1. without careful thought or investigation
(don't) know facts/figures offhand
The phrase to say something 'offhand' means to say something or give information without checking first if the information is correct or accurate. This phrase is similar to 'off the top of my head' or 'as far as I can remember' and it is a good expression to use if you want to warn others that the answer you are giving might not be 100% correct or you are giving an estimate. If you 'know something offhand' it means you know the information correctly without checking.