Roman Numeral Converter

Convert between numbers and Roman numerals, either direction

Converting between standard numbers and Roman numerals in either direction follows a specific set of additive and subtractive rules — Roman numerals aren't a simple substitution cipher for digits, and the subtractive notation convention (where a smaller-value symbol placed before a larger one means subtraction rather than addition) is where most conversion errors actually happen.

Why Roman numerals aren't a straightforward digit substitution

Roman numerals are built from a fixed set of symbols with fixed values, combined according to specific rules — when a symbol of equal or lesser value follows a larger one, the values add; but when a smaller-value symbol precedes a larger one, that specific pairing represents subtraction, not addition (only specific pairings are valid this way, not any arbitrary smaller-before-larger combination). This subtractive notation exists specifically to avoid stringing together excessive repetitions of the same symbol, and it's the rule most commonly misapplied when converting by hand, since it requires recognizing which specific symbol pairs are valid subtractive combinations rather than treating every smaller-before-larger arrangement as automatically subtractive.

A worked example

A number requiring a subtractive pairing in its Roman numeral representation looks structurally different from one that only needs additive combinations — converting it by simply adding up symbol values without checking for valid subtractive pairs produces an incorrect (typically inflated) numeral, since the subtractive convention specifically exists to represent certain values more compactly than pure addition would.

How this connects to your other number-representation tools

Roman numerals are one of several alternative number-representation systems on this site — for converting between binary, octal, decimal, and hexadecimal instead, the Number Base Converter handles that different (positional, base-driven) numbering system, which follows entirely different rules from the additive/subtractive Roman numeral system.

Common mistakes

Treating every instance of a smaller-value symbol appearing before a larger one as automatically subtractive, rather than checking whether that specific symbol pairing is actually a valid subtractive combination under the Roman numeral rules, is the most common conversion error — not every smaller-before-larger arrangement is valid subtractive notation, and applying the rule too liberally produces an invalid or incorrect Roman numeral.