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Python Program to Convert Roman Numerals to Integers

Intermediate · Numbers

Roman numerals use letters for values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000. The values are normally added, but a smaller letter placed before a bigger one is subtracted, so IV is 4 and XC is 90. This program converts a Roman numeral like MCMXCIV into the number 1994.

Program

roman_to_integer.py
roman = "MCMXCIV" # or: roman = input("Enter a Roman numeral: ").upper()
values = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
total = 0
for i in range(len(roman)):
value = values[roman[i]]
# Subtract if a bigger letter comes next (like the I in IV), else add
if i + 1 < len(roman) and value < values[roman[i + 1]]:
total -= value
else:
total += value
print(roman, "=", total)
Output
MCMXCIV = 1994

How it works

  1. The dictionary values maps each Roman letter to its number.
  2. The loop looks at each letter together with the one after it.
  3. If the next letter is worth more, the current letter is subtracted, as in CM = 1000 - 100; otherwise it is added.
  4. i + 1 < len(roman) makes sure the last letter, which has nothing after it, is simply added.
  5. For MCMXCIV that gives 1000 + 900 + 90 + 4 = 1994.

Other ways to write it

Reading from right to left

Reading from right to left
def roman_to_int(s):
values = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
total = 0
previous = 0
for letter in reversed(s):
value = values[letter]
if value < previous:
total -= value # smaller than the letter to its right
else:
total += value
previous = value
return total
for r in ["III", "IX", "LVIII", "MMXXVI"]:
print(r, "=", roman_to_int(r))
Output
III = 3
IX = 9
LVIII = 58
MMXXVI = 2026

Going backwards, a letter is subtracted when it is smaller than the letter just after it, so there is no need to look ahead.

Integer to Roman, the other way

Integer to Roman, the other way
def int_to_roman(n):
pairs = [(1000, "M"), (900, "CM"), (500, "D"), (400, "CD"), (100, "C"),
(90, "XC"), (50, "L"), (40, "XL"), (10, "X"), (9, "IX"),
(5, "V"), (4, "IV"), (1, "I")]
result = ""
for value, letters in pairs:
while n >= value:
result += letters
n -= value
return result
for n in [4, 1994, 2026, 3999]:
print(n, "=", int_to_roman(n))
Output
4 = IV
1994 = MCMXCIV
2026 = MMXXVI
3999 = MMMCMXCIX

This takes the largest value that still fits, again and again. Listing 900, 400, 90, 40, 9 and 4 as their own pairs handles the subtraction cases.

Try it yourself

Add a check that prints a friendly message when the text contains a letter that is not a Roman numeral.

Edit the program above and press Run, or open it in the full editor to save it and share it. To watch it run line by line, open it in the visualizer.

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