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Category Unit Converters

Enter Arabic Number or Roman Numeral

Type digits for Arabic → Roman, or letters for Roman → Arabic. Range: 1–3,999,999.

Examples:

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About

Roman numeral encoding follows a subtractive notation system where 13 distinct symbol pairs map every positive integer from 1 to 3999 in standard form. Misreading a single numeral on a legal document, clock face, or manuscript index corrupts the referenced value entirely. The algorithm here implements the canonical greedy decomposition: iterate through the ordered value table V = {1000, 900, 500, …, 1}, subtracting each entry and appending its corresponding symbol until the remainder reaches zero. Reverse parsing applies the left-to-right comparison rule: if a symbol's value is less than its successor's, subtract it. This tool extends coverage to 3,999,999 via vinculum (overline) notation, where a bar above a numeral multiplies its value by 1000.

Input validation rejects malformed sequences such as IIII or VV that violate repetition rules. The converter also detects input type automatically. Type digits and receive roman numerals. Type roman letters and receive the arabic equivalent. Note: this tool assumes standard Western roman numeral conventions. Medieval and Unicode variant forms are not supported.

Formulas

The arabic-to-roman conversion uses a greedy decomposition algorithm. Given an input integer n, the algorithm iterates through an ordered lookup table of 13 value-symbol pairs and repeatedly subtracts the largest applicable value:

result = ""
for each (value, symbol) in table:
while n ≥ value:
result += symbol
n −= value

The reverse operation (roman-to-arabic) applies the subtractive comparison rule:

total = 0
for i = 0 to len(s) − 1:
if val(s_i) < val(s_i+1):
total −= val(s_i)
else:
total += val(s_i)

Where val(s_i) returns the numeric value of the roman character at position i. The subtractive rule handles pairs like IV (4) and CM (900). Vinculum notation multiplies base values by 1000 for numbers exceeding 3999.

Reference Data

Roman Numeral	Arabic Value	Rule
I	1	Base unit
IV	4	Subtractive: 5 − 1
V	5	Base unit
IX	9	Subtractive: 10 − 1
X	10	Base unit
XL	40	Subtractive: 50 − 10
L	50	Base unit
XC	90	Subtractive: 100 − 10
C	100	Base unit
CD	400	Subtractive: 500 − 100
D	500	Base unit
CM	900	Subtractive: 1000 − 100
M	1000	Base unit
I̅V̅	4,000	Vinculum: 4 × 1000
V̅	5,000	Vinculum: 5 × 1000
X̅	10,000	Vinculum: 10 × 1000
L̅	50,000	Vinculum: 50 × 1000
C̅	100,000	Vinculum: 100 × 1000
D̅	500,000	Vinculum: 500 × 1000
M̅	1,000,000	Vinculum: 1000 × 1000
MCMXCIX	1999	Common example
MMXXV	2025	Current year
MMMCMXCIX	3999	Max standard value

Frequently Asked Questions

Standard roman numerals use seven symbols: I, V, X, L, C, D, M. The largest is M = 1000, and repetition rules allow at most three consecutive identical symbols. Therefore MMM = 3000 is the highest thousands digit, and MMMCMXCIX = 3999 is the maximum. Vinculum (overline) notation extends this by placing a bar over a numeral to multiply its value by 1000, enabling representation up to 3,999,999.

Subtractive notation places a smaller numeral before a larger one to indicate subtraction. Only six subtractive pairs are valid: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900). Only powers of ten (I, X, C) can be subtracted, and only from the two next-higher symbols. Sequences like IL (49) or IC (99) are invalid; the correct forms are XLIX and XCIX.

Symbols I, X, C, and M may appear up to three times consecutively. Symbols V, L, and D must never repeat. Writing IIII instead of IV or VV instead of X is structurally invalid. This converter enforces these rules during roman-to-arabic parsing and flags violations.

The converter applies a strict regular expression that encodes all valid symbol combinations and repetition limits. For values 1 - 3999, the pattern is: ^M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$. Any input that does not match this pattern is rejected with a specific error message. For extended range inputs using vinculum notation, the overline portion is parsed separately with equivalent rules.

No. The roman numeral system has no symbol for zero and no mechanism for negative values or fractions. The concept of zero entered European mathematics centuries after the roman system was established. This converter accepts only positive integers. Historical roman fraction systems (using S for 1/2 and dots for twelfths) are not standardized and are not supported here.

Vinculum notation places a horizontal bar (overline) above a roman numeral to multiply its value by 1000. For example, V̅ = 5000 and X̅ = 10,000. This tool renders overlined characters in the output for any input value from 4000 to 3,999,999. The overline portion follows the same subtractive and repetition rules as standard numerals.