Obligation: must and have to

Both must and have to express obligation — something that is necessary.

VerbSource of obligationExample
must internal / the speaker decides it's necessary I must call my mum — it's her birthday! · You must try this cake.
have to external / a rule, law, or other person requires it I have to wear a uniform at work. · She has to be home by 10.
In everyday speech: "Must" and "have to" often feel the same. "Have to" is more common in everyday conversation. "Must" sounds stronger or more urgent. In the past, only "had to" exists — "musted" is not a word.

No obligation: don't have to

Don't have to / doesn't have to means something is not necessary — you have a choice. There is NO obligation.

You don't have to come if you don't want to. (= it's OK if you stay)
She doesn't have to work on Sundays. (= Sundays are free)
I don't have to cook tonight — we're ordering pizza.

Prohibition: mustn't

Mustn't means something is forbidden or not allowed. It is much stronger than "don't have to".

You mustn't smoke in here. (= it's forbidden)
Students mustn't use their phones during the exam.
You mustn't park here — it's a fire exit.
Don't have to ≠ Mustn't — crucial difference! "You don't have to wear a tie." = You can wear one if you like, but it's not required. "You mustn't wear a tie." = Ties are forbidden here. One means no obligation, the other means prohibition.
ExpressionMeaning
must / have toobligation — it is necessary
don't have tono obligation — it is not necessary (but possible)
mustn'tprohibition — it is forbidden / not allowed

Exercises

Choose the correct modal verb.

1. In this country, children ___ go to school until they are 16. It's the law.

2. You ___ bring food to the party — I'm making everything myself.

3. You ___ touch that wire — it's live and very dangerous!

4. I ___ remember to post this letter — it's really important.

5. She ___ speak Spanish at work. Her boss prefers English.