How do Roman numerals work?

Seven letters are added together, or subtracted when a smaller one precedes a larger one.

Why is there no zero in Roman numerals?

The system is additive and predates the concept, so there's no symbol for nothing.

Roman Numerals Explained

Published 10/14/2025 · 2 min read · Everyday calculators

Lena Hoffmann — Science & education writer at Allin

Mathematics · Physics

Checked against 2 sources

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In short

Roman numerals use seven letters — I=1, V=5, X=10, L=50, C=100, D=500, M=1000 — combined by adding, or subtracting when a smaller letter comes before a larger one. So VI is 6 (5+1) and IV is 4 (5−1); 2024 is MMXXIV. Read left to right, adding, and treat the subtractive pairs (IV, IX, XL, XC, CD, CM) as single chunks.

Seven letters, added or subtracted. Here's what each stands for, how the subtractive pairs work, how to write any number, and where they still appear.

The seven letters

The whole system is built from seven letters: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1,000. Notice they alternate between ones and fives — 1, 5, 10, 50, 100, 500, 1,000 — which is why five of one unit rolls up into the next letter. Learn these seven and you already have everything you need; the rest is just rules for putting them together.

Adding and subtracting

Normally you add: when a letter is followed by one of equal or smaller value, you sum them, so VI is 5+1 = 6 and XV is 15. But to avoid four repeats in a row, a smaller letter placed before a larger one is subtracted: IV is 5−1 = 4, IX is 9, XL is 40, XC is 90, CD is 400 and CM is 900. Those six pairs are the only subtractive combinations allowed — you'll never see IL or IC.

Reading and writing a number

To write a number, break it into thousands, hundreds, tens and units and convert each part, then string them together largest first. Take 2,024: 2,000 is MM, 0 hundreds add nothing, 20 is XX, and 4 is IV — so 2,024 is MMXXIV. Reading works the reverse way: scan left to right, add each letter, but subtract whenever a smaller one sits before a bigger one. Work in place-value chunks and even long years stay manageable.

Where you still see them

Though no one calculates with them anymore, Roman numerals survive as decoration and numbering: clock faces, book chapters and volumes, the copyright year at the end of films, the names of monarchs and popes (Louis XIV, Elizabeth II), and event editions like the Super Bowl. Two quirks explain why they vanished from maths: there is no symbol for zero, and no way to write fractions — which makes arithmetic clumsy compared with our decimal digits.

Roman numeral converterConvert numbers to Roman numerals and back, one per line. Only the strict subtractive form counts: IIII, VV and IM are rejected, and the range is 1–3999.Try the tool →

Frequently asked questions

How do Roman numerals work?: Seven letters are added together, or subtracted when a smaller one precedes a larger one.
What is 2024 in Roman numerals?: MMXXIV.
Why is there no zero in Roman numerals?: The system is additive and predates the concept, so there's no symbol for nothing.

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