Imperial is about empires, emperors and the British system of measurement, while imperious describes someone bossy and domineering. Think of the extra -ious as extra attitude: an imperious manager gives orders as if ruling an empire.
The core difference
Imperial relates to an empire or emperor, whereas imperious describes a domineering, overbearing manner.
- imperial — relating to an empire or emperor, or to the British system of units: The recipe still uses imperial units like pints and ounces.
- imperious — domineering, arrogant or overbearing: She gave an imperious wave of the hand and the waiter hurried over.
How to tell them apart
Both words come from the Latin imperium, meaning command or power, which is why they look so alike. But they have gone different ways: imperial describes things connected with an empire (an imperial palace) or the traditional British measurements, while imperious describes how a person behaves.
A simple test: if you are describing a thing, a ruler or a unit of measure, you almost certainly want imperial. If you are describing someone's bossy tone or attitude, you want imperious. The mix-up tends to appear when writers reach for a grand-sounding word to describe a commanding personality.