Does the time difference between Karachi and Rome change during the year?

Yes. Because of daylight saving time the gap moves between +3h and +4h.

When is the best time to call Rome from Karachi?

Between 12:00 and 17:00 in Karachi, which is 09:00 to 14:00 in Rome.

Karachi is 3h ahead of Rome. This gap is not fixed: daylight saving time moves it between +3h and +4h during the year.

Karachi

Pakistan

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Rome

Italy

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A 9-to-5 day in each city overlaps for 5h. That is 12:00–17:00 in Karachi, which is 09:00–14:00 in Rome.

City	Time zone	UTC offset
Karachi · Pakistan	Asia/Karachi	UTC+5
Rome · Italy	Europe/Rome	UTC+2

What is the time difference between Karachi and Rome?: Karachi is 3h ahead of Rome. This gap is not fixed: daylight saving time moves it between +3h and +4h during the year.
Does the time difference between Karachi and Rome change during the year?: Yes. Because of daylight saving time the gap moves between +3h and +4h.
When is the best time to call Rome from Karachi?: Between 12:00 and 17:00 in Karachi, which is 09:00 to 14:00 in Rome.