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All About Numbers

Roman Numeral Rules

Knowing the seven symbols is only half the story — the real skill is combining them correctly. Roman numerals follow just two rules working together, and once you know them, you can build (or read) any number from 1 to 3,999 without memorising a single extra symbol.

In the earliest Roman inscriptions, numbers were often written by addition alone — 4 appeared as IIII, not IV. Over the centuries, scribes and stonemasons increasingly used a shorter subtractive style for numbers like 4, 9, 40 and 90, and by the late medieval period that shorthand had become the standard most people are taught today. The older additive style never fully disappeared, though — you’ll still spot IIII instead of IV on plenty of traditional clock faces, which we’ll come back to later in this section.

Rule 1: The Additive Rule

When a symbol is followed by one of equal or smaller value, simply add the values together, reading left to right.

NumeralBreakdownValue
II1 + 12
VI5 + 16
VIII5 + 1 + 1 + 18
XV10 + 515
XXX10 + 10 + 1030
LX50 + 1060
CX100 + 10110
DCC500 + 100 + 100700

Rule 2: The Subtractive Rule

When a smaller symbol comes immediately before a larger one, subtract the smaller from the larger instead of adding it.

This shorthand isn’t a free-for-all — there are exactly six valid subtractive pairs in the entire system, and no others exist:

PairCalculationValue
IV5 − 14
IX10 − 19
XL50 − 1040
XC100 − 1090
CD500 − 100400
CM1000 − 100900

Notice the pattern: it’s always one of the “repeatable” symbols (I, X, C) placed directly before the next two symbols above it.

The precedence rule: a symbol may only be subtracted from the two symbols immediately above it in value — never any further.
  • I may only come before V or X (never L, C, D or M).
  • X may only come before L or C (never D or M).
  • C may only come before D or M.
  • V, L and D are never subtracted — they never appear before a larger symbol.

Step by Step: Writing a Number as a Roman Numeral

Combining both rules together is easiest if you break the number into its place-value parts first — thousands, hundreds, tens, ones — convert each part on its own, then write the parts down in order from largest to smallest.

  1. Split the number into thousands, hundreds, tens and ones, just like expanded form (e.g. 246 = 200 + 40 + 6).
  2. Convert each part separately, using the additive or subtractive rule as needed for that part alone.
  3. Join the parts together, largest first.
Example 1 — Write 246 as a Roman numeral

Split: 246 = 200 + 40 + 6.

200 = CC  |  40 = XL (subtractive: 50−10)  |  6 = VI (additive: 5+1)

Join largest to smallest: CCXLVI

Example 2 — Write 749 as a Roman numeral

Split: 749 = 700 + 40 + 9.

700 = DCC  |  40 = XL  |  9 = IX (subtractive: 10−1)

Join: DCCXLIX

Example 3 — Write 1994 as a Roman numeral

Split: 1994 = 1000 + 900 + 90 + 4.

1000 = M  |  900 = CM (1000−100)  |  90 = XC (100−10)  |  4 = IV (5−1)

Join: MCMXCIV

Step by Step: Reading a Roman Numeral

Going the other way works the same way in reverse — scan the numeral and pull out recognisable chunks (a subtractive pair, or a run of repeated symbols), find the value of each chunk, then add the chunks together.

Example — Read DCCLXXVII

Split into chunks: D | CC | LXX | VII

D = 500  |  CC = 200  |  LXX = 70  |  VII = 7

Add: 500 + 200 + 70 + 7 = 777

Example — Read MCMXCIV

Split into chunks: M | CM | XC | IV

M = 1000  |  CM = 900  |  XC = 90  |  IV = 4

Add: 1000 + 900 + 90 + 4 = 1994

Key Points
  • Additive rule: equal-or-smaller symbols after a larger one are added (VI = 6).
  • Subtractive rule: a smaller symbol immediately before a larger one is subtracted — but only for six specific pairs: IV, IX, XL, XC, CD, CM.
  • A symbol can only be subtracted from the two symbols directly above it in value (I from V/X, X from L/C, C from D/M).
  • To write a number, split it into thousands/hundreds/tens/ones, convert each part, then join largest to smallest.
  • To read a numeral, split it into chunks (subtractive pairs or repeated runs), find each chunk’s value, then add.

Practice: Roman Numeral Rules

Apply the additive or subtractive rule to find a value.