Deductions about the past: must have, can't have, might have

Build a past deduction

Use modal + have + past participle. A past participle is the form used after have, such as worked, eaten, gone or seen. With irregular verbs, it may differ from the past simple: took becomes taken, not took.

The modal and have stay the same with every subject: I might have taken it and She might have taken it. Do not change have to has or had. Do not put to between the modal and have.

These are statements about your judgement. The evidence can be incomplete or mistaken. You can say I thought she must have left, but she was still upstairs without making the grammar inconsistent: you are correcting the conclusion.

Must have: a strong positive conclusion

Use must have + past participle when the evidence makes you feel sure about a past event or situation. This is stronger than merely offering a possible explanation.

• Every shelf is empty and the removal van has gone. They must have moved out.
• You must have felt relieved when the missing documents turned up.

The second example is a reaction based on what you have heard. You did not necessarily observe the feeling yourself. A deduction can concern a past state as well as an action.

Compare They moved out yesterday, a direct statement, with They must have moved out, a conclusion. If you need a verified answer, check the fact rather than relying on the modal.

Must have is not the ordinary way to report a past requirement. We had to replace the lock reports a necessity. We must have replaced the lock gives a conclusion that the replacement happened. See Have to and must: obligation.

May have, might have and could have: a possibility

Use these forms when you think a past event is possible but do not claim to know. They can offer an explanation that still needs checking.

• The noise might have come from the lift. I didn't see what caused it.
• The envelope may have arrived after we left. Can you check the tray?
• The number could have been copied incorrectly. We need to compare the original.

In this deduction use, these forms overlap. British Council calls may have more formal than might have and says could have is less common in this context. Those are source-specific usage notes, not reasons to mark one of the three ungrammatical. Do not attach fixed percentages to them.

That is not a claim that all three have different numerical probabilities. See May and might: possibility and other meanings and Could and could have: possibilities and missed chances for their wider meanings.

An uncertain conclusion need not refer to a dated event. The builders might have finished by now means completion before now is possible; it is not confirmed. Have still introduces the perfect form, even without yesterday or last week.

May not have is different from can't have

Perhaps it did not happen

May not have and might not have leave open the possibility that an event did not happen. They do not rule out the alternative.

• Amira might not have received the invitation. I'll ask her before I assume she declined.

She may have received it, or she may not have received it. The speaker has not settled which is true.

I judge it impossible

Can't have and couldn't have express a strong negative conclusion about the past. You treat the evidence as ruling out the event.

• That can't have been the original contract. The original was destroyed years ago.
• The parcel couldn't have fitted through that opening. It was wider than the gap.

Both forms can make a past deduction. Can't have does not mean the event is happening now, and couldn't have does not automatically make the speaker less certain. The past reference comes from have + past participle and the context.

Compare He might not have entered, which leaves his entry uncertain, with He couldn't have entered, which rejects it. Do not use couldn't have when all you mean is perhaps not.

Negative must: avoid an absolute rule

For the core negative-deduction pattern, choose can't have or couldn't have. Cambridge, British Council and Test-English teach these as the counterparts of must have. Mustn't normally expresses prohibition in examples such as You mustn't open this door.

However, do not claim that every must not have deduction is wrong. A sentence such as It must not have been comfortable waiting outside all night can express a conclusion about discomfort, not a past prohibition.

Keep this as a later extension, not a replacement for the core pattern in every sentence. To report an ordinary past ban, say We weren't allowed to enter. Neither We can't have entered nor We must not have been inside simply reports that rule. See Have to and must: obligation.

An action in progress or a passive event

Looking back at something in progress

Use have been + -ing to focus on an action in progress at a past time. Been is the past participle of be; the following -ing form names the activity.

• There was music coming from the hall at midnight. The band must have been rehearsing.
• I didn't hear the bell. I might have been using the vacuum cleaner.

Compare They must have repaired the pump, a conclusion about the repair, with They must have been repairing the pump when we passed, a conclusion about an activity then in progress. The second does not by itself establish a completed repair.

Putting the affected thing first

A passive makes the person or thing affected the subject. Use have been + past participle, not have be.

• The seal is broken. The container must have been opened.
• The file may have been saved in a different folder. We are searching for it.

Been working is progressive: someone was working. Been repaired is passive: someone repaired something. Check the verb after been rather than treating every been-pattern as the same. See The passive in many tenses and with modal verbs.

Questions and replies

Put a modal before the subject to form a question. Do not add do, does or did. Could and can questions can ask whether a past explanation is possible.

• Could the ticket have fallen out of your pocket?

You can also ask Do you think the ticket might have fallen out? or Is it possible that it fell out?. The do in the first question belongs to think; it does not form a question directly with might.

A reply can accept, leave open or reject the explanation: Yes, it could have; Perhaps, but I haven't checked; No, it can't have. The pocket was zipped shut. These express judgements, not identical degrees of certainty.

The same form can have another meaning

A modal-perfect form is not automatically a deduction. Read the whole situation before choosing a meaning.

Could have does not always imply that something failed to happen. Should have does not always mean regret or criticism. Conversely, a complaint with might have does not mean the speaker is merely unsure whether you acted. See Could and could have: possibilities and missed chances, Should, ought to and had better: advice and expectation and The third conditional: unreal past situations for the full contrasts.

What comes next

Compare present deductions in Deductions about the present: must, can't, may, might and could and Must and can't for deductions. Explore wider possibility in May and might: possibility and other meanings, unused chances in Could and could have: possibilities and missed chances, requirements in Have to and must: obligation, expectations in Should, ought to and had better: advice and expectation and longer patterns in Advanced probability: may, might, could, should and can.