The negative form of can is cannot or can't. Cannot is never written 'can not'. The negative form of could is could not or couldn't. To form the negative of be able to, you either put not or another negative word in front of able, or you use the expression be unable to.

Can, could, and be able to are all used to talk about a person's ability to do something. You use can or be able to to talk about ability in the present. Be able to is more formal than can.

Could is also used to talk about ability in the present, but it has a special meaning. If you say that someone could do something, you mean that they have the ability to do it, but they don't in fact do it.

You use could or a past form of be able to to talk about ability in the past.

If you say that someone was able to do something, you usually mean that they had the ability to do it and they did it. Could does not have this meaning.

If you want to say that someone had the ability to do something but did not in fact do it, you say that they could have done it.

If you want to say that someone did not do something because they did not have the ability to do it, you say that they could not have done it.

If you want to say that someone had the ability to do something in the past, although they don't now have this ability, you say that they used to be able to do it.

You use a future form of be able to to talk about ability in the future.

Could is often used in reporting structures. For example, if a woman says 'I can speak Arabic', you usually report this as 'She said she could speak Arabic'.

Be able to is sometimes used after modals such as might or should, and after verbs such as want, hope, or expect.

Don't use can or could after any other verbs.

You can use an -ing form of be able to.

There is no -ing form of can or could.

Can and could are used with verbs such as see, hear, and smell to say that someone is or was aware of something through one of their senses.

Could and can are used to talk about possibility in the present or future.

You use could to say that there is a possibility that something is or will be true.

Might and may can be used in a similar way.

Be Careful!
Don't use 'could not' to say that there is a possibility that something is not true. Instead you use might not or may not.

If you want to say that it is impossible that something is true, you use cannot or could not.

You use can to say that something is sometimes possible.

You use could have to say that there is a possibility that something was true in the past.

Might have and may have can be used in a similar way.

You also use could have to say that there was a possibility of something being true in the past, although it was not in fact true.

Be Careful!
Don't use 'could not have' to say that there is a possibility that something was not true. Instead you use might not have or may not have.

If you want to say that it is impossible that something was true, you use could not have.

Can and could are used to say that someone is allowed to do something.

Cannot and could not are used to say that someone is or was forbidden to do something.