Learn how to convert Roman numerals to Hindu-Arabic numbers:

Identify and calculate the value of each group of numerals written in subtractive notation.

Calculate the Hindu-Arabic number: add up all the values of the individual Roman numerals (written in additive notation) and of the groups of numerals written in subtractive notation.

The major set of symbols on which the rest of the Roman numberals were built:

• I = 1 (one); V = 5 (five);

• X = 10 (ten); L = 50 (fifty);

• C = 100 (one hundred);

• D = 500 (five hundred);

• M = 1,000 (one thousand);

• • For larger numbers:

  • (*) V = 5,000 or |V| = 5,000 (five thousand); see below why we prefer this notation: (V) = 5,000.

  • (*) X = 10,000 or |X| = 10,000 (ten thousand); see below why we prefer this notation: (X) = 10,000.

  • (*) L = 50,000 or |L| = 50,000 (fifty thousand); see below why we prefer this notation: (L) = 50,000.

  • (*) C = 100,000 or |C| = 100,000 (one hundred thousand); see below why we prefer this notation: (C) = 100,000.

  • (*) D = 500,000 or |D| = 500,000 (five hundred thousand); see below why we prefer this notation: (D) = 500,000.

  • (*) M = 1,000,000 or |M| = 1,000,000 (one million); see below why we prefer this notation: (M) = 1,000,000.

(*) These numbers were written with an overline (a bar above) or between two vertical lines. Instead, we prefer to write these larger numerals between brackets, ie: "(" and ")", because:

• 1) when compared to the overline - it is easier for the computer users to add brackets around a letter than to add the overline to it and
• 2) when compared to the vertical lines - it avoids any possible confusion between the vertical line "|" and the Roman numeral "I" (1).

(*) An overline (a bar over the symbol), two vertical lines or two brackets around the symbol indicate "1,000 times". See below...

Logic of the numerals written between brackets, ie: (L) = 50,000; the rule is that the initial numeral, in our case, L, was multiplied by 1,000: L = 50 => (L) = 50 × 1,000 = 50,000. Simple.

(*) At the beginning Romans did not use numbers larger than 3,999; as a result they had no symbols in their system for these larger numbers, they were added on later and for them various different notations were used, not necessarily the ones we've just seen above.

Thus, initially, the largest number that could be written using Roman numerals was:

• MMMCMXCIX = 3,999.

I. The set of the basic symbols of the Roman numerals

II. The rule of the repetition of the Roman numerals

III. The groups of the Roman numerals written in subtractive notation

IV. The additive notation of the Roman numerals

How to convert the Hindu-Arabic numbers to Roman numerals: breaking down the numbers into place value subgroups

Examples of converting Hindu-Arabic numbers to Roman numerals

The list of the first 100 Roman numerals: the Roman numerals from 1 to 100

The list of the first 1,000 Roman numerals: the Roman numerals from 1 to 1,000

I. Addition. Learn by an example how to add the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

II. Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

III. Addition and subtraction. Learn by an example how to add and subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations