Without any involved research into the matter.
If somebody asks me how many employees my company has, I might immediately answer:
"Offhand, I'd say about 110." I am not sure, but I know about what it is. I have not taken the time to make sure.
If I go to the human resources department and find out. I can say.
"The number is exactly 112." I would no longer use 'offhand', because I have given thought to this and done some research.