Roman Numerals: Chart, Rules, History And Modern Uses

What Are Roman Numerals?

Roman numerals are letters used as numbers. The Romans built every number from a small set of symbols with fixed values.

The system has no place value. In our usual Hindu-Arabic numbers, the 2 in 200 means something different from the 2 in 20 because of its position. In Roman numerals, X always means 10, wherever it sits. Its position only tells you whether to add it or subtract it.

The 7 Roman Numeral Symbols

Every Roman numeral uses just these seven letters.

A popular memory line, in order from I to M, is: I Value Xylophones Like Cows Do Milk.

How Roman Numerals Work: The 4 Rules

Roman numerals follow four simple rules. Once you know them, you can read and write any number from 1 to 3,999.

Rule 1: Add When Values Go Down Or Stay The Same

When symbols go from largest to smallest, left to right, you add them.

• VI = 5 + 1 = 6
• XV = 10 + 5 = 15
• CLX = 100 + 50 + 10 = 160

Rule 2: Subtract When A Smaller Symbol Comes First

When a smaller symbol sits just before a larger one, you subtract it.

• IV = 5 – 1 = 4
• IX = 10 – 1 = 9
• XL = 50 – 10 = 40
• XC = 100 – 10 = 90
• CD = 500 – 100 = 400
• CM = 1,000 – 100 = 900

Only these six pairs are standard. I goes only before V or X, X only before L or C, and C only before D or M. V, L and D never subtract.

Rule 3: Repeat A Symbol No More Than Three Times

I, X, C and M can repeat up to three times in a row: III = 3, XXX = 30, CCC = 300, MMM = 3,000. For 4, you write IV, not IIII.

V, L and D never repeat. You write X, not VV, for 10.

Rule 4: Build Big Numbers One Place At A Time

To write a large number, split it into thousands, hundreds, tens and ones. Then write each part and join them.

Example: 1984

1. 1,000 = M
2. 900 = CM
3. 80 = LXXX
4. 4 = IV
5. Put it together: MCMLXXXIV

How To Read A Roman Numeral

To read a Roman numeral, go left to right. If a symbol is smaller than the one after it, subtract it. Otherwise, add it.

Example: XLIX

• X (10) is smaller than L (50), so subtract: -10
• L = +50
• I (1) is smaller than X (10), so subtract: -1
• X = +10
• Total: -10 + 50 – 1 + 10 = 49

Roman Numerals Chart: 1 To 100

The chart below shows 1 to 20, then counts by tens to 100. Any number in between is just a tens part plus a ones part. For example, 37 = XXX + VII = XXXVII.

Writing Numbers Above 3,999

Standard Roman numerals stop at 3,999 (MMMCMXCIX) because M cannot repeat a fourth time. For bigger numbers, a line called a vinculum is drawn over a numeral. The bar multiplies its value by 1,000.

So 4,000 can be written as IV with a bar over both letters. Some old sources also wrote 4,000 as MMMM, which breaks the three-in-a-row rule but was used in practice.

For truly huge values, modern math uses scientific notation, which depends on the place value the Romans lacked.

How To Write Dates In Roman Numerals

To write a date, convert the month, day and year separately, then join them with dots, dashes or slashes.

Example: July 4, 1776

• Month: 7 = VII
• Day: 4 = IV
• Year: 1776 = MDCCLXXVI
• US order (month.day.year): VII.IV.MDCCLXXVI

Check the order before using a date on a tattoo or ring. Americans write month first, but many countries put the day first, so VII.IV could be read as April 7.

The History Of Roman Numerals

Roman numerals grew out of numerals used by the Etruscans, a people of central Italy, and spread across Europe with the Roman Empire. They stayed Europe's main way to write numbers for well over 1,000 years.

Etruscan Roots

According to Britannica's history of Roman numerals, the Romans adopted their numerals from the Etruscans beginning around the 5th century BCE. The Etruscans wrote right to left, while the Romans wrote left to right.

The Roman I, V and X looked much like the Etruscan forms. The Etruscan sign for 100 looked a bit like an asterisk, and the Roman C likely grew out of it. L, D and M took their final shapes later, starting around the 1st century BCE. M did not become the standard sign for 1,000 until the Middle Ages.

IIII Or IV? The Romans Used Both

The Romans were not as strict as today's rules. They wrote both IIII and IV for 4, and inscriptions often preferred the longer, additive form.

That habit lives on in clocks: most Roman numeral dials still show IIII for 4. Many say it balances the VIII opposite, but no one knows for sure.

Fractions Without Decimals

The Romans had no decimal point. They handled fractions with a system based on twelfths. One twelfth was called an uncia, which gave English the words "ounce" and "inch." Half was written with S, for semis.

Twelfths suited trade because 12 splits evenly into halves, thirds, quarters and sixths. Today you can work with fractions or reduce a fraction to lowest terms without any of that.

Why Europe Switched To Hindu-Arabic Numbers

Roman numerals were fine for recording numbers but slow for math. Merchants did the real work on counting boards and the abacus.

The change came slowly:

The winning features were place value and zero, which made adding columns and carrying digits quick for anyone.

Where You See Roman Numerals Today

Roman numerals survive mostly as a style choice because they look formal and timeless.

Common Mistakes To Avoid

Most errors come from breaking the subtraction rule or skipping place values.

Summary

Roman numerals use seven symbols (I, V, X, L, C, D, M) that you add or subtract based on their order. Learn the six subtraction pairs, never repeat a symbol more than three times, and build big numbers one place at a time.

The system grew from Etruscan signs, ruled European writing for centuries, then gave way to Hindu-Arabic numbers. Today it lives on in clocks, royal names and Super Bowls.

Next step: write your birth year in Roman numerals, then read it back to check. For everyday number work, try the free math tools on the Calc Solver homepage.

Frequently Asked Questions