'can' and 'could'

It can be very cold here in winter. (= It is sometimes very cold here in winter.)
You can easily get lost in this town. (= People often get lost in this town.)

We use can't or cannot to say that something is impossible:

That can't be true.
You cannot be serious.

Level: intermediate

We use could have to make guesses about the past:

It's ten o'clock. They could have arrived by now.
Where are they? They could have got lost.

We use could to make general statements about the past:

It could be very cold there in winter. (= It was sometimes very cold there in winter.)
You could easily get lost in that town. (= People often got lost in that town.)

We use can't have or couldn't have to say that a past event was impossible:

They know the way here. They can't have got lost!
If Jones was at work until six, he couldn't have done the murder.

Ability

Level: beginner

We use can and can't to talk about someone's skill or general abilities:

She can speak several languages.
He can swim like a fish.
They can't dance very well.

We use can and can't to talk about the ability to do something at a specific time in the present or future:

I can see you.
Help! I can't breathe.

We use could and couldn't to talk about the past:

She could speak several languages.
They couldn't dance very well.

Level: intermediate

We use could have to say that someone had the ability or opportunity to do something, but did not do it:

She could have learned Swahili, but she didn't want to.
I could have danced all night. [but I didn't]

Permission

Level: beginner

We use can to ask for permission to do something:

Can I ask a question, please?
Can we go home now?

could is more formal and polite than can:

Could I ask a question please?
Could we go home now?

We use can to give permission:

You can go home now.
You can borrow my pen if you like.

We use can to say that someone has permission to do something:

We can go out whenever we want.
Students can travel for free.

We use can't to refuse permission or say that someone does not have permission:

You can't go home yet.
Students can't travel for free.

Requests

We use could you … as a polite way of telling or asking someone to do something:

Could you take a message, please?
Could I have my bill, please?

can is less polite:

Can you take a message, please?

Offers

We use can I … to make offers:

Can I help you?
Can I do that for you?

We sometimes say I can ... or I could ... to make an offer:

I can do that for you if you like.
I could give you a lift to the station.

Suggestions

We use could to make suggestions:

We could meet at the weekend.
You could eat out tonight.

Questions and negatives

We make questions by putting the subject after can/could:

The negative form is can't in spoken English and cannot in written English.

We sometimes say cannot, but it is very emphatic.

The negative form of could is couldn't in spoken English and could not in written English.

Modal verbs

"Put your question in the box"