What is the Greek root for automatic?

The Greek root for "automatic" is "auto-", meaning "self" or "one's own".

This root is combined with the Greek word "matos", meaning "tool" or "instrument", to form the word "automatos", meaning "self-acting" or "self-moving".

Therefore, the term "automatic" derives from the Greek phrase "self-acting instrument", which aptly describes the nature of automation.