About

Roman numeral notation remains a requirement in legal documents, clock faces, chapter numbering, and monument inscriptions. Misreading IV as 6 instead of 4 propagates errors through outlines, pagination, and formal citations. The subtractive principle (where placing a smaller value before a larger one signals subtraction, e.g. IX = 9) is the primary source of conversion mistakes. This tool implements the full canonical ruleset for values from 1 to 3,999,999, extending the standard 1 - 3,999 range via vinculum (overline) notation where a bar multiplies a symbol’s value by 1,000.

The converter validates input against the strict formation rules: no more than three consecutive identical symbols, correct subtractive pairs only (IV, IX, XL, XC, CD, CM), and no invalid characters. Malformed input like IC or VV is rejected with an explanation. Note: this tool follows the modern standard form. Historical variants (e.g. IIII on clock dials) are intentionally excluded as they lack a single canonical definition.

Formulas

Arabic-to-Roman encoding uses a greedy decomposition. Given an input n, the algorithm iterates a lookup table sorted by descending value and repeatedly subtracts the largest fitting value while appending the corresponding symbol.

while n > 0 :
find largest v_i ≤ n
result += symbol_i
n −= v_i

Roman-to-Arabic decoding scans left to right. For each symbol at position i, compare its value to the symbol at position i + 1.

result = n∑i=1

{

−v_i if v_i < v_i+1+v_i otherwise

Where v_i is the numeric value of the Roman symbol at index i, and n is the total number of symbols in the input string. The vinculum extension multiplies each overlined symbol's base value by 1,000: V̅ = 5 × 1,000 = 5,000.

Reference Data

Roman Symbol	Arabic Value	Unicode	Subtractive Form	Subtractive Value	Max Consecutive
I	1	U+0049	IV	4	3
			IX	9
V	5	U+0056	-	-	1
X	10	U+0058	XL	40	3
			XC	90
L	50	U+004C	-	-	1
C	100	U+0043	CD	400	3
			CM	900
D	500	U+0044	-	-	1
M	1,000	U+004D	-	-	3
V̅	5,000	V + U+0305	-	-	1
X̅	10,000	X + U+0305	-	-	3
L̅	50,000	L + U+0305	-	-	1
C̅	100,000	C + U+0305	-	-	3
D̅	500,000	D + U+0305	-	-	1
M̅	1,000,000	M + U+0305	-	-	3
Notable Year Conversions
MCMLXIX	1969	Apollo 11 Moon Landing
MCMXCIX	1999	End of 20th Century
MMXXV	2025	Current Year
MMMCMXCIX	3999	Maximum Standard Roman

Frequently Asked Questions

The standard system uses seven symbols: I (1), V (5), X (10), L (50), C (100), D (500), and M (1,000). Since M is the largest and no more than three consecutive identical symbols are permitted, the maximum is MMM + CM + XC + IX = 3,999. Values above this require vinculum (overline) notation, where a bar over a symbol multiplies it by 1,000. This converter supports vinculum up to 3,999,999.

The subtractive rule only permits six specific pairs: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900). A smaller symbol may only precede a symbol that is at most 10 times its value, and only powers of ten (I, X, C) can act as subtractors. V, L, and D are never used in subtractive position. IC would imply 99, but the correct form is XCIX.

The converter normalizes input to uppercase before processing. Entering "xiv", "XIV", or "Xiv" all produce the same result: 14. The output always uses uppercase symbols per convention.

No. The Roman numeral system has no symbol for zero (the concept was absent from Roman mathematics). It does not support negative values or fractional notation. The valid input range is strictly 1 to 3,999 in standard form, or 1 to 3,999,999 with vinculum extension. Entering 0 or negative numbers produces a validation error.

Five checks are applied: (1) only valid characters M, D, C, L, X, V, I are accepted; (2) no symbol repeats more than three times consecutively (and V, L, D never repeat); (3) only the six canonical subtractive pairs are permitted; (4) a subtractive pair cannot be followed by a symbol of equal or greater value than the larger element of the pair; (5) the round-trip test confirms encoding the decoded value reproduces the original input, catching non-canonical forms.

Strictly yes. Symbols must appear in descending order of value, except for the six subtractive pairs. MDCLXVI (1,666) is valid because each symbol is smaller than or equal to the one before it. Writing IVXLCDM would be invalid because smaller values precede larger ones outside the subtractive rule. The converter rejects any input that violates this ordering constraint.