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How can I calculate the time elapsed in hours between two times (possibly occurring on different days) in iOS?

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The NSDate function timeIntervalSinceDate: will give you the difference of two dates in seconds.

 NSDate* date1 = someDate;
 NSDate* date2 = someOtherDate;
 NSTimeInterval distanceBetweenDates = [date1 timeIntervalSinceDate:date2];
 double secondsInAnHour = 3600;
 NSInteger hoursBetweenDates = distanceBetweenDates / secondsInAnHour;

See, the apple reference library http://developer.apple.com/library/mac/navigation/ or if you are using Xcode just select help/documentation from the menu.

See: how-to-convert-an-nstimeinterval-seconds-into-minutes

--edit: See D?r?D?vil's answer below for correctly handling daylight savings/leap seconds


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