'normal order' is a compound of 'normal' and 'order'. 'normal' originates from Latin, specifically the word 'normalis' (from 'norma') where 'norma' meant 'a carpenter's square, rule' and thus 'pattern' or 'rule'; 'order' originates from Latin 'ordo' meaning 'row, rank' and passed into Old French as 'ordre'.

'normal' entered English via Old French/Latin (Old French 'norme', Late Latin 'normalis') and became 'normal' in Modern English; 'order' passed from Latin 'ordo' through Old French 'ordre' into Middle English as 'ordre/ordr' and later became Modern English 'order'. The compound phrase 'normal order' developed by combining these two words to mean the customary arrangement.

Initially, the elements referred to 'a rule/pattern' ('normal') and 'a row/rank' ('order'); over time the compound came to mean 'the usual or expected arrangement' in general usage and extended to technical senses (e.g., grammatical word order, operator ordering in physics).