Sprint 8 Converter + Math
Decimal to Roman Numeral
Convert integer to Roman numeral.
Roman
X
How it works
Converting a decimal integer to a Roman numeral is a classic algorithm problem as well as a practical tool for anyone needing Roman numerals for clockfaces, outline numbering (Chapter I, II, III), copyright dates, or ceremonial inscriptions. The Decimal to Roman Numeral Converter handles all valid inputs from 1 to 3999 and explains the conversion step by step.
**Conversion algorithm** Use a greedy algorithm with the 13 value-symbol pairs in descending order: 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). For each pair, subtract the value and append the symbol as many times as possible (max 3 for M, C, X, I; max 1 for D, L, V, and subtractive pairs).
**Example: 1994** 1994 ≥ 1000 → M (994 left). 994 ≥ 900 → CM (94 left). 94 ≥ 90 → XC (4 left). 4 ≥ 4 → IV (0 left). Result: MCMXCIV.
**Year conversions cheat sheet** 2000 = MM. 2024 = MMXXIV. 1999 = MCMXCIX. 1776 = MDCCLXXVI. 1066 = MLXVI. 100 = C. 50 = L.
**Outline numbering** Academic outlines use Roman numerals for top-level headings (I, II, III, IV, V), capital letters for second level (A, B, C), Arabic numerals for third (1, 2, 3), and lowercase letters for fourth (a, b, c). The converter can generate a list of Roman numerals for any range — useful for creating outline templates.
**Super Bowl / Olympic numbering** Major events use Roman numerals to avoid confusion between editions. Super Bowl LVIII = 58th Super Bowl. The Olympic Games number Summer and Winter separately with Roman numerals.
Privacy: all conversion runs in the browser. No data is transmitted.
Frequently Asked Questions
- Break it into recognisable subtractive pairs working left to right: M = 1000; CM = 900 (C before M = 1000−100); XC = 90 (X before C = 100−10); IX = 9 (I before X = 10−1). Total: 1000 + 900 + 90 + 9 = 1999. The pattern MCMXCIX appears frequently as a 'challenging' Roman numeral; memorising it directly is useful since it was the year of many late-20th-century events. Similarly, MMXXIV (2024) = MM(2000) + XX(20) + IV(4).
- Key years: MCM = 1900 (century prefix for 1900s). MCMXLV = 1945; MCMLXIX = 1969; MCMXCIX = 1999; MM = 2000; MMXII = 2012 (London Olympics); MMXVI = 2016; MMXX = 2020; MMXXIV = 2024 (Paris Olympics). For film credits, spotting the production year: MCMXCVIII = 1998 (C=900, wait — actually CM=900 so MCMXCVIII: M=1000 + CM=900 + XC=90 + VIII=8 = 1998 ✓). The converter shows step-by-step working to help you read any year.
- Yes — the Romans had a fraction system based on twelfths (duodecimal), using the uncia (1/12, symbol: •), semuncia (1/24), and other symbols. The as (whole unit) was divided into 12 unciae: • = 1/12, •• = 2/12, ••• = 3/12 (triens), •••• = 4/12 (quadrans), ••••• = 5/12, S = 6/12 = ½ (semis), S• = 7/12, etc. These fractional symbols appear in Roman-era texts and inscriptions but are almost never used today. Modern use of Roman numerals is confined to integers.
- Roman numbers are a tallying system, not a positional system. Each symbol has a fixed value regardless of its position relative to others (except for the six subtractive combinations). Zero is needed in positional systems to hold place (distinguish 100 from 10 from 1). Since Roman numerals don't use position to change value, there's no conceptual need for a placeholder zero. The Roman word for nothing was 'nulla' — the phrase 'nulla' appears in Roman administrative texts when a count was zero, but it was a word, not a numeral symbol.