All Roman numerals were formed by using a combination of seven basic symbols, each representing a specific numeric value:

Roman Symbol | Name | Arabic Value | Derivation of Roman Figure |
---|---|---|---|

I | unus | 1 | A single digit. |

V | quinque | 5 | Graphic representation of five fingers. |

X | decem | 10 | Symbolises two hands joined together. |

L | quinquaginta | 50 | Adapted from a Chalcidic sign. |

C | centum | 100 | The first letter of the Roman word for one-hundred. |

D | quingenti | 500 | One half of the Chalcidic sign for one-thousand; . |

M | mille | 1,000 | The first letter of the Roman word for one-thousand. |

To express numbers which were multiples of the seven standard values, the symbols could simply be duplicated;

II | = 2 | 'two digits' |

XXX | = 30 | 'three tens' |

CC | = 200 | 'two hundreds' |

**Note** that the Roman symbols V, L and D are **not**
duplicated, as their combined values can be expressed by other symbols;
e.g. VV = 10 = X. Also, duplication was not carried beyond two or three
symbols in practice, fourfold duplication being quite rare. The figure
IIII = 4 was a common exception, though this and other instances were
more usually expressed by subordinate subtraction *vide infra*.

All numbers could be formed simply by listing down the appropriate number of required symbols, listing subordinate symbols to the right of those higher in value.

VIII | = 8 | 'a five and three digits' |

LXXV | = 75 | 'a fifty, two tens and a five' |

CLXVI | = 166 | 'one-hundred, a fifty, a ten, a five and one digit' |

Decimal numbers containing the digits 9 or 4, however, look decidedly dodgy when translated in this manner, for example 949 would be DCCCCXXXXVIIII, and 494 would be CCCCLXXXXIIII. The chances of making a mistake when copying down values using this annotation would be pretty high.

To avoid duplication mistakes, the Roman accountant also formed compound numerals by the process of subordinate subtraction. In this process subordinates symbols were placed prior to the higher symbol and their numeric value subtracted from that of the higher numeral;

IV | = 4 | 'one digit before five' |

XLIX | = 49 | 'ten before fifty and one digit before ten' |

CD | = 400 | 'one-hundred before five-hundred' |

**Note** that subordinate subtraction was **rarely**
performed with duplicated symbols. The numerals IIX and CCD are both
syntactically correct, but would more properly be represented by VIII
and CCC respectively.

I | = 5,000 | |

CI | = 10,000 | |

I | = 50,000 | |

CCI | = 100,000 | |

I | = 500,000 | |

CCCI | = 1,000,000 |

Numbers in the thousands were at first represented by the Romans with further adaptations of earlier Chalcidic signs. These adapted figures and their numeric values are listed on the right.

During the later Republic thousands were represented by a line inscribed above the appropriate numeral; e.g. I = 1,000 and V = 5,000. Hundreds of thousands were denoted by additional lines on each side of the numeral; e.g. |V| = 500,000 and |X| = 1,000,000 or a million, literally 'ten hundred-thousands'. The M symbol was not used to denote thousands until the second century AD.

A Roman number may employ any or all of the above processes to further complicate matters. To translate any Roman numeral one should first break the number down into separate processes; these breaks are indicated wherever a subordinate symbol follows one of higher value. Each part of the number may then be dealt with separately, and the results combined to give the final figure. These steps are indicated in the following examples;

CCXLVIII = | CC+XL+V+III 'two hundreds' (= 200), 'ten before fifty' (= 40), 'five and three digits' (= 8) | = 248 |

CDXXIX = | CD+XX+IX 'one-hundred before five-hundred' (= 400), 'two tens' (= 20), 'one digit before ten' (= 9) | = 429 |

MCDLXXIV = | M+CD+L+XX+IV 'one-thousand' (= 1,000), 'one-hundred before five-hundred' (= 400), 'fifty and two tens' (= 70) 'one digit before five' (= 4) | = 1,474 |

It is quite a complicated task to add two Roman numerals together or
even to subtract one from another, and multiplication and division are
both extremely difficult. Mental arithmetic using the Roman numeric
system would be beyond the capabilities of most mortal men. The dreary
toil of the Roman accountant is reflected in the Latin name for the
occupation, *Tabularius* 'the worker of tables'. The *tabularius*
was a highly skilled - and thus highly valued - member of any senators
household, though usually of the slave class, the lowest order of Roman
society, he would be well looked-after for his services. The Roman
accountant's task would be simplified to some extent by the use of an *abacus*, or by utilising a complicated system of counting using both the digits and finger joints of each hand.

Arabic | Roman | Cardinal¹ | Ordinal² | Adverbial³ |
---|---|---|---|---|

1 | I | unus | primus | semel |

2 | II | duo | secundus | bis |

3 | III | tres | tertius | ter |

4 | IV | quattuor | quartus | quater |

5 | V | quinque | quintus | quinquies |

6 | VI | sex | sextus | sexies |

7 | VII | septem | septimus | septies |

8 | VIII | octo | octavus | octies |

9 | IX | novem | nonus | novies |

10 | X | decem | decimus | decies |

11 | XI | undecim | undecimus | undecies |

12 | XII | duodecim | duodecimus | duodecies |

13 | XIII | tredecim | tertius decimus | ter decies |

14 | XIV | quattuordecim | quartus decimus | quattuordecies |

15 | XV | quindecim | quintus decimus | quindecies |

16 | XVI | sedecim | sextus decimus | sedecies |

17 | XVII | septendecim | septimus decimus | septies decies |

18 | XVIII | duodeviginti | duodevicesimus | duodevicies |

19 | XIX | undeviginti | undevicesimus | undevicies |

20 | XX | viginti | vicesimus | vicies |

- Cardinal numbers answer the question 'how many?': one, two, three, etc.
- Ordinal numbers answer the question 'in which order?': first, second, third, etc.
- Adverbial numbers state 'how many times?': once, twice, thrice (three times), etc.

*The main references used in the construction of this page were; The Collins Gem Latin Dictionary, and The Romans - An Introduction by Antony Kamm. Large amounts of coffee were also imbibed.*