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According to the website, Perfect English Grammar the modal verbs of obligation

have to / don't have to: strong obligation (possibly from outside)

Children have to go to school. (maybe the law forces children to go to school) (sometimes 'have got to')

must / mustn't: strong obligation (possibly based on the speaker's opinion)

I must study today. (I force myself to study)

In natural native speaking, do you care about that difference?

However, if we want to use must in the past, then we have to use "had to". E.g., ‘I had to study yesterday’.

So, are "I must go to school" and "I have to go to school" interchangeable or non interchangeable?**

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  • There are other differences, but if a child's friend asks her to play baseball, and she can't because she is required to go to school instead, she will never say: "I wish I could, but I must go to school." Instead she will say: "I wish I could, but I have to go to school."
    – P. E. Dant Reinstate Monica
    Commented Oct 6, 2016 at 5:09
  • Just a note, don't have to isn't used to express obligation. It means don't need to and used to express the abscense of obligation. Also for _mustn't it's better to say prohibition.
    – Yuri
    Commented Oct 6, 2016 at 8:10
  • Based on English Granmar in Use, They're intrchangeable and sometimes it doesn't matter which you use as in oh, it's later than I thought. I must/have to go. The difference is imporatant here though I must get up early tomorrow. There are a lot of things I want to do (personal) vs I have to get up early. My train leaves at 8 (impersonal). If you're not sure which to use have to is usually safer to use. In your sentence, I'd say it depends what you have in mind. A: Children must go to school to be well-educated. B: I don't think so. They can be home-schooled.
    – Yuri
    Commented Oct 6, 2016 at 8:29

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Must is also used in the past, it depends on the context:

The modal verb must has two past tense forms: ‘had to’ and ‘must have.’ Which form we use depends on whether we want to express obligation or if we want to say how certain we are about the probability of something happening.

When expressing obligation, we say:

‘I must go’ or ‘I have to’

When expressing obligation, the past of ‘must’ and ‘have to’ is always ‘had to’:

I had to wash my car yesterday.
We had to go to bed at 8 o’clock when we were kids.

When expressing a personal opinion about probability (deduction), we mostly use ‘must’ to express that we feel something is true:

He must be fit if he can run 10 kilometres
It must be great to be rich.

When expressing a personal opinion in the past, we mostly use ‘must have’, NOT ‘had to’:

He must have been fit - NOT (He had to be fit.)

It must have been great - NOT (It had to be great.)

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Focusing on the present tense, the words can be used interchangeably. The website's use of "possibly" indicates that the distinction they are making is not mandatory.

In American conversational English, the real distinction is that you should probably use "must" to indicate strong obligation only rarely (notice I didn't say never). "Have to" is much more common in conversation, and "must" tends to sound a little bit formal.

When the obligation is internal, as in the "must" example from the website, "need to" would be more common in conversation. So, for example, "I need to study today."

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