かな is a sentence-final particle that softens a question into an inner thought. It’s often used when you’re thinking to yourself, but you can also say it to others to show hesitation. When you use it with a verb in the plain form, it can mean 'I wonder if...' or 'Should I...?'. For example, 行こうかな means 'Should I go?' and 行くかな can mean 'I wonder if he will go' or 'I wonder whether to go' depending on context.

With nouns and な-adjectives, you need か before かな, like 先生かな ('I wonder if it's the teacher') or 静かかな ('I wonder if it's quiet'). With い-adjectives, just add かな directly: 暑いかな ('I wonder if it's hot').

This is casual, spoken Japanese. In writing, it’s often used for inner monologue. It’s not rude, but it’s not polite either. If you’re speaking to a superior, you would avoid it and use でしょうか instead.