Both are real words meaning the state of being normal. Normality is the usual British form and the older of the two. Normalcy is common in American English and was popularised by Warren Harding's 1920 campaign slogan "return to normalcy" — which is also why it was mocked as an invention, though it predates him.
The core difference
A variety split with an unusually well-documented origin story.
- normality — standard in British English and widely used everywhere.
- normalcy — common in American English; unremarkable in US usage.
The Harding story
Harding's 1920 slogan drew ridicule, with critics claiming he had invented the word out of ignorance. He had not — normalcy is recorded decades earlier, originally in mathematics. But the campaign made it famous and fixed its American association permanently.
Which to write
For British readers, normality. For American readers, either. Normalcy in British writing will read as an Americanism to some, and there is no reason to invite the distraction.
