Roman Numeral Converter
Convert between Roman numerals and Arabic numbers in both directions.
About Roman Numeral Converter
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
Worked example
With the default values below, Roman Numeral Converter returns Roman Numeral of MMXXIV. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Convertone of Arabic → Roman, Roman → Arabic
- Arabic → Roman
- Arabic Numberaccepts 1–3,999
- 2,024
- Roman Numeral
- MMXXIV
Results
- Roman Numeral
- MMXXIV
- Arabic Number
- 2,024
Step by step
- 1Decompose into Roman symbols= MMXXIV
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.