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How to use this calculator#
- Choose the direction you needNumber to numeral takes a whole number from 1 to 3,999. Numeral to number accepts the seven letters in any case — MCMXCIV and mcmxciv both decode to 1994.
- Break a large number into place valuesTo write 1984 by hand, split it into 1000 + 900 + 80 + 4 and convert each part: M + CM + LXXX + IV = MCMLXXXIV. Always work from the largest place down.
- Use only the six legal subtractive pairsIV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). Nothing else subtracts. IL for 49 and IC for 99 are not valid — 49 is XLIX and 99 is XCIX.
- Check the result round-tripsConvert your numeral back to a number. This converter rejects malformed input such as IIII or VX precisely because they fail that round trip, so a rejection means the numeral is non-standard rather than that the tool broke.
The formula#
Greedy subtractive notation
value = Σ (symbol values), subtracting any symbol that sits immediately before a larger one
- I
- 1 — may repeat up to three times, may precede V or X to subtract
- V
- 5 — never repeats, never subtracts
- X
- 10 — may repeat up to three times, may precede L or C to subtract
- L
- 50 — never repeats, never subtracts
- C
- 100 — may repeat up to three times, may precede D or M to subtract
- D
- 500 — never repeats, never subtracts
- M
- 1000 — may repeat up to three times; three Ms is the ceiling at 3,999
Writing a number uses the greedy method: repeatedly take the largest value in the list (1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1) that still fits and subtract it. The trap is that the system has no zero and no place value, so there is nothing to hold a column open. 1900 is MCM, not M0CM or MDCCCC — and 2026 needs no marker at all for the empty hundreds place.
How Roman numerals work#
Roman numerals are built from seven letters: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1,000. Values are normally added from largest to smallest, so CLX reads as 100 + 50 + 10 = 160. When a smaller symbol sits immediately before a larger one it is subtracted instead, which is exactly how IV means 4 and IX means 9.
Only six subtractive pairs are valid in the standard form: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). No symbol may repeat more than three times in a row, and V, L and D never repeat at all. Those rules are why 1994 is written MCMXCIV, made of M + CM + XC + IV, rather than the shorter but invalid MIM.
Reading years and common numerals#
Years are the most common reason people reach for a converter. 2024 is MMXXIV, 2025 is MMXXV, 2026 is MMXXVI and 1969 is MCMLXIX. Film copyright lines, cornerstones and Super Bowl numbering all use the same system. Read them left to right in chunks: MCMLXXXIV splits into M (1000), CM (900), LXXX (80) and IV (4), which totals 1984.
Smaller numerals turn up on clock faces and in book prefaces. Four is usually IV, though many clocks use IIII instead for visual balance against the VIII opposite it — a long-standing exception rather than a rule. Other landmarks worth recognising are XL for 40, LX for 60, XC for 90, CD for 400 and DCCC for 800. Chapter and volume numbers rarely climb beyond a few dozen.
Limits, zero and the history#
Standard Roman numerals run from 1 (I) to 3,999 (MMMCMXCIX). Beyond that the system needs a vinculum, a bar drawn over a numeral to multiply it by 1,000, which has no agreed plain-text equivalent — so most converters, this one included, stop at 3,999. There is also no symbol for zero, and no way at all to write a negative number or a fraction.
The numerals grew out of Etruscan tally marks and served Rome for centuries, but arithmetic with them is painful because there are no place values to line up in columns. Hindu-Arabic numerals reached Europe through Fibonacci's Liber Abaci in 1202 and had largely displaced Roman numerals in commerce by the 1500s, leaving them to clocks, monuments, outlines and sequel titles.
Worked examples#
Writing 1994 in Roman numerals
A film copyright line or a cornerstone needs the year 1994.
- Largest value that fits 1994 is 1000 → M, remainder 994
- Largest that fits 994 is 900 → CM, remainder 94
- Largest that fits 94 is 90 → XC, remainder 4
- Largest that fits 4 is 4 → IV, remainder 0
- Join them: M + CM + XC + IV
1994 = MCMXCIV. The tempting shortcut MIM is invalid, because only I, X and C may ever be subtracted.
Reading MMXXVI
Decoding a numeral found on a plaque.
- M = 1000, and the next symbol M is not larger, so add: running total 1000
- M = 1000, next is X which is smaller, so add: 2000
- X = 10, next is X, add: 2010
- X = 10, next is V which is smaller, add: 2020
- V = 5, next is I, add: 2025
- I = 1, nothing follows, add: 2026
MMXXVI = 2026. No symbol was ever followed by a larger one, so nothing was subtracted.
Reference tables#
| Number | Numeral | Number | Numeral |
|---|---|---|---|
| 1 | I | 11 | XI |
| 2 | II | 12 | XII |
| 3 | III | 13 | XIII |
| 4 | IV | 14 | XIV |
| 5 | V | 15 | XV |
| 6 | VI | 16 | XVI |
| 7 | VII | 17 | XVII |
| 8 | VIII | 18 | XVIII |
| 9 | IX | 19 | XIX |
| 10 | X | 20 | XX |
Clock faces often print IIII rather than IV for visual balance against the VIII opposite. It is a long-standing exception, not a valid alternative form.
| Tens | Numeral | Hundreds | Numeral | Thousands | Numeral |
|---|---|---|---|---|---|
| 10 | X | 100 | C | 1000 | M |
| 20 | XX | 200 | CC | 2000 | MM |
| 30 | XXX | 300 | CCC | 3000 | MMM |
| 40 | XL | 400 | CD | — | — |
| 50 | L | 500 | D | — | — |
| 60 | LX | 600 | DC | — | — |
| 70 | LXX | 700 | DCC | — | — |
| 80 | LXXX | 800 | DCCC | — | — |
| 90 | XC | 900 | CM | — | — |
Thousands stop at MMM because a fourth M is not allowed. That caps standard notation at MMMCMXCIX = 3,999.
| Number | Numeral | Breakdown |
|---|---|---|
| 49 | XLIX | XL (40) + IX (9) |
| 99 | XCIX | XC (90) + IX (9) |
| 1900 | MCM | M (1000) + CM (900) |
| 1969 | MCMLXIX | M + CM + LX (60) + IX (9) |
| 1984 | MCMLXXXIV | M + CM + LXXX (80) + IV (4) |
| 1999 | MCMXCIX | M + CM + XC (90) + IX (9) |
| 2000 | MM | M + M |
| 2020 | MMXX | MM (2000) + XX (20) |
| 2024 | MMXXIV | MM + XX + IV (4) |
| 2025 | MMXXV | MM + XX + V (5) |
| 2026 | MMXXVI | MM + XX + V + I |
| 2050 | MML | MM (2000) + L (50) |
| 3999 | MMMCMXCIX | MMM + CM + XC + IX — the largest standard numeral |
1999 is MCMXCIX, not MIM. The false shorthand is the most frequently reproduced Roman numeral error on the internet.
Common mistakes#
- Inventing subtractive pairsOnly IV, IX, XL, XC, CD and CM are valid. MIM for 1999, IL for 49 and IC for 99 all break the rule that a subtracted symbol must be a power of ten (I, X or C) and no more than one order of magnitude below the symbol it precedes. The correct forms are MCMXCIX, XLIX and XCIX.
- Repeating a symbol four timesIIII, XXXX and CCCC are non-standard; the fourth repetition is what the subtractive pairs exist to avoid. V, L and D may never repeat at all, so VV for 10 and DD for 1000 are wrong even once doubled.
- Expecting a zero or a value above 3,999There is no Roman zero, no negative and no fraction in the standard system, and no agreed plain-text way to write 4,000 or more. Larger values need a vinculum — an overbar multiplying a numeral by 1,000 — which cannot be typed reliably, so this converter stops at MMMCMXCIX.
- Reading a subtractive pair as two separate symbolsMCMXCIV is not M + C + M + X + C + I + V. Split that way it reads 1000 + 100 + 1000 + 10 + 100 + 1 + 5 = 2216. Scan left to right and check each symbol against the one after it before deciding to add or subtract.
Frequently asked questions#
What is the largest Roman numeral?
In standard notation it is MMMCMXCIX, which is 3,999. Larger values need an overbar to multiply a numeral by 1,000, and that is not part of ordinary written form.
Why is 4 sometimes written IIII?
IV is the correct standard form, but clockmakers have long used IIII because it balances the VIII on the opposite side of the dial and reads more clearly at a glance.
How do you write 2025 in Roman numerals?
MMXXV — two thousands (MM), two tens (XX) and a five (V), written in descending order of value.
Is there a Roman numeral for zero?
No. The system has no zero and no place value. When Romans needed to express nothing they used the Latin word nulla instead of a symbol.
Key terms#
- Subtractive notation
- The convention where a smaller symbol placed immediately before a larger one is subtracted rather than added, giving IV = 4 and CM = 900. It keeps numerals short and caps any symbol at three repetitions.
- Additive notation
- The default rule: symbols written in descending order are summed. DCCLXVI is 500 + 100 + 100 + 50 + 10 + 5 + 1 = 766.
- Vinculum
- A bar drawn over a numeral to multiply its value by 1,000, used in antiquity for large numbers. V with a bar is 5,000. It has no standard plain-text form, which is why most converters cap at 3,999.
- Place value
- The property of Hindu-Arabic numerals where a digit's position sets its magnitude. Roman numerals have no place value and no zero, which is why written arithmetic with them is so awkward and why they were displaced in commerce.
- Round trip
- Converting a number to a numeral and straight back to confirm the two agree. It is the standard validity test for Roman numerals, and it is what rejects IIII, VX and MIM.
Sources#
- Roman numeral — history and rules — Encyclopaedia Britannica
- Roman numerals — MacTutor History of Mathematics Archive, University of St Andrews
Figures last checked .
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