Must and Have (got) to

When we say that it is NECESSARY to do something, we use must or have (got) to:
• To get a cheap ticket, you must / have (got) to book in advance.
• Every animal on the island must / has (got) to be destroyed.
When we want to say that it will be necessary for someone to do something in the future, we use must, have (got) to, or will have to:
• To get there on time, I must / have (got) to / will have to leave home by 8.30.
Have got to is less formal than the others, and is particularly common in spoken English. We can often use need (to) with a similar meaning:
• Before you buy a house, you need to / must / have (got) to consider all the costs.
Using have (got) to suggests that someone else or some outside circumstances or authority makes something necessary.We use must when the speaker decides it is necessary. Compare:
• I have to see the head teacher, (...she has called me to her office)
• I must see the head teacher. (...I want to discuss something with her)
We prefer have (got) to when we talk about a necessity that is characteristic of a person:
• Ann has got to have at least eight hours' sleep a night.
• She has to drink two cups of coffee in the morning before she feels really awake.
We normally use must, not have (got) to, when we CONCLUDE that something (has) happened or that something is true:
• With that pile of papers on his desk, Tony must be wishing he'd never taken the job.
• The hall's packed. There must be about 2,000 people at the meeting.
However, in informal speech, we can use have (got) to:
• Look at all those penguins. There's got to be about a million of them!
• You want to borrow more money from me? You've got to be joking!
When we give a negative conclusion we rarely use either must not or hasn't / haven't got to. Instead, we use can't (cannot) or couldn't:
• 'I'm seeing Dr Evans next week.' 'That can't be right. He's on holiday then.'
• He wasn't there at the time. It couldn't have been his fault.
Must has no other forms than the present tense (no past tense, no participles, etc.) and in past tense sentences which say that it was necessary to do something, we use had to instead:
• Bill's not here. He had to leave early. • The car broke down and we had to get a taxi.
To draw a conclusion about something in the past, we use must + have + past participle:
• You must have been upset when you heard the news.
• She must have played really well to win. I wish I'd seen the match.
Sometimes we can use either have to or have got to. However, we prefer have to with frequency adverbs such as always, never, normally, rarely, sometimes, etc.:
• I often have to work at the weekend to get everything done.
With the past simple, we use had to, especially in questions and negative sentences:
• When did you have to give the books back? {not When had you got to...)
• We didn't have to wait too long for an answer, (not We hadn't got to...)
After contracted forms of have, has or had (e.g. I've, He's, It'd) we use got:
• It's got to work this time, [not It's to work...)
In formal English we prefer have to rather than have got to.