Decimal to Roman Numeral Converter

What the decimal to Roman numeral converter does

This turns an ordinary number into its Roman numeral. Type a number between 1 and 3999, press the button, and copy out the numeral.

Roman numerals are not a place-value system like ours, so they work by a different and rather charming logic: a handful of letters, each worth a fixed amount, combined by adding and occasionally subtracting. Once you see the pattern, you can read the clock face or the film credits without a second thought.

How to use it

1. Enter your number. Type a whole number from 1 to 3999, for example 1994.
2. Press Convert. The Roman numeral appears in the output box.
3. Click the result to copy it. Tap the output to send it to your clipboard.

Press Reset to clear both boxes.

The seven symbols

The whole system is built from just seven letters, each with a set value:

• I is 1
• V is 5
• X is 10
• L is 50
• C is 100
• D is 500
• M is 1000

Notice they come in a rhythm of ones and fives: 1 and 5, 10 and 50, 100 and 500, then 1000. That pattern is worth holding onto, because it is exactly what the subtraction rule below depends on.

Building a numeral from the top down

To write a number as a numeral, you work from the largest symbol downward. Take as many thousands as you can and write an M for each, then move to the hundreds, then the tens, then the ones, writing the right symbols at each step. You never write the same symbol more than three times in a row, though. The moment you would need a fourth, the subtraction rule takes over instead.

The fours and nines: subtraction

Since four of a symbol is not allowed, the Romans wrote a 4 as a 5 with a 1 taken off the front, and a 9 as a 10 with a 1 off the front. Putting a smaller symbol before a larger one means subtract it. So:

• 4 is IV, that is one less than five, and 9 is IX, one less than ten
• 40 is XL and 90 is XC
• 400 is CD and 900 is CM

These six pairs are the only subtractions you ever need. Everywhere else you simply add.

A worked example with a real number

Let us convert 1994. Break it into its parts and handle each from the top:

• 1000 is M
• 900 is CM
• 90 is XC
• 4 is IV

String those together in order and you get MCMXCIV. Read it back and it checks out: M is 1000, CM adds 900, XC adds 90, and IV adds 4, which is 1994. Three of the four parts used the subtraction trick, which is common in numbers full of 4s and 9s.

The range, and the missing zero

This converter covers 1 to 3999, which is the span the seven standard symbols can express, since writing larger numbers needs special marks the Romans added later. There is also no Roman numeral for zero, and none for negative numbers. The Romans simply had no symbol for nothing, so counting started at one, which is why the everyday range begins there.

Questions people ask

How do I write a number in Roman numerals?

Work from the largest symbol down, writing each up to three times, and use the subtraction pairs for the 4s and 9s. So 1994 becomes M, then CM, then XC, then IV, giving MCMXCIV.

Why is 4 written IV and not IIII?

Because a symbol is not repeated more than three times. Instead, 4 is written as one less than five, IV, putting the smaller I before the V to mean subtract it.

What numbers can it handle?

1 to 3999. That is the range the seven standard symbols cover; larger numbers need extra notation the converter does not use.

Is there a Roman numeral for zero?

No. The Romans had no symbol for zero, so the system has no zero and no negative numbers, and counting begins at one.

References

1. Weisstein, Eric W. "Roman Numerals." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/RomanNumerals.html