# The rules of roman numerals

# The rules of roman numerals

There are six basic rules when it comes to roman numerals. Stick to these rules and you'll be writing perfect numerals in no time.

If in doubt, use our numeral converter. If you make a mistake, our numeral converter will tell you where you made the mistake and provide you with the correct solution too! If you want to quickly convert a number to numerals, use our number converter.

## Rule 1: The numerals

**All roman numerals are written using a combination of base numerals and subtractive numerals.**

There are only seven base numerals which can be used to create any numeral sequence or number representation:

Number | Numeral | Words |
---|---|---|

1 | I | one |

5 | V | five |

10 | X | ten |

50 | L | fifty |

100 | C | one hundred |

500 | D | five hundred |

1000 | M | one thousand |

Utilising the base numerals, there are also six subtractive numerals which act as shortcuts to represent numerals which would otherwise require four or five individual numerals:

Number | Numeral | Words |
---|---|---|

4 | IV | four |

9 | IX | nine |

40 | XL | forty |

90 | XC | ninety |

400 | CD | four hundred |

900 | CM | nine hundred |

Combining the base numerals and the subtractive numerals, this gives a total of 13 individual numerals which can be used in combination in any sequence.

Number | Numeral | Words |
---|---|---|

1 | I | one |

4 | IV | four |

5 | V | five |

9 | IX | nine |

10 | X | ten |

40 | XL | forty |

50 | L | fifty |

90 | XC | ninety |

100 | C | one hundred |

400 | CD | four hundred |

500 | D | five hundred |

900 | CM | nine hundred |

1000 | M | one thousand |

## Rule 2: The calculation

**The value of a roman numeral sequence is calculated by simply adding together the numerals, from left to right.**

Be careful though! Remember to look out for (and utilise when appropriate) subtractive numerals.

For example, the number 1988 converted to roman numerals is MCMLXXXVIII which is calculated from left-to-right as:

## Rule 3: Number limits

**Any sequence of standard roman numerals can only represent numbers from 1 to 3999.**

There is no zero in roman numerals.

Using bracket notation or vinculum notation we can write roman numerals from 4000 to 3999999.

## Rule 4: Sequencing

**Roman numerals are written from left to right, and from highest to lowest (in terms of individual numeral value).**

A higher value numeral cannot appear after a lower value numeral (unless in the context of an individual subtractive numeral).

## Rule 5: Repetition

**An individual numeral cannot appear more than three times consecutively in any sequence.**

If you find yourself with four same-value numerals consecutively, it can always be simplified by using a subtractive numeral in its place.

A special case for this simplification rule is four M's. This exceeds the 3999 limit and would be invalid unless vinculum notation or bracket notation were adopted. Using bracket notation, four M's becomes (IV).

## Rule 6: Single use numerals

**There are individual numerals which can only appear once in any sequence.**

All subtractive numerals can only appear once in any sequence.

From the set of base numerals: V, L, and D should only appear once.

The only caveat to this is when using another notation such as bracket notation. A single-use numeral can appear once within the brackets and once outside the brackets. For example, 5005 in bracket notation is (V)V.

Number | Numeral | Words |
---|---|---|

4 | IV | four |

5 | V | five |

9 | IX | nine |

40 | XL | forty |

50 | L | fifty |

90 | XC | ninety |

400 | CD | four hundred |

500 | D | five hundred |

900 | CM | nine hundred |