How to Read Roman Numerals

For example:

XIV = X + IV
XIV = 10 + 4
XIV = 14

The important point is that IV is read as one accepted pair representing 4. It is not treated as two separate values that are simply added together.

Key takeaways

• Roman numerals use the symbols I, V, X, L, C, D and M.
• Most values are read by adding symbols or groups from left to right.
• Six standard subtractive pairs represent 4, 9, 40, 90, 400 and 900.
• A long Roman numeral becomes easier when it is split into meaningful groups.
• The final result can be checked by converting the number back into Roman numerals.

Roman numeral values

The seven standard symbols have fixed decimal values:

You do not need to memorise every complete Roman numeral. Once the seven symbols are familiar, longer numerals can be separated into smaller groups.

For example:

VIII contains V + I + I + I.
LXX contains L + X + X.
MM contains M + M.

The Roman Numeral Symbols and Their Values guide explains the symbol system in more detail. This article focuses on turning a complete Roman numeral into an ordinary number.

The six subtractive pairs

Most Roman numeral values are added. Standard modern notation also uses six accepted subtractive pairs:

Read each pair as one value.

Examples:

IV = 4
IX = 9
XL = 40
CM = 900

This makes a numeral such as XCIV easier to understand:

XCIV = XC + IV
XCIV = 90 + 4
XCIV = 94

Do not assume that every smaller symbol before a larger symbol must be subtracted. Standard notation uses only recognised arrangements. The complete restrictions are covered in the later rules and subtractive-notation guides.

How to read a Roman numeral

Step 1 — identify the symbols and accepted pairs

Read the numeral from left to right.

First, identify any of the six accepted subtractive pairs. Then recognise the remaining symbols or repeated groups.

For MCMLXXXII:

M | CM | LXXX | II

The groups are:

M = 1,000
CM = 900
LXXX = 80
II = 2

For XLII:

XL | II

The groups are:

XL = 40
II = 2

The aim is not to split every character apart. It is to recognise complete value groups.

Step 2 — split the numeral into meaningful groups

A useful group may be:

• one symbol, such as M;
• repeated symbols, such as XXX;
• an additive group, such as VIII;
• one of the six subtractive pairs, such as CM.

Examples:

XIV → X + IV
XLII → XL + II
XCIV → XC + IV
CMXLIV → CM + XL + IV
MCMLXXXII → M + CM + LXXX + II

Standard Roman numerals usually move from larger values to smaller values, except where an accepted subtractive pair appears.

For example:

LXXX = L + X + X + X
LXXX = 50 + 10 + 10 + 10
LXXX = 80

Once the groups are clear, the final calculation is straightforward.

Step 3 — add the group values

Add the decimal value of each group.

Using MCMLXXXII:

MCMLXXXII = M + CM + LXXX + II
MCMLXXXII = 1,000 + 900 + 80 + 2
MCMLXXXII = 1,982

Using CMXLIV:

CMXLIV = CM + XL + IV
CMXLIV = 900 + 40 + 4
CMXLIV = 944

Using MMXXVI:

MMXXVI = MM + XX + VI
MMXXVI = 2,000 + 20 + 6
MMXXVI = 2,026

A concise way to remember the method is:

Recognise a group → assign its value → move right → add the total

Worked examples

VIII represents 8

VIII contains no subtractive pair.

VIII = V + I + I + I
VIII = 5 + 1 + 1 + 1
VIII = 8

XIV represents 14

XIV contains the subtractive pair IV.

XIV = X + IV
XIV = 10 + 4
XIV = 14

XCIV represents 94

XCIV contains two subtractive pairs.

XCIV = XC + IV
XCIV = 90 + 4
XCIV = 94

MCMLXXXII represents 1,982

MCMLXXXII combines thousands, hundreds, tens and units.

MCMLXXXII = M + CM + LXXX + II
MCMLXXXII = 1,000 + 900 + 80 + 2
MCMLXXXII = 1,982

MMXXVI represents 2,026

MMXXVI uses addition throughout.

MMXXVI = MM + XX + VI
MMXXVI = 2,000 + 20 + 6
MMXXVI = 2,026

These examples show the same method working for short, long, additive and subtractive numerals.

How to check your answer

A reliable check is to reverse the conversion.

Suppose you read XLIV as 44:

XLIV = XL + IV
XLIV = 40 + 4
XLIV = 44

Now convert 44 back into Roman numerals:

44 = 40 + 4
44 = XL + IV
44 = XLIV

The result matches the original numeral, so the round-trip check succeeds.

The Roman numeral converter can perform the same check. Enter the numeral, confirm its decimal value and compare the standard Roman output with the original form.

When a Roman numeral may not be standard

A string can contain Roman numeral symbols without being a valid standard Roman numeral.

Examples include:

IIII
IC
VX

When a form looks unusual:

1. Check whether it contains only I, V, X, L, C, D and M.
2. Check whether any apparent subtraction is one of the six accepted pairs.
3. Convert the apparent value back into standard Roman numeral form.
4. Compare the standard result with the original input.

This check helps distinguish a recognisable value from the standard modern form without assuming that every arrangement of Roman numeral symbols is valid.

Continue learning

After learning how to read Roman numerals, continue with:

• How to Write Roman Numerals
• Roman Numeral Rules
• Additive Notation in Roman Numerals
• Subtractive Notation in Roman Numerals