Adding up time durations (hours, minutes, seconds) resembles ordinary decimal addition, but with one key difference: carrying happens not at 10, but at 60.
The carrying principle
Adding 1:45:30 and 0:30:45, the seconds give 30 + 45 = 75, which is over 60 — so you write down 15 seconds and carry 1 minute forward. The minutes give 45 + 30 + 1(carried) = 76, again over 60 — write down 16 minutes and carry 1 hour. The result is 2:16:15.
Why this isn't intuitive at first
Since we're used to decimal arithmetic, the temptation to just add "45 + 30 = 75 minutes" and leave it there is natural — but wrong for the standard time-writing format, where minutes and seconds have to stay within 0–59.
Subtracting durations
Subtraction works like "borrowing" in decimal subtraction: if the subtrahend's minutes are larger than the minuend's, you borrow 60 minutes from the hours place before subtracting.
Why you'd need this
- Totaling up work hours from several timesheet entries — useful for checking against the 40-hour week the US Fair Labor Standards Act uses as the overtime threshold.
- Calculating the total length of a playlist or video sequence from individual clips.
- Double-checking manually calculated durations in reports.
Why "42 hours" is a perfectly normal weekly total
Unlike the time of day on a clock, which always stays within 0–23 hours, a sum of durations can easily exceed a day — and that's not an error. Under the FLSA, hours worked past 40 in a week trigger overtime pay rather than resetting anything, so a weekly timesheet totaling "42h 15m" is completely routine — exactly why the duration format doesn't automatically carry hours into days the same way 60 minutes carry into an hour.