The spellings hare-brained and hair-brained are both accepted. (The hyphen is preferred in Canadian spelling, but the terms may also be written without it.)
Hare-brained is the more common spelling and more accurately reflects the origin of the term, which was first used in the 16th century to describe a foolish person—one “with the brain of a hare”:
The modifier is also applied to anything that might have been created by someone with the brain of a hare:
Since hare was sometimes spelled haire or hair in 16th-century English, the spelling hair-brained also has a long history:
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