The seven symbols
Roman numerals build every number from seven letters. There is no symbol for zero and no place value: an X means ten wherever it stands, and the total comes from adding the symbols up, with a few pairs subtracted.
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
In the standard form used today, symbols run from largest to smallest and are added: MDCLXVI is 1,000 + 500 + 100 + 50 + 10 + 5 + 1 = 1,666. I, X, C and M may repeat up to three times in a row (III is 3, XXX is 30); V, L and D never repeat, because two of them would equal the next symbol up.
The six subtractive pairs
A smaller symbol written before a larger one is subtracted from it. Standard form allows exactly six of these pairs, each a power of ten placed before the next five or ten times as large:
| Pair | Value | Instead of |
|---|---|---|
| IV | 4 | IIII |
| IX | 9 | VIIII |
| XL | 40 | XXXX |
| XC | 90 | LXXXX |
| CD | 400 | CCCC |
| CM | 900 | DCCCC |
Nothing else is subtracted. 99 is XCIX (90 + 9), not IC, and 49 is XLIX, not IL. V, L and D are never placed in front of a larger symbol. MathWorld, citing historians of mathematical notation, notes that the Romans themselves hardly ever wrote a smaller symbol before a larger one to mean subtraction; the practice became popular in Europe after the invention of the printing press.
How the converter works in each direction
Number to numeral: take the largest value from the list below that fits, write its symbols, subtract it, and repeat until nothing is left. Including the subtractive pairs in the list makes the result standard form automatically.
Taking the largest value that fits at each step gives the one standard numeral for every number from 1 to 3999. The breakdown under the result groups the symbols by place value: for 2026 it shows 2000 = MM, 20 = XX, 6 = VI.
Numeral to number: read left to right, adding each symbol’s value, except that a symbol followed by a larger one is subtracted. The converter then writes the total back as a standard numeral and compares it with what you typed. If the two differ, as with IIII, VX, MMMM or IC, the input is reported as not standard instead of being given a value. Lowercase letters are accepted, so iv reads as 4.
Worked examples
- Split into pieces from the left: M, CM, XC, IV.
- M = 1,000; CM = 1,000 − 100 = 900; XC = 100 − 10 = 90; IV = 5 − 1 = 4.
- Add: 1,000 + 900 + 90 + 4 = 1,994.
- 2,000 is two thousands: MM.
- 26 is 10 + 10 + 5 + 1: XXVI.
- Together: MMXXVI. No subtractive pair is needed because no digit is a 4 or a 9.
- Thousands: 3,000 = MMM.
- Hundreds: 900 = CM.
- Tens: 90 = XC.
- Units: 9 = IX.
A useful shortcut follows from the last two examples: convert one decimal digit at a time. Thousands, hundreds, tens and units each become their own small group of symbols, and the groups are written side by side. 1945 is M + CM + XL + V = MCMXLV.
Why 3999 is the limit
The largest symbol is M, and standard form allows at most three of a symbol in a row, so MMM is the most thousands you can write. Add the largest hundreds, tens and units (CM, XC, IX) and you reach MMMCMXCIX, 3999. Writing 4000 would need MMMM, which breaks the three-in-a-row rule. For larger values the Romans used several devices, among them a bar (vinculum) drawn over a numeral to multiply it by 1,000 and frames or parentheses around it. None of them became a single agreed system, so this converter stays within 1 to 3999.
Why clocks show IIII
Clock and watch dials usually show four as IIII rather than IV, as MathWorld notes. Several explanations circulate, such as visual balance with VIII on the opposite side of the dial, but none is documented as the single reason. Treat IIII on a dial as a long-standing design convention, not as an error. The converter still marks IIII as non-standard, because outside clock faces IV is the accepted form.
Misreadings to avoid
- Subtracting from any larger symbol. IM for 999 is not valid. Break 999 into 900 + 90 + 9 to get CMXCIX.
- Reading a numeral as a sequence of digits. MCMXCIV is not “M, C, M…” added in order; the C before M and the I before V are subtracted.
- Four of a kind. XXXX and CCCC are additive spellings of 40 and 400; standard form uses XL and CD.
- Confusing years with ordinal numbers. Monarchs and popes use numerals as ordinals (Elizabeth II is “the second”), while film credits and cornerstones use them for years. The conversion is the same either way.
Roman numerals have no way to write zero, fractions or negative numbers in standard form, so the converter accepts only whole numbers from 1 to 3999.
Sources
- Roman Numerals, Wolfram MathWorld.