What is the difference between can and may?

Traditionally, can expresses ability and may expresses permission.

Can you swim? — are you able? May I leave early? — am I permitted?

This is the distinction behind the classroom exchange where a child asks "Can I go to the toilet?" and is told "I don't know, can you?"

The honest position is that the distinction has weakened considerably, and can for permission is now standard in all but the most formal contexts. Can I get a coffee? is unremarkable everywhere. Insisting on may in ordinary conversation reads as affectation more often than as correctness.

Where the distinction still earns its place is in writing where precision matters, particularly anything contractual or instructional. Members can attend describes what is possible; members may attend grants permission. In a policy document those are different statements, and technical standards go further, defining may as optional, must as required and should as recommended.

May has a second sense that can does not share: possibility. It may rain means it is possible. This is why may can be ambiguous in a way can is not — you may leave could mean permission or prediction.

Might is conventionally the more tentative of the two for possibility, and is also the past form: he said I might go.

In negatives, cannot denies ability or permission, while may not usually denies permission — though it can also express possibility, which is a genuine ambiguity worth avoiding in formal writing by rephrasing.

Could is worth adding to the set. It softens a request — could I leave early? — and is now the most common polite form, sidestepping the can/may argument entirely. It also expresses past ability: I could swim at four.