I think there isn't any clear definition. Mostly they have same usage, but to know the differences I think the only way is you read more texts. Then you can know in every case which one is more suitable. Some examples: About hours we use نیم not نصف نیم ساعت دیگه میام ساعت الآن ده و نیمه but نصف ساعت seems wrong نصف آب رو خالی کن نیمی از آب رو خالی کن In this case both of them are correct, but in colloquial conversations the first one seems better. نصف راهو رفتیم نیمی از راهو رفتیم نصف اونو بده من نیمی از اونو بده به من In colloquial way the first one seems better again سادندویچو دو نصف کن ساندویچو دو نیم کن نیمه شب نصف شب Look at these compound words: نیمروز، نیم فاصله، نیمسال، نیم تنه We don't use نصف in these cases. I hope it helped.

They are synonyms, meaning half [of]. نصف is a loan word from Arabic, so it might be better to use نیم. Also, there's a slight difference in the common usage: half the books/money = نیمی از کتاب‌ها/پول = نصفِ کتاب‌ها/پول

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