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be able to

We use able especially in the structure be able to + infinitive. This often has the same meaning as can (see here). There is a negative form unable.

  • Some people are able to / can walk on their hands.
  • I am unable to / can’t understand what she wants.

Can is preferred in the sense of ‘know how to’, and in expressions like can see, can hear, etc (see here).

  • Can you knit? (More natural than Are you able to knit?)
  • I can see a ship. (More natural than I am able to see a ship.)

Be able to is used most often for people or other living things. Compare:

  • Jake can lift / is able to lift 150 kilos.
  • This crane can lift 30 tonnes. (More natural than This crane is able to lift 30 tonnes.)

Be able to is used in cases (e.g. future, present perfect) where can/could is not grammatically possible because it has no infinitive or participles (see here).

  • One day scientists will be able to find a cure for cancer. (not … will can find …)
  • What have you been able to find out? (not What have you could …?)
  • I might be able to help you. (not I might can …)

Able is not often followed by passive infinitives.

  • He can’t be understood. (More natural than He’s not able to be understood.)

For differences between could and was able to, (see here), (see here).