And of the 56% who admitted nodding off, as many as 29% said they awoke to find the other pilot asleep.
Of the 500 commercial pilots polled, 43% said they believed their abilities had been compromised at least once a month in the past six months by tiredness, with 84% saying it has been compromised at some stage during the past six months.
Also, 31% did not believe their airline had a culture that lent itself to reporting tiredness concerns, with only half (51%) saying they believed their airline chief executive would back them if they refused to fly because of tiredness.
Unprompted, 49% said pilot tiredness was the biggest threat to flight safety - three times more than any other threat.
The poll results come ahead of a European Parliament vote on new EU rules on pilot flying hours next Monday.
Balpa believes the new regulations will cut UK safety standards and wants MEPs to vote against them.