Calculation of Roman Numerals

If you've made it this far, it's because you're looking for a method to calculate Roman numerals, and we, not content with giving you just one, are going to teach you two.

If you need to do it automatically, use our online Roman numeral converter, which will process it in a matter of seconds and in a fully automated manner. To learn how to use it, read the specifications we've left you below.

On the other hand, if you want to learn how to perform operations with the Roman numeral system by hand, we've also thought of you and we're going to tell you how to do it in a simple way, step by step and totally free of charge.

If you want to decipher the numerical secrets of the civilization that dominated the world and laid the foundations of the modern world, keep reading, you won't regret it!

What are Roman numerals?

Roman numerals are an additive-subtractive numbering system and, therefore, non-positional. They have their origins in the ancient Roman Empire (chronology), where figures were expressed through alphabetical characters.

It is a really complex system, which led to its disuse over the years in favor of the so-called Arabic numbers, which we currently use.

In this article about Roman numerals, we want to break down this complicated numerical system for you so that you can carry out all kinds of operations, whether with our Roman numeral converter or by hand on your own.

We will also explain all the rules for composing them and how you can convert from a Roman numeral to a natural number, and vice versa. There's a lot of work ahead, shall we start?

How to convert Roman numerals

As we mentioned above, this numbering system is additive-subtractive, but in no case is it positional. What does this mean? Well, it has two very distinctive characteristics:

It's not positional since, unlike our numbering system, the different numbers (which are expressed in letters) always assume the same value regardless of their position.

And it's additive because the resulting figure is, in reality, the subtraction or addition of the different numbers that we can find in its composition.

The letters used and their corresponding value in the decimal system are as follows:

With these seven letters, the Romans were able to form their entire numerical system, and, to obtain larger figures, they combined them and used other symbols.

Curious, right? Keep reading and discover how they managed to do it.

Rules for composing Roman numerals

So far, you have learned what Roman numerals are and how to interpret their basic units, which are fundamentally letters from the Roman alphabet. Now, we're going to explain the rules you must apply if you want to convert Roman numerals:

1. They are written and read always from left to right.
2. The letters I, X, C, and M can be repeated up to 3 times in a number, whereas the letters V, L, and D can appear only once.
3. If a letter is followed by another of higher value, the value of the first will be subtracted from the second, whereas if a Roman numeral is followed by one of lesser value, both are added.

If a number is trapped between two figures of higher value, it must be subtracted from the figure on the right.

1. In the case of the letters I, X, and C, they are susceptible to having their value subtracted if they have a lower figure placed to their left, and this diminishing operation can only take place once.
2. The letter to be subtracted must not be less than one-tenth of the value from which it is to be subtracted.

Examples of operations with Roman numerals

Theory is all well and good and essential, but let's move on to a bit of practice so you can see everything more clearly.

For example, the number 15 written with the Roman numeral system would be XV and not VVV, as one of the previously mentioned rules reminds us that the letter V can only appear once. It would also be incorrect to write VXX, which should be 5-20, because rule number 4 prevents it.

Another example with the number 400, its correct form of representation would be CD. Indeed, it would be wrong to write CCCC, since the symbol C (100) can appear a maximum of three times in a single figure. Being on the right of D (500), the symbol of lesser value C (100), you must subtract its amount, resulting in 400 (CD).

As a last example, the value 99 is represented by XCIX and not as IC because I=1 is less than one-tenth of C = 100 and would violate rule number 5.

Follow the rules above and start forming Roman numerals little by little and trying not to skip any of them. If you want to check the results, here we leave you a table of Roman numerals from 1 to 100:

How to multiply Roman numerals

So far, you have learned to calculate Roman numerals with small figures, the most used in the daily life of the ancient world. Now, we're going to explain how to multiply those figures to get results with more zeros. Here we go!

If you underline or draw a line above a Roman numeral, it means that its value is multiplied by a thousand.

The ancient Romans, in fact, did not have a specific word to say millions, nor billions, nor even trillions, because their maximum numerical expression were the hundreds of thousands. To talk about millions, they used the Latin expression “mille mila”.

Although they didn't have a word for it, you can still form this figure, it will be enough to add two horizontal lines above the letter.

Operations with Roman numerals

Roman numerals are considered an elegant script but are usually not very useful for performing calculations.

Operations as such were done by an external instrument to the Roman numeration, such as the abacus.

In any case, it is likely that the subtractive principle facilitated the invention of algebra and chronometry, which is nothing else than the scientific discipline that allows us to say “it's a quarter to five” and understand it without problems, when our numerical system does not give us the tools to comprehend it.

Now that you know how to proceed with the digits of the ancient Roman empire, use our transformer to contrast the results and find out if you control the technique or still need to practice a bit.

Is there something you didn't understand? Are you having problems with the calculator? Tell us on the contact page so we can improve our network of free calculators and build a healthy community around them.

We only ask you to share this Roman numeral converter on your social networks so that all your contacts can learn about the intricacies of the ancient world and an empire that dominated Europe for centuries.