Roman numerals build every number from seven fixed symbols: I=1, V=5, X=10, L=50, C=100, D=500, M=1000. Two rules combine these symbols into any value from 1 to 3,999.
**The addition rule.** Symbols of equal or decreasing value, written left to right, are added together. VI = 5+1 = 6. XVI = 10+5+1 = 16. LXVI = 50+10+5+1 = 66. Notice each symbol's value is equal to or smaller than the one before it — that's what signals "add."
**The subtraction rule.** A smaller-value symbol placed immediately *before* a larger one is subtracted rather than added. This exists specifically to avoid writing four of the same symbol in a row. Rather than IIII for 4, standard notation uses IV (5−1=4). Rather than VIIII for 9, it uses IX (10−1=9).
**The subtraction rule only applies to six specific pairs — memorize these, not a general principle:** IV (4), IX (9), XL (40), XC (90), CD (400), CM (900). No other smaller-before-larger combination is valid; you can't write IL for 49 by subtracting 1 from 50 across two symbol tiers — the correct form is XLIX (40+9).
**Writing a number: the greedy method.** Work from the largest value down. At each step, take the biggest single symbol or subtractive pair that fits without exceeding what's left, subtract it from your remaining total, and repeat.
**Worked example: write 1,994 in Roman numerals.** Largest fitting value: M (1000), remaining 994. Next: CM (900, since 994 ≥ 900), remaining 94. Next: XC (90), remaining 4. Next: IV (4), remaining 0. Combined: M + CM + XC + IV = MCMXCIV.
**Worked example: write 358 in Roman numerals.** Largest fitting: C×3 = CCC (300), remaining 58. Next: L (50), remaining 8. Next: V (5), remaining 3. Next: III (3), remaining 0. Combined: CCC + L + V + III = CCCLVIII.
**Why the same symbol never repeats more than three times in a row.** Repeating a symbol a fourth time in a row is exactly the situation the subtractive pairs exist to avoid — that's why 4 is IV, not IIII, and why 40 is XL, not XXXX. Three repeats (III, XXX, CCC) is the maximum for any single symbol under standard rules.
**The historical note worth knowing honestly:** the strict subtractive-notation rules taught today weren't applied with total consistency by the Romans themselves — inscriptions and clock faces from various periods show both additive forms (IIII appears on many clock faces, quite possibly for visual balance with VIII across the dial, or reflecting earlier convention) and subtractive forms coexisting. The standardized rule set in this guide reflects the convention taught in modern math education and used in essentially all contemporary contexts, which is what this site's Roman numeral pages and converter follow consistently.
**The upper limit.** Standard Roman numerals top out at 3,999 (MMMCMXCIX), because there's no standard single-symbol way to represent 5,000 or above within the basic seven-symbol system. Historically, a horizontal line (vinculum) over a symbol multiplied its value by 1,000 for larger numbers, but this notation is rare in modern use.
**Common mistakes.** Writing four of the same symbol in a row (IIII instead of IV) is the most frequent, usually from applying only the addition rule and forgetting the subtractive pairs exist. A second common mistake is misapplying subtraction across too wide a value gap — trying IC for 99 (which isn't standard; the correct form is XCIX: 90+9) — the subtraction rule only pairs symbols from directly adjacent value tiers, not distant ones.
**Worked example: write 2,026 in Roman numerals.** Largest fitting: M×2=MM (2000), remaining 26. Next: XX (20), remaining 6. Next: V (5), remaining 1. Next: I (1), remaining 0. Combined: MM+XX+V+I = MMXXVI.
**Worked example: write 3,999 in Roman numerals — the largest standard value.** Largest fitting: M×3=MMM (3000), remaining 999. Next: CM (900), remaining 99. Next: XC (90), remaining 9. Next: IX (9), remaining 0. Combined: MMM+CM+XC+IX = MMMCMXCIX. Notice this uses three of the six subtractive pairs (CM, XC, IX) in a single numeral — the densest a standard Roman numeral ever gets, since 3,999 sits one short of the conventional upper limit.
**Practice recognizing subtractive pairs at a glance, since this speeds up both reading and writing considerably.** IV=4, IX=9, XL=40, XC=90, CD=400, CM=900 — these six pairs are worth committing to memory as fixed units rather than re-deriving the subtraction each time you encounter them, the same way multiplication facts get memorized rather than recalculated.
**Worked example: write 444, a number requiring three different subtractive pairs from three different value tiers.** Largest fitting: CD (400), remaining 44. Next: XL (40), remaining 4. Next: IV (4), remaining 0. Combined: CD+XL+IV = CDXLIV — notably, no addition-rule symbols appear at all in this particular numeral, built entirely from subtractive pairs.
**Worked example: write 88 in Roman numerals, a value using several repeated symbols without any subtraction at all.** Largest fitting: L (50), remaining 38. Next: X×3=XXX (30), remaining 8. Next: V (5), remaining 3. Next: III (3), remaining 0. Combined: L+XXX+V+III = LXXXVIII — eight symbols total, the longest a two-digit number's standard numeral ever gets, since 88 needs no subtractive shortcuts anywhere in its construction.
**Worked example: write 1,776 in Roman numerals, a historically resonant year.** Largest fitting: M (1000), remaining 776. Next: D (500), remaining 276. Next: CC (200), remaining 76. Next: L (50), remaining 26. Next: X×2=XX (20), remaining 6. Next: V (5), remaining 1. Next: I (1), remaining 0. Combined: M+D+CC+L+XX+V+I = MDCCLXXVI.
**A quick sanity check worth running on any Roman numeral you write: no more than three of the same symbol in a row, ever.** If your result contains IIII, XXXX, or CCCC anywhere, that's an immediate signal a subtractive pair was missed somewhere in the process — go back and check whether that section should have used IV, XL, or CD instead.
For converting the other direction — reading an existing Roman numeral back into its Arabic value — see the companion guide, How to Convert Roman Numerals to Numbers.