscripts to express numbers above 3,999. Not supported by this converter because standard notation ends at MMMCMXCIX (3,999).

MMXXVI The Roman numeral for 2026. MM = 2,000, XX = 20, VI = 6.

Nulla The Latin word for "nothing." Roman numerals have no symbol for zero — nulla was used as a word, not a numeral. The concept of zero as a digit entered Europe via Arabic numerals around the 12th century.

Place value Roman numerals are not a place-value system. Their value comes from the symbols themselves, not their position in a base-ten grid. This is why multiplication and long division in Roman numerals were extremely cumbersome.

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History student

Converting the year of American independence

Direction Decimal → Roman Decimal Number 1776

1776 converts to MDCCLXXVI. The greedy algorithm first subtracts M (1,000), leaving 776. Then D (500) leaves 276. Two Cs (200) leave 76. L (50) leaves 26. Two Xs (20) leave 6. V (5) leaves 1. Finally I. Seven steps, seven symbols — a memorable numeral for a memorable year.

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Curious traveler

Decoding a year carved above a museum entrance

Direction Roman → Decimal Roman Numeral MCMXCIX

MCMXCIX = 1999. Step by step: M (1000) + CM (900) + XC (90) + IX (9) = 1999. The three subtractive pairs — CM, XC, IX — each follow the rule that a smaller value before a larger one means subtraction. A building inscribed MCMXCIX was completed or founded in 1999.

Roman numerals are an ancient number system that has survived into modern use on clock faces, royal titles, film copyright dates, and building cornerstones. This converter translates any number from 1 to 3,999 into Roman numerals — and decodes any Roman numeral back into a decimal — with a step-by-step breakdown so you can learn the system, not just look up an answer.

The seven symbols and how they combine

The Roman numeral system uses seven letters: I (1), V (5), X (10), L (50), C (100), D (500), and M (1,000). Numbers are formed by writing symbols in decreasing order and summing them — III = 3, VIII = 8, LXX = 70. There is one important exception: the subtractive principle.

Six subtractive pairs shorten notation: IV (4), IX (9), XL (40), XC (90), CD (400), CM (900). In each pair, a smaller symbol before a larger one signals subtraction. XLII, for example, is XL (40) + II (2) = 42. Without subtractive notation the number would be written XXXXII — four Xs instead of XL.

Rules for valid Roman numerals

Not every arrangement of Roman letters is valid. Standard notation follows three constraints: (1) I, X, C, and M can appear at most three consecutive times; V, L, and D can appear only once. (2) Only one smaller symbol may precede a larger one in a subtractive pair. (3) A numeral must decode to a value between 1 and 3,999 and then re-encode to exactly the same string — this is the round-trip test this converter uses to detect invalid input like IIII or VV.

Where Roman numerals are still used today

Despite being replaced by Hindu-Arabic numerals for arithmetic, Roman numerals remain standard in several contexts. Clock faces traditionally mark hours with I–XII (though IIII rather than IV is common on clock faces, a historical anomaly). Super Bowl editions, Olympic Games, and major sporting events use Roman numerals to avoid implying a specific year. Movie copyright lines at the end of films are almost always in Roman numerals. Monarchs and popes are numbered in Roman numerals — King Charles III, Pope John Paul II. Outlines in legal documents, academic papers, and legislation use Roman numerals for primary sections.

Why Roman numerals stop at 3,999

Standard Roman notation cannot exceed 3,999 (MMMCMXCIX) because the symbol M can appear at most three times consecutively, giving a maximum of 3,000 for the thousands place. Medieval scribes extended the system using the vinculum — an overline that multiplied a symbol by 1,000 — allowing numbers in the millions, but this extension is not part of standard notation and is not supported here. For everyday use — years, chapter numbers, Super Bowl editions — the range 1–3,999 covers everything you are likely to need.

What is the largest Roman numeral?+

Using standard notation, the largest Roman numeral is 3,999 — written as MMMCMXCIX. The symbol M can appear at most three times consecutively, capping the thousands place at 3,000. Everything else — CM (900), XC (90), IX (9) — fills in the remaining digits.

Why is there no zero in Roman numerals?+

Roman numerals are an additive (and partly subtractive) system based on counting objects, not a place-value system where position carries meaning. There was no concept of an empty position to represent. The Latin word nulla ("nothing") was used in texts, but never as a numeral. Zero as a digit entered Western mathematics from Hindu-Arabic numeration around the 12th century.

What does XLII mean?+

XLII equals 42. XL is the subtractive notation for 40 (X = 10 placed before L = 50, meaning 50 − 10 = 40), and II adds 2. XLII is famously the answer in The Hitchhiker's Guide to the Galaxy — Douglas Adams chose it partly because it is an unremarkable, perfectly ordinary number.

How do I read CM in Roman numerals?+

CM represents 900. C (100) is placed before M (1,000), triggering the subtractive rule: 1,000 − 100 = 900. The full list of subtractive pairs is: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900. Only these six combinations are valid — IIX and VX, for example, are not.

Are Roman numerals still used today?+

Yes, in several contexts. Clock faces mark hours I–XII. Film and TV copyright lines use Roman numerals (e.g. © MMXXVI). The Super Bowl and Olympics are identified by Roman numerals. Monarchs and popes are numbered in Roman numerals (King Charles III, Pope Francis I). Academic outlines, legal documents, and chapter headings also use them. Roman numerals signal permanence and tradition in ways Arabic numerals do not.

Inputs

Result

Year in Roman Numerals

How to Use This Calculator

Choose a conversion direction

Enter your value

Read the result and breakdown

Formula & Methodology

Key Terms Explained

Real-World Examples

History student

Curious traveler