h₃reǵ-mn̥
“rule, direction, standard”Source of Latin regula, English rule, regulate, rail
Nominal of the rule root, yielding Latin regula and English rule, regulate, rail, regular.
Discussion
The PIE form *h₃reǵ-mn̥ (rule, direction, standard of correctness) is a nominal derivative of *h₃reǵ- (to straighten, to direct), formed with the *-mn̥ suffix that produces result nouns. The meaning is "that which results from directing" — a rule, a regulation, a standard.
Latin rēgula (a straight stick, a ruler, a standard of measurement) continues this formation and gave English: rule (the standard by which things are measured), regular (conforming to the rule), regulate (to apply rules to), and the measuring tool ruler (a straight edge used for drawing lines — the most literal descendant). The word regulation encodes the PIE concept transparently: to regulate is to make straight by applying the *h₃reǵ- standard.
The derivative irregular (in-rēgulāris, "not conforming to the rule") shows the negative: what fails to be straight is irregular. Compare the related *h₃reǵ-tó- ("made straight" → English right/correct) for the participial formation.
Latin norma (a carpenter's square — another straightening tool, possibly from a related root) gave English normal, norm, and abnormal — extending the straightness vocabulary into statistical and psychological domains. What is normal is what conforms to the standard of straightness.
The *-mn̥ suffix is the same formation found in *srew-mn̥- (stream), *sengʷʰ-mn̥- (song), and other PIE result nouns — confirming the productivity of this derivational pattern.