Time adds in base-60, so it carries
Adding durations is not decimal arithmetic. Sixty seconds make a minute and sixty minutes make an hour, so any total that reaches 60 rolls up into the next unit. Work from the smallest unit up: seconds first, then minutes, then hours.
The classic mistake is treating 1:30 as 1.30 and adding it like money. 1:30 is 1½ hours; two of them make 3:00, not 2:60.
How the carry works in each direction
| Sum | Before carry | Result |
|---|---|---|
| 30 min + 30 min | 60 min | 1:00:00 |
| 0:55 + 0:30 | 85 min | 1:25:00 |
| 1:30 + 2:45 | 3 h 75 min | 4:15:00 |
| 59:59:59 + 0:00:01 | 59 h 59 m 60 s | 60:00:00 |
Subtracting reverses it: if you run short of minutes, borrow one hour as 60 minutes before taking the difference. A result cannot go below zero.
Decimal hours vs clock time
- To go decimal → clock, multiply the fraction by 60. 1.75 h is 1 hour plus 0.75 × 60 = 45 minutes, so 1:45.
- To go clock → decimal, divide the minutes by 60. 1:15 is 1 + 15/60 = 1.25 hours — the form payroll and timesheets usually want.
- Round last, not first. Keep full seconds through the sum and round only the final answer, or small errors stack up across several entries.
Common questions
Why can I not just add the times like decimals?
Time is base-60, not base-10. 1:30 plus 1:30 is 3:00, not 3.0 as a decimal sum would suggest, because 30 plus 30 minutes carries a full hour. Add the minutes, roll any 60 into the hours, and the seconds the same way.
What does carry-over mean here?
When seconds reach 60 they become one minute, and when minutes reach 60 they become one hour. 45 minutes plus 30 minutes is 75 minutes, which carries to 1 hour 15 minutes.
What is 1:30 in decimal hours?
1 hour 30 minutes is 1.5 hours, because 30 minutes is half an hour. Do not confuse 1.30 (which would be 1 hour 18 minutes) with the clock time 1:30.
Can the result be more than 24 hours?
Yes. Adding several durations can total 24:15 or more. The result is an elapsed duration, not a time of day, so it is not wrapped back to a 24-hour clock.
