http://www.usingenglish.com/forum/ask-teacher/104328-can-vs-able.html

can/could/be able to (ability and possibility)

Can is a modal verb. It only has a present, past, and conditional form (but can also be used with a future meaning).

I can speak Spanish very well.
She could play the violin when she was three.
She can't come tonight. She's ill.
They couldn't wait because they were in a hurry.
Could you open that door, please?

You can use be able to in the present, past, future, present perfect, and as a gerund or infinitive.
be able to in the present and past is more formal than can and could.

I am able to accept your invitation.
They weren't able to come.
I'll be able to practise my English in London.
She has been able to speak French since she was a child.
I'd like to be able to ski.
I love being able to sleep late at weekends.

It's simpler and more direct to use "can". Using "be able to" can sound more formal.

Compare:

I am not able to answer your call now.
I can't answer your call now.

It's not possible to express ability using the present perfect with "can". You have to use "be able to".

Have you been able to contact Eric at Universal Electronics?

I've been trying, but I haven't been able to talk to him. I left a message

http://www.englishclub.com/grammar/verbs-modals_can_3.htm

Be able to
Although we look at be able to here, it is not a modal verb. It is simply the verb be plus an adjective (able) followed by the infinitive. We look at be able to here because we sometimes use it instead of can and could.
We use be able to:
• to talk about ability
Structure of Be able to
The structure of be able to is:
subject + be + able + infinitive
subject be
main verb able
adjective infinitive
+ I am able to drive.
- She is not able to drive.
isn't
? Are you able to drive?
Notice that be able to is possible in all tenses, for example:
• I was able to drive...
• I will be able to drive...
• I have been able to drive...
Notice too that be able to has an infinitive form:
• I would like to be able to speak Chinese.
Use of Be able to
Be able to is not a modal auxiliary verb. We include it here for convenience, because it is often used like "can" and "could", which are modal auxiliary verbs.
be able to: ability
We use be able to to express ability. "Able" is an adjective meaning: having the power, skill or means to do something. If we say "I am able to swim", it is like saying "I can swim". We sometimes use "be able to" instead of "can" or "could" for ability. "Be able to" is possible in all tenses - but "can" is possible only in the present and "could" is possible only in the past for ability. In addition, "can" and "could" have no infinitive form. So we use "be able to" when we want to use other tenses or the infinitive. Look at these examples:
• I have been able to swim since I was five. (present perfect)
• You will be able to speak perfect English very soon. (future simple)
• I would like to be able to fly an airplane. (infinitive)
Now check your understanding »