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Summary
Time arithmetic — adding, subtracting, and converting between hours, minutes, and seconds — comes up constantly in everyday life: tracking work hours, timing recipes, logging exercise, calculating travel duration, and scheduling events. Unlike decimal arithmetic, time uses a base-60 system (sexagesimal) for minutes and seconds, which makes carrying and borrowing less intuitive. This calculator handles the conversions automatically.
How it works
The calculator normalizes all time values to a single unit (seconds), performs the arithmetic, and then converts back to hours, minutes, and seconds:
- Convert to total seconds — hours * 3600 + minutes * 60 + seconds.
- Perform arithmetic — add or subtract the total seconds.
- Convert back to HMS — divide by 3600 for hours, then by 60 for minutes, with the remainder as seconds.
This approach avoids the complexity of carrying across the 60-second and 60-minute boundaries.
The formulas
Where
Where
Worked examples
Add 2h 45m 30s and 1h 30m 50s
Convert first time to seconds
= 9,930 seconds
Convert second time to seconds
= 5,450 seconds
Add totals
= 15,380 seconds
Convert back to HMS
= 4h 16m 20s
Result
2h 45m 30s + 1h 30m 50s = 4h 16m 20s
Subtract 45 minutes from 1h 20m
Convert 1h 20m to seconds
= 4,800 seconds
Convert 45m to seconds
= 2,700 seconds
Subtract
= 2,100 seconds
Convert back to HMS
= 0h 35m 0s
Result
1h 20m - 45m = 35 minutes
Practical uses
- Work time tracking — adding up time entries for timesheets or project billing.
- Cooking — combining prep time and cook time to know total recipe duration.
- Exercise logging — summing lap times, intervals, or workout segments.
- Travel — adding flight time, layover, and ground transport to calculate total journey duration.
- Media production — calculating total runtime from individual segment durations.
Assumptions & limitations
- No date rollover — the calculator works with durations, not clock times. Adding 5 hours to 10:00 PM gives a 15-hour duration total, not “3:00 AM tomorrow.” For clock-time arithmetic, use a date-time calculator.
- Negative results — subtracting a larger time from a smaller one produces a negative duration, displayed with a minus sign.
- Precision — the calculator works with whole seconds. Sub-second precision (milliseconds) is not supported.
- 24-hour format — when displaying results as clock time equivalents, the calculator uses 24-hour format. Times beyond 24 hours are shown as total hours (e.g., 26h 30m), not as days.