Read

Identifying the Value of a Roman Numeral

This lesson teaches how to identify the value of a Roman numeral by learning the seven basic symbols, the addition rule, and the subtraction rule, then practicing with a full chart and step by step examples covering numerals from 1 to 100.

Introduction

Long before the number system you use every day existed, people in ancient Rome recorded amounts using letters instead of digits. That system is still around today on clocks, in movie credits, and in outlines, so being able to read it, that is, identifying the value of a Roman numeral, is a useful number skill. This lesson breaks the system down into two simple rules so you can turn any short string of letters into the number it represents.

The seven basic symbols

Every Roman numeral is built from just seven letters. Each letter always stands for the same fixed value, no matter where it appears.

Roman numerals 1 to 10

The most common numerals you will meet are the ones from 1 to 10. Reading this short list first makes every bigger numeral easier to figure out:

I = 1, II = 2, III = 3, IV = 4, V = 5, VI = 6, VII = 7, VIII = 8, IX = 9, X = 10.

Notice that III repeats the symbol I three times, which is the most any symbol is normally repeated in a row. IV and IX look different because they use a smaller symbol placed in front of a bigger one, which leads to the second rule below.

Rule 1: the addition rule

When a smaller (or equal) symbol comes after a bigger symbol, add the values together. This is the rule you use most of the time. For example, in VII the symbols are read left to right as \( 5 + 1 + 1 = 7 \). In XVI, you get \( 10 + 5 + 1 = 16 \).

Rule 2: the subtraction rule

When a smaller symbol is placed immediately before a bigger symbol, subtract the small value from the big one instead of adding it. Only one smaller symbol can be placed this way, and only certain pairs are allowed: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900). For example, IX is read as \( 10 - 1 = 9 \), not \( 10 + 1 \).

Worked example: reading a mixed numeral

Find the value of XXIV.

Split the numeral into chunks you recognize: XX and IV. XX uses the addition rule, so \( 10 + 10 = 20 \). IV uses the subtraction rule, so \( 5 - 1 = 4 \). Add the chunks together: \( 20 + 4 = 24 \). So XXIV represents 24.

Worked example: building up to 100 in Roman numerals

Find the value of LXXXVIII.

Break it into chunks: L, XXX, and VIII. L is worth 50. XXX is three tens added together, \( 10 + 10 + 10 = 30 \). VIII is \( 5 + 1 + 1 + 1 = 8 \). Adding all three chunks gives \( 50 + 30 + 8 = 88 \).

Since C stands for exactly 100, the number 100 in Roman numerals is simply C. Anything just under it, like 90, uses the subtraction rule as XC, since \( 100 - 10 = 90 \).

Putting it all together

To identify the value of any Roman numeral, work from left to right, group the letters into small chunks, decide whether each chunk uses the addition rule or the subtraction rule, and add the chunk values together. This same left-to-right, chunk-by-chunk thinking is closely related to how you read place value in ordinary numbers, so skills like counting values in a number grid up to 100 and finding missing values in a number grid up to 100 make a great companion practice alongside Roman numerals. Noticing patterns as symbols repeat also connects nicely with number sequences with 1, 2, 3, 5, 10.

Related lessons

Math 1