Britannica Sources used in this answer

How does the subtractive rule work in Roman numerals?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

Two vertical tablets display ancient symbols for the numbers one and ten from Egyptian hieroglyphic, Egyptian hieratic, Sumerian, and Cretan scripts, with each symbol shown in red next to its culture and approximate date. — numerals and numeral systems Examples of ancient symbols for the numbers 1 and 10.

In the Roman numeral system, the subtractive rule is used primarily to express numbers beginning with a 4 or a 9, such as 4 (IV), 9 (IX), 40 (XL), or 90 (XC).1

When a symbol is placed before another symbol of greater value, its value is subtracted from the larger value. For example, in the numeral IV, the I (1) is subtracted from the V (5), resulting in 4. Similarly, in LIX, the I (1) is subtracted from the X (10), which is then added to the L (50) to total 59.12

While this principle is standard in modern usage, it was used inconsistently during the Classical period. Romans often preferred additive forms, such as using IIII to represent 4 instead of the subtractive IV, a practice that still persists on many clock faces today. The subtractive principle was generally little used in the numerals of the Classical period and was rarely applied to larger numbers like 99.31