Does the time difference between Cairo and New York change during the year?

Yes. Because of daylight saving time the gap moves between +6h and +7h.

When is the best time to call New York from Cairo?

Between 16:00 and 17:00 in Cairo, which is 09:00 to 10:00 in New York.

Cairo is 7h ahead of New York. This gap is not fixed: daylight saving time moves it between +6h and +7h during the year.

Cairo

Egypt

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New York

United States

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A 9-to-5 day in each city overlaps for 1h. That is 16:00–17:00 in Cairo, which is 09:00–10:00 in New York.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
New York · United States	America/New_York	UTC−4

What is the time difference between Cairo and New York?: Cairo is 7h ahead of New York. This gap is not fixed: daylight saving time moves it between +6h and +7h during the year.
Does the time difference between Cairo and New York change during the year?: Yes. Because of daylight saving time the gap moves between +6h and +7h.
When is the best time to call New York from Cairo?: Between 16:00 and 17:00 in Cairo, which is 09:00 to 10:00 in New York.