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.
| Numeral | Breakdown | Value |
|---|---|---|
| II | 1 + 1 | 2 |
| VI | 5 + 1 | 6 |
| VIII | 5 + 1 + 1 + 1 | 8 |
| XV | 10 + 5 | 15 |
| XXX | 10 + 10 + 10 | 30 |
| LX | 50 + 10 | 60 |
| CX | 100 + 10 | 110 |
| DCC | 500 + 100 + 100 | 700 |
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:
| Pair | Calculation | Value |
|---|---|---|
| IV | 5 − 1 | 4 |
| IX | 10 − 1 | 9 |
| XL | 50 − 10 | 40 |
| XC | 100 − 10 | 90 |
| CD | 500 − 100 | 400 |
| CM | 1000 − 100 | 900 |
Notice the pattern: it’s always one of the “repeatable” symbols (I, X, C) placed directly before the next two symbols above it.
- 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.
- Split the number into thousands, hundreds, tens and ones, just like expanded form (e.g. 246 = 200 + 40 + 6).
- Convert each part separately, using the additive or subtractive rule as needed for that part alone.
- Join the parts together, largest first.
Split: 246 = 200 + 40 + 6.
200 = CC | 40 = XL (subtractive: 50−10) | 6 = VI (additive: 5+1)
Join largest to smallest: CCXLVI
Split: 749 = 700 + 40 + 9.
700 = DCC | 40 = XL | 9 = IX (subtractive: 10−1)
Join: DCCXLIX
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.
Split into chunks: D | CC | LXX | VII
D = 500 | CC = 200 | LXX = 70 | VII = 7
Add: 500 + 200 + 70 + 7 = 777
Split into chunks: M | CM | XC | IV
M = 1000 | CM = 900 | XC = 90 | IV = 4
Add: 1000 + 900 + 90 + 4 = 1994
- 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.