Number systems
Roman Numeral Converter
Convert numbers to Roman numerals and back, with the working shown and strict validation of standard form. Includes a symbol reference chart and covers the full valid range from I to MMMCMXCIX.
The seven symbols
| Symbol | Value | Memory hook |
|---|---|---|
| I | 1 | One finger |
| V | 5 | An open hand |
| X | 10 | Two hands crossed |
| L | 50 | “Lucy Can’t Drink Milk” |
| C | 100 | |
| D | 500 | |
| M | 1000 |
The three rules
- Add when descending. Symbols run largest to smallest and you add them up: MMXXVI = 1000 + 1000 + 10 + 10 + 5 + 1 = 2026.
- Subtract when ascending. A smaller symbol before a larger one is subtracted: IX = 10 − 1 = 9. Only IV, IX, XL, XC, CD and CM are permitted.
- Never repeat more than three times. III is fine, IIII is not — use IV. V, L and D never repeat at all.
Converting by hand
Work from the largest value down, taking as many of each as will fit. For 1987:
- 1000 fits once → M, 987 left
- 900 fits once → CM, 87 left
- 50 fits once → L, 37 left
- 10 fits three times → XXX, 7 left
- 5 fits once → V, 2 left
- 1 fits twice → II
Result: MCMLXXXVII. That greedy method is exactly what the tool above displays in its breakdown panel.
Where you still meet Roman numerals
- Clock faces — often with IIII rather than IV, a long-standing horological convention.
- Film and book credits — copyright years, chapter and volume numbers.
- Monarchs and popes — Elizabeth II, Louis XIV.
- Sporting events — Super Bowl LVIII, Olympiads.
- Outlines and page numbering — front matter numbered i, ii, iii.
- Buildings and monuments — foundation dates carved above doorways.
Quick reference
1 = I · 2 = II · 3 = III · 4 = IV · 5 = V · 6 = VI · 7 = VII · 8 = VIII · 9 = IX · 10 = X · 20 = XX · 30 = XXX · 40 = XL · 50 = L · 60 = LX · 70 = LXX · 80 = LXXX · 90 = XC · 100 = C · 400 = CD · 500 = D · 900 = CM · 1000 = M · 2026 = MMXXVI
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