Math Tables
Roman Numeral Table
Roman numerals are an additive system with one refinement. Seven symbols carry the values 1, 5, 10, 50, 100, 500 and 1,000, and you write a number by repeating and adding them from largest to smallest. That alone would turn 9 into VIIII, so a subtractive rule was added: a smaller symbol placed before a larger one is subtracted rather than added, giving IX.
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The subtraction rule is narrower than most people assume. Only I, X and C can be subtracted, and only from the two symbols immediately above them: I from V or X, X from L or C, C from D or M. V, L and D are never subtracted. That is why 45 is XLV and not VL, and why 99 is XCIX rather than IC.
The system has no zero and no place value, which is why arithmetic in it is genuinely hard rather than merely unfamiliar. Multiplying MCMXCIV by XLII requires an abacus or a conversion to something positional. Europe kept Roman numerals for inscriptions and dropped them for calculation as soon as Indian numerals arrived.
What survives is ceremonial: clock faces, copyright years, monarch numbering, Super Bowl numbering and the occasional building date. For all of these, the practical need is a lookup rather than a rule, which is what the tables below provide — including the values above 3,999 that the basic seven symbols cannot express.
The seven symbols and the six subtractive pairs
| Symbol | Value | Comes before | Why |
|---|---|---|---|
| I | 1 | V and X | IV is 4, IX is 9 |
| V | 5 | — | Never subtracted |
| X | 10 | L and C | XL is 40, XC is 90 |
| L | 50 | — | Never subtracted |
| C | 100 | D and M | CD is 400, CM is 900 |
| D | 500 | — | Never subtracted |
| M | 1,000 | — | Never subtracted |
Only I, X and C can be subtracted, and only from the two symbols above them. V, L and D are never subtracted, which is why 45 is XLV and not VL.
1 to 100 in one table
| Number | Roman | Number | Roman |
|---|---|---|---|
| 1 | I | 51 | LI |
| 2 | II | 52 | LII |
| 3 | III | 53 | LIII |
| 4 | IV | 54 | LIV |
| 5 | V | 55 | LV |
| 6 | VI | 56 | LVI |
| 7 | VII | 57 | LVII |
| 8 | VIII | 58 | LVIII |
| 9 | IX | 59 | LIX |
| 10 | X | 60 | LX |
| 11 | XI | 61 | LXI |
| 12 | XII | 62 | LXII |
| 13 | XIII | 63 | LXIII |
| 14 | XIV | 64 | LXIV |
| 15 | XV | 65 | LXV |
| 16 | XVI | 66 | LXVI |
| 17 | XVII | 67 | LXVII |
| 18 | XVIII | 68 | LXVIII |
| 19 | XIX | 69 | LXIX |
| 20 | XX | 70 | LXX |
| 21 | XXI | 71 | LXXI |
| 22 | XXII | 72 | LXXII |
| 23 | XXIII | 73 | LXXIII |
| 24 | XXIV | 74 | LXXIV |
| 25 | XXV | 75 | LXXV |
| 26 | XXVI | 76 | LXXVI |
| 27 | XXVII | 77 | LXXVII |
| 28 | XXVIII | 78 | LXXVIII |
| 29 | XXIX | 79 | LXXIX |
| 30 | XXX | 80 | LXXX |
| 31 | XXXI | 81 | LXXXI |
| 32 | XXXII | 82 | LXXXII |
| 33 | XXXIII | 83 | LXXXIII |
| 34 | XXXIV | 84 | LXXXIV |
| 35 | XXXV | 85 | LXXXV |
| 36 | XXXVI | 86 | LXXXVI |
| 37 | XXXVII | 87 | LXXXVII |
| 38 | XXXVIII | 88 | LXXXVIII |
| 39 | XXXIX | 89 | LXXXIX |
| 40 | XL | 90 | XC |
| 41 | XLI | 91 | XCI |
| 42 | XLII | 92 | XCII |
| 43 | XLIII | 93 | XCIII |
| 44 | XLIV | 94 | XCIV |
| 45 | XLV | 95 | XCV |
| 46 | XLVI | 96 | XCVI |
| 47 | XLVII | 97 | XCVII |
| 48 | XLVIII | 98 | XCVIII |
| 49 | XLIX | 99 | XCIX |
| 50 | L | 100 | C |
The pattern repeats every ten: 1 to 9 use I, V and X, 10 to 39 repeat it with X and L, 40 to 49 use XL, and 90 to 99 use XC.
