Roman Numeral Converter

Convert numbers to Roman numerals and back free online. Real algorithmic conversion following standard subtractive notation rules, not a lookup table.

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How to Use This Tool

Choose a directionNumber to Roman, or Roman to number

Enter your valueA number (1-3999) or a Roman numeral string

See the converted resultCalculated with the real subtractive notation algorithm

A Genuine Algorithm, Not a Lookup Table

Converting between numbers and Roman numerals isn't simple digit substitution -- the subtractive notation rule (where IV means 4, not "1 then 5") requires an actual algorithm that checks for specific value patterns and applies subtraction logic, working through a table of value-symbol pairs from largest to smallest.

How the Conversion Algorithm Actually Works

Converting a number to Roman numerals repeatedly finds the largest value-symbol pair (including subtractive pairs like 900 for CM) that fits within the remaining number, subtracts that value, appends the symbol, and repeats until nothing remains. Converting the other direction reads through the Roman numeral symbols, adding values but subtracting when a smaller symbol precedes a larger one.

Where the Standard System Reaches Its Limit

Using just I, V, X, L, C, D, and M, standard Roman numeral notation reliably represents numbers up to 3,999. Beyond that, historical extensions exist (like a bar over a numeral indicating multiplication by 1,000), but these aren't part of the commonly used standard notation this converter implements.

Frequently Asked Questions

Subtractive notation is the rule that a smaller numeral placed before a larger one means subtraction -- IV means 4 (5 minus 1), not 6. This rule is what makes Roman numeral conversion a genuine algorithm rather than simple digit substitution, since the algorithm must check for these specific subtractive pairs.

Standard Roman numerals, without extended notation conventions, typically handle up to 3,999 reliably using the standard symbol set (I, V, X, L, C, D, M). Numbers beyond that traditionally require additional notation conventions like a bar over a numeral to indicate multiplication by 1,000.

It works through a value-symbol pair table from largest to smallest (including the subtractive pairs like 900=CM, 400=CD), repeatedly subtracting the largest value that fits and appending its symbol, until the remaining number reaches zero.

Yes, the reverse algorithm reads through the Roman numeral symbols, adding each symbol's value, but subtracting when a smaller-value symbol appears before a larger one, correctly handling the subtractive notation in that direction as well.

Clock faces, building cornerstones marking construction year, movie/book sequel numbering, outline formatting, and Super Bowl numbering are all common contemporary contexts where Roman numerals persist as a stylistic or traditional convention.