Examples: I can teach a lesson off the top my head if I have to take a class for a sick teacher. He can tell you what salaries people earn, off the top of his head. Our school principal can make a speech about anything, off the top of his head.

a manner doing without advance taught.

"Off the top of my head" can mean "the first thing I can think of". It means the person didn't think very long about the answer. The answer was just the first thing that came to mind. In a related way, it can also mean what you know without access to a computer or reference book. Person A: What restaurant is open after midnight? Person B: Off the top of my head, the only place I can think of is McDonalds. Person A: How many people live in China? Person B: I'm not sure. Off the top of my head, I'd guess around 1.5 billion?.