# When did subtractive notation become common for Roman numerals?

The additive notation of Roman numerals for 4 and 9 is `IIII` and `VIIII`. The subtractive notation is `IV` and `IX`.

Wikipedia doesn't go into detail about which form was known and popular during which period. Going by "Why Do Clocks and Watches Use the Roman Numeral IIII instead of IV?" the additive form is more ancient. But beyond that it doesn't make the timeline very clear.

When did the subtractive notation become widely known? When did it become more common than the additive notation?

• Do you require accuracy beyond "Medieval Era"? All claims I've seen is that the Romans themselves only used additive notation, and at some point Medieval scribes adopted and popularized subtractive notation (except on clocks). Commented Sep 2, 2022 at 0:21
• That's exactly what I told a friend! Then I wanted to support this with references and couldn't find any. So yeah, if you can show that Romans only used additive notation I'd be very happy with that! Thank you! Commented Sep 2, 2022 at 8:31
• Interesting answer to a question I've wondered about for many years, thank you. You say the subtractive form was also in use bu the Romans from late Etruscan times (say 100 BCE?). Can you provide any actual examples of Roman use of the subtractive form? I've not been able to find any and have long doubted this question? Thanks, Jonathan Betts Commented May 27 at 6:56

Romans used both additive and subtractive and this is true from late Etruscan times up to middle ages (1100 Arabic numbers spread into Europe).

Roman numerals were never a standardized notation system, but a rather simple tally-mark system that got complex on some use-cases. There were variations that depended on context and user (writer). For instance, the notation of large numbers over thousands was crazy varied.

Regarding subtractive/additive, the numerals for 4 and 9 only had two options each, but consider that the numerals for 17, 18, 19 when written had three options each (18= decem et octo, duodeviginti, octodecim). All three options are still used in different Romance languages. So, their use never did stop.

Here is a list of major factors on popularity for each system:

1. Large percentage of illiterate people. Many people never wrote the number 50, or 29, ever in their lifetime. This sets the basic context.
2. Tally Marks. The use of numerals was mostly as simple, practical tally marks. Did you wrote 5 but you really meant 4? Here you go IV! Are you counting from 1 to 4, here you go IIII.
3. We know it was common to mistake III and IIII, also VIII and VIIII when badly written, or written in a poor writing surface (like a brick wall), so that factor probably drove the use of the subtractive system.
4. Clash with the mindset of local languages. In the Greek speaking area all subtractives between 20 and 99 were replaced by additives. So use does not really depend on time period, but by region and the other factors.
5. Literary use. To stress the point, same writer can use both systems, like "one hundred minus one killed in that battle".
6. Space available. Roman Republican calendars use XXIX for 29th, but then, they also use IIII for 4th.

It is true that IIII is the simplest and earliest form to write 4. During early Roman times the additive form is preferred, but we don't know for sure wheter it was exclusive, since you will find IV in quite early republican inscriptions in the CIL.

The theory of "avoiding Jupiter wrath" by not using the abbreviation IV, in my opinion, makes no sense. The ancient and earliest Roman (read: Etruscan) name of Ivpiter was Iovis, so there would be no clash and no God's wrath by writing IV in early Roman times. It just makes no sense. The "simplest tally mark" hypothesis is more valid in my opinion, by Occam's razor argument.

On another topic, the reason that clocks use IIII and not IV might be to avoid confusion with VI when numbers are written aligned along the perimeter (you can write both inwards OR outwards along the perimeter), and not vertically aligned. In fact both clocks with inward and outward Roman numerals exist. Big Ben is inward, most watches are outward. Yet, this is only my personal opinion. I see that IX and XI face same problem.