Roman Numeral Converter
Convert between Roman numerals and Arabic numbers in both directions.
Inputs
Roman Numeral
MMXXIV
Arabic Number
2,024
Step by step
Decompose into Roman symbols
2 × M (1000) + 2 × X (10) + 1 × IV (4)
= MMXXIV
How it works
Roman numerals use seven letters: I=1, V=5, X=10, L=50, C=100, D=500, M=1000. When a smaller value appears before a larger one it is subtracted (e.g., IV=4, IX=9). The system encodes integers 1–3999; classical convention avoids MMMM, using instead MMMDCCCXCIX for 3999. Non-canonical forms like IIII or IIX are rejected because they have unambiguous canonical equivalents.
Formula
Subtractive rule
Sum all symbol values; subtract a value when the next symbol is larger.
- v_i
- Numeric value of symbol i
- s_i
- Signed contribution of symbol i
Frequently Asked Questions
What is the largest number expressible in Roman numerals?
Using the standard seven symbols without vinculum (overline), the largest is 3999 = MMMDCCCXCIX. The numeral MMMM for 4000 is non-standard and not supported.
Why does 'IIII' get rejected?
IIII is non-canonical. The standard rule limits consecutive identical symbols to three, so 4 is always IV. IIII appears on some clock faces as an aesthetic tradition, not standard notation.
What does MCMXCIV equal?
MCMXCIV = M(1000) + CM(900) + XC(90) + IV(4) = 1994. You may recognise it from the copyright date in Roman numerals at the end of TV programmes.
Is MMM the year 3000 in Roman numerals?
Yes. MMM = 3000. The full year 3000 in Roman numerals is simply MMM.