Years that appear on buildings and documents
| Year | Roman | Characters |
|---|---|---|
| 1,066 | MLXVI | 5 |
| 1,215 | MCCXV | 5 |
| 1,492 | MCDXCII | 7 |
| 1,776 | MDCCLXXVI | 9 |
| 1,900 | MCM | 3 |
| 1,914 | MCMXIV | 6 |
| 1,945 | MCMXLV | 6 |
| 1,969 | MCMLXIX | 7 |
| 1,984 | MCMLXXXIV | 9 |
| 1,999 | MCMXCIX | 7 |
| 2,000 | MM | 2 |
| 2,024 | MMXXIV | 6 |
| 2,026 | MMXXVI | 6 |
| 2,050 | MML | 3 |
| 2,100 | MMC | 3 |
2026 is MMXXVI. Modern dates rarely use the subtractive forms because years above 1000 are mostly M followed by simple additions.
Values above 3,999
| Value | Written as | How it is marked |
|---|---|---|
| 4,000 | IV with a bar over both | The bar multiplies by 1,000 |
| 5,000 | V with a bar | The bar multiplies by 1,000 |
| 10,000 | X with a bar | The bar multiplies by 1,000 |
| 50,000 | L with a bar | The bar multiplies by 1,000 |
| 100,000 | C with a bar | The bar multiplies by 1,000 |
| 500,000 | D with a bar | The bar multiplies by 1,000 |
| 1,000,000 | M with a bar | The bar multiplies by 1,000 |
The overline convention is medieval and never had a single standard. Modern practice avoids it by writing large numbers in Arabic numerals.
How to Use These Tables
- Reading a copyright year: break it into thousands, hundreds, tens and units. MMXXVI is 2000 + 20 + 6, or 2026.
- Writing a year: 1984 is M + CM + LXXX + IV, which is MCMLXXXIV. Check that no symbol repeats more than three times in a row.
- Checking a suspicious numeral: if a V, L or D appears before a larger symbol, the numeral is wrong. VL is not a valid way to write 45.
- Clock faces: the traditional form uses IIII rather than IV for four, a convention that predates the subtractive rule and is still standard on clock dials.
- Values above 3,999: either use the overline convention or switch to Arabic numerals. Modern documents do the latter.
Common Questions
Why is 4 written IV and not IIII?
The subtractive form is the classical standard, but clock faces kept IIII for symmetry with VIII on the opposite side. Both appear in historical inscriptions; IV is correct in modern use.
What is the largest number Roman numerals can write?
3,999 with the seven basic symbols, which is MMMCMXCIX. Above that the overline convention multiplies by 1,000, but it was never standardised and modern practice avoids it.
Is there a Roman numeral for zero?
No. The system has no zero, which is one reason it was replaced for arithmetic. Medieval scribes sometimes wrote nulla, but that is a word, not a numeral.
Can a symbol repeat more than three times?
Not in standard form. I, X, C and M may repeat up to three times; V, L and D never repeat at all. MMMM for 4,000 appears in some inscriptions but is normally written with an overline instead.
How do I convert a Roman numeral back to a number?
Add the symbols left to right, but subtract any symbol that is smaller than the one after it. In MCMXCIV, the C before M subtracts 100, the X before C subtracts 10, and the I before V subtracts 1, giving 1994.
Why do some clocks show IIII instead of IV?
For visual balance: IIII mirrors VIII on the other side of the dial, and it avoids the V and X crowding. The convention is called the clockmaker's four and is centuries old.
More Math Tables
Sources
- ISO 8601 — date and time representation (numeral systems annex) — International Organization for Standardization
- The Unicode Standard — Number Forms block, Roman numerals — Unicode Consortium
- Encyclopaedia Britannica — Roman numerals, notation and history — Encyclopaedia Britannica
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