In general, Roman numerals can be converted mathematically by simply assigning a numerical value to each letter, according to the chart below, and calculating a total:
M=1000 | D=500 | C=100 | L=50 | X=10 | V=5 | I=1
Although the historical practice has varied, the modern convention has been to arrange the letters from left to right in order of decreasing value; the total is then calculated by adding the numerical values of all the letters in the sequence.
For example, MDCLXVI (one of each valid letter) = 1000 + 500 + 100 + 50 + 10 + 5 + 1 = 1666.
A well-known, but still often confusing feature of modern Roman numerals is the subtraction principle, which requires that a lower numeral appearing before a higher one be subtracted from the higher value, not added to the total. For example, IX is the Roman numeral for 9 (that is, 10 - 1). In the same way XIX represents the number 19 (X + IX, or 10 + 9) rather than 21, which is written as XXI (10 + 10 + 1). Likewise the Roman numeral for the year 1995 is usually written as MCMXCV (M + CM + XC + V, or 1000 + 900 + 90 + 5). Many other similar examples can be found which strictly follows this subtraction convention.
Another present-day convention is the avoidance of more than three consecutive occurrences of the same letter in favor of the more succinct forms achieved by using the subtraction principle -- for example, IV for IIII (4), XL for XXXX (40), and CD for CCCC (400). An exception is the numeral M, or 1000, which is used 4 times to represent our number 4000, since the Romans had no single-letter numeral representing a higher value than M. It is now also customary not to repeat the values V, L, or D (5, 50, or 500) in the same numeral.