(Tài liệu bằng tiếng Anh)
What it does
Converts integers (1 to 3,999,999) to Roman numerals and back. Values above 3,999 use vinculum notation: a bar over a symbol multiplies its value by 1,000, so the range extends a thousandfold. Every input is validated against the canonical form, so IIII, VV, IC, and plain MMMM are rejected with a clear message. The breakdown panel shows exactly how each result was built, step by step.
How to use it
- Pick a direction: Number → Roman or Roman → Number. A valid value carries across the switch, so you can convert back without retyping.
- Type or paste a value. You can also tap an example chip.
- The result appears in large type. Below it, the Breakdown panel lists each greedy step with its value. Copy the result, the breakdown, or a share link to your exact input.
Examples
| Number | Roman | Note |
|---|---|---|
| 44 | XLIV | 40 + 4 |
| 1994 | MCMXCIV | 1,000 + 900 + 90 + 4 |
| 3,999 | MMMCMXCIX | the largest plain numeral |
| 4,000 | I̅V̅ | first vinculum value: IV x 1,000 |
| 1,234,567 | M̅C̅C̅X̅X̅X̅I̅V̅DLXVII | overlined 1,234 + plain 567 |
| 3,999,999 | M̅M̅M̅C̅M̅X̅C̅I̅X̅CMXCIX | the largest value the tool accepts |
How Roman numerals work
Roman numerals use seven letters. That is the entire system:
| Symbol | I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|---|
| Value | 1 | 5 | 10 | 50 | 100 | 500 | 1,000 |
Two rules produce every canonical numeral:
- Additive rule. Read left to right and add.
VIIIis 5 + 1 + 1 + 1 = 8. Bigger letters come first. - Subtractive rule. A smaller letter placed before a larger one subtracts.
IVis 5 - 1 = 4,CMis 1,000 - 100 = 900. Exactly six pairs are legal:IV(4),IX(9),XL(40),XC(90),CD(400),CM(900). The rule exists to keep numerals short and each value’s spelling unique: 4 isIV, neverIIII.
The conversion algorithm is ten lines. Put the 13 values largest-first in one table (the seven letters plus the six subtractive pairs), then walk it greedily:
VALUES = [1000 M, 900 CM, 500 D, 400 CD, 100 C, 90 XC,
50 L, 40 XL, 10 X, 9 IX, 5 V, 4 IV, 1 I]
to_roman(n):
result = ""
for (value, symbol) in VALUES: # largest first
while n >= value:
result += symbol
n -= value
return resultFor 1994 that walk emits M (1,000), then CM (900), then XC (90), then IV (4). That is exactly the breakdown panel. Parsing runs the same logic in reverse: scan left to right, subtract when a smaller letter precedes a larger one, then re-render the total and compare. Any spelling that survives the round-trip is canonical, which is how IIII and IC get rejected with one check.
Above 3,999: the vinculum. The letters stop at M = 1,000, so classical usage capped at 3,999. The medieval vinculum extends the system: an overline multiplies a symbol by 1,000 (V̅ = 5,000, M̅ = 1,000,000). The canonical form renders the thousands part with the same greedy table, then bars every glyph: 4,000 is I̅V̅ (4 x 1,000), and 3,999,999 is the overlined MMMCMXCIX followed by the plain remainder CMXCIX. The tool carries the bar as a combining character (U+0305), so the numeral copies and parses as ordinary text. A pasted macron (U+0304, visually near-identical) is accepted and normalized.
Good to know
- Canonical only. One accepted spelling per value. Non-canonical input is rejected, not guessed.
- Strict range. 1 to 3,999,999. Above that, medieval writers stacked a second bar (x 1,000,000); the tool stops at one.
- Private: all conversion runs locally in your browser. Nothing is sent anywhere.
- Related tools: Number Base Converter, Bitwise Calculator.