Elapsed time: convert to seconds, subtract, convert back
Clock arithmetic is awkward because there are 60 seconds in a minute and 60 minutes in an hour, not 100. The clean way is to collapse each time to a single number of seconds, do the maths, then rebuild it.
Turning seconds back into h:m:s
Once you have a difference in seconds, split it back out with whole-number division and remainders.
- Hours — the whole part of total seconds ÷ 3600.
- Minutes — take what is left after the hours (the remainder), divide by 60, keep the whole part.
- Seconds — the final remainder, what is left after minutes.
- Crossing midnight — if the end clock time is smaller than the start, add 24 hours (86,400 s) to the end before subtracting, or the answer comes out negative.
Time units at a glance
| Unit | Seconds | Minutes | Hours |
|---|---|---|---|
| 1 minute | 60 | 1 | — |
| 1 hour | 3,600 | 60 | 1 |
| 1 day | 86,400 | 1,440 | 24 |
| 1 week | 604,800 | 10,080 | 168 |
To read a time as a decimal (useful for pay and billing), use hours + minutes÷60 + seconds÷3600. So 90 minutes is 1.5 hours, and 15 minutes is 0.25 hours.
Work hours: subtract the unpaid break
A shift is the span from clock-in to clock-out, minus any unpaid break. Find the elapsed time first, then take off the break as its own duration. A break of 30 minutes or more is usually unpaid; a short 20-minute one is often paid.
Common questions
How do I find the time between two clock times?
Turn both times into total seconds, subtract, then turn the result back into hours, minutes and seconds. If the end time is earlier on the clock, the span crosses midnight, so add 24 hours to the end before subtracting.
How do I add a duration to a time and carry over?
Add the seconds, then the minutes, then the hours. Whenever seconds reach 60 carry one minute; whenever minutes reach 60 carry one hour. Anything past 24 hours rolls into the next day.
What is the difference between 12 AM and 12 PM?
12 AM is midnight, the start of the day (00:00 on a 24-hour clock). 12 PM is noon (12:00). Mixing these up is the most common error when reading a 12-hour time.
