This calculator converts in both directions: type a number and get its Roman numeral form, or type a Roman numeral and get its Arabic-number value. Both directions use the same underlying rules — seven fixed symbols (I=1, V=5, X=10, L=50, C=100, D=500, M=1000) combined by an addition rule (equal-or-decreasing values left to right are summed) and a subtraction rule (a smaller symbol immediately before a larger one is subtracted, limited to exactly six pairs: IV, IX, XL, XC, CD, CM).
Converting Arabic to Roman works greedily from the largest value down: take the biggest symbol or subtractive pair that fits without going over, subtract it, and repeat with what's left. For 2,024: the largest fitting chunk is M×2 = 2000 (MM), leaving 24; then XX (20), leaving 4; then IV (4). Combined: MMXXIV.
Converting Roman to Arabic works left to right, comparing each symbol to the one after it: if a symbol's value is less than the next symbol's value, subtract it; otherwise, add it. For MCMXCIV: M(1000) is followed by a smaller-valued C, so add 1000. C(100) is followed by a larger M, so subtract 100. M(1000) is followed by a smaller X, so add 1000. X(10) is followed by a larger C, so subtract 10. C(100) is followed by a larger... wait — reading it correctly symbol by symbol (M, C, M, X, C, I, V): M is followed by C (smaller) → add 1000; C is followed by M (larger) → subtract 100; M is followed by X (smaller) → add 1000; X is followed by C (larger) → subtract 10; C is followed by I (smaller) → add 100; I is followed by V (larger) → subtract 1; V is the last symbol → add 5. Total: 1000 − 100 + 1000 − 10 + 100 − 1 + 5 = 1994.
This calculator also validates canonical form on the Roman-to-Arabic side: a numeral like IIII or VV isn't standard notation (the correct forms are IV and X respectively), so a non-canonical input is flagged rather than silently accepted, since there's exactly one correct standard way to write any number from 1 to 3,999 in Roman numerals.
The standard range is 1 to 3,999 (MMMCMXCIX), because the basic seven-symbol system has no standard way to represent 5,000 or above without extending the notation (historically, a horizontal line over a symbol multiplied its value by 1,000, but that convention is rare in modern use).
A second worked example in the Arabic-to-Roman direction, chosen specifically because it uses several subtractive pairs in a row: convert 944. Largest fitting chunk under M is CM (900), leaving 44; next is XL (40), leaving 4; next is IV (4). Combined: CMXLIV. Note there's no D (500) in this numeral at all — 944 is closer to 1000 than to 500, so the greedy method correctly skips straight to the CM subtractive pair rather than using D plus a pile of C's.
A common mistake when converting by hand is applying the subtraction rule too liberally — treating any smaller-before-larger pair as valid subtraction, when only six specific pairs are allowed. IL is not a valid way to write 49 (the correct form is XLIX: 40 + 9); the subtraction rule only works one "step" at a time between adjacent value tiers, not across two tiers at once. Roman numerals also appear regularly in contexts most people encounter without necessarily reading them as numbers at all — Super Bowl numbering (Super Bowl LVIII = 58), the copyright years quietly listed at the end of film credits, monarch and pope ordinal numbers (Elizabeth II, John Paul II), and outline or appendix numbering in formal documents. In each of these everyday contexts the numeral is almost always in the standard 1-3,999 canonical form covered by this calculator, which is part of why validating canonical form (rather than just any symbol combination that happens to add up correctly) matters for a tool meant to be practically useful rather than purely academic.
For the full rule set worked through step by step, see How to Read and Write Roman Numerals and How to Convert Roman Numerals to Numbers